Motion Motion Simulation Simulation and Mechanism (Design with COSMOSMotion 2007
Kuang-Hua Chang, Ph.D. School of Aerospace and Mechanical Engineering The University of Oklahoma
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Motion Motion Simulatio Simulation n m£ Mechanism (Design with
COSMOSMotion
2007
Kuang-Hua Chang, Ph.D. School of Aerospace and Mechanical Engineering The University of Oklahoma
ISBN: 978-1-58503-482-6
PUBLICATIONS
Copyright © 2008 by Kuang-Hua Chang. All rights reserved. This document may not be copied, photocopied, reproduced, transmitted, or translated in any form or for any purpose without the express written consent of the publisher Scnroff Development Corporation.
Examination Copies: Books received as examination copies are for review purposes only and may not be made available for student use. Resale of examination copies is prohibited.
Electronic Files: Any electronic files associated with this book are licensee to the original user only. These files may not be transferred to any other party
Mechanism
Design
with
COSMOSMotion
Preface This book is written to help you become familiar with COSMOSMotion, an add- on modu le of the SolidWorks software family, which suppo rts model ing and analysis (or simula tion) of mec han ism s in a virtual (computer) environment. Capabilities in COSMOSMotion support you to use solid models created in SolidWorks to simulate and visualize mechanism motion and performance. Us ing COSMOSMotion early in the product development stage could prevent costly (and sometimes pai nful) redesign due to design defects found in the physical testing phase. Therefore, using COSMOSMotion for support of design decision making contributes to a more cost effective, reliable, and efficient product design proce ss. This book covers the basic concepts and frequently used commands required to advance readers from a novice to an intermediate level in using COSMOSMotion. Basic concepts discussed in this book include mode l generation, such as ass igning mov ing parts and creating join ts and constrai nts; carr ying out simulation and animation; and visualizing simulation results, such as graphs and spreadsheet da ta. These concepts are introduced using simple, yet realistic examples. Verifying the results obt ained from the comp uter simu lation is ext reme ly important. On e of the uni que features of this book is the incorpo ration of theoreti cal discus sions for kinem atic an d dynamic analyses in conjunction with the simulation results obtained using COSMOSMotion. The pur pose of the theoretical discussions lies in solely supporting the verification of simulation results, rather than prov idin g an in-dep th discussi on on the subject of me cha nis m design. COSMOSMotion is not foolproof. It requi res a certain level of exper ience and expertise to master the software. Before ar riving at that level, it is critical for you to verify the simulation results whenever possible. Verifying the simulation results will increase your confidence in using the software and prevent you from being fooled (hopefully, only occasionally) by any erroneous simulations produced by the software. Example files have been prepared for you to go through the lessons, including SolidWorks parts and assemblies, as well as completed COSMOSMotion models. You may want to start each lesson by reviewing the introduction and model sections and opening the assembly in COSMOSMotion to see the moti on simulation, in hop e of gainin g mo re underst andin g about the exam ple problem s. In addition, Excel spread sheets that support the theoreti cal verifications of selected examp les are also available . Yo u ma y download all model files and Excel spreadsheets from the web site of Schroff Development Corporation at : http://www.schroff.com/resources This book is written following a project-based learning approach and is intentionally kept simple to help you learn COSMOSMotion. Therefore, this book may not contain every single detail about COSMOSMotion. For a complete reference of COSMOSMotion, you may use on-line help in COSMOSMotion, or visit the web site of SolidWorks Corporation at : http://www.solidworks.com/ This book should serve self-learners well. If such describes you, you are expect ed to have basic Physics and Mathematics background, preferably a Bachelor's degree in science or engin eering. In addition, this book assumes that you are familiar with the basic concept and operation of SolidWorks part and assembly modes. A self-learner should be able to complete all lessons in this book in about fifty hour s. An inve stme nt of fifty hours shoul d advanc e you from a novice to an inter mediat e level user. This book also serves class instructions well. The book will most likely be used as a supplemental Mechanism Design, Rigid Body Dynamics, Computer-Aided Design, textbook for courses like or
ii
Mechanism
Design
with
COSMOSMotion
This boo k should cover four to six week s of class instru ction, de pend ing on ho w the courses are taught and the technical bac kgr ound of the students . Som e of the exerci se probl ems g iven at the end of the lessons m ay require significant effort for students to compl ete. The author strongly encourages instructors and/or teaching assistants to go through t hose exercises before assigning them to students. Computer-Aided Engineering.
KHC Norman, Oklahoma May 15,2008 Copyright 2008 by Kuang-Hua Chang. All rights reserved. This document may not be copied, photocopied, reproduced, transmitted, or translated in any form or for any purpose wi thout the express written con sent of the publishe r Schroff Dev elo pme nt Corpor ation.
Acknowledgements I would like to thank my family for the patience and support they have given to me in completing this book, especially, my wife Sheng-Mei for her unconditional giving and encouragement . Thanks are due to my children, Charles and Annie, for their understanding, caring, and appreciat ion. Especially, I appreciate their patience in reviewing the whole book and correcting a few sentences for me. Ack now led gme nt is due to Mr.
Steph en Schroff at Schroff Dev elo pme nt Corporati on for his
encouragement and help. Without his encouragement, this book would still be in its primitive stage. Tha nks are also due to under grad uate stud ents at the Uni versity of Okl aho ma (OU) for their help in testing examples included in this book. They made numerous suggestions that improved clarity of presentation and found numerous errors that would have other wise crept into the book. Their contributions to this book are greatly appreciated. I am grateful to my current and former students, Thomas Cates, Petr Sramek, and Tyler Bunting, for their excellent contribution in creating examples for the application lesson; i.e., Lesson 8. The assistive device project employed as the example in Lesson 8 was successful and well recognized. Finally, I would like to thank our Creator, who has given me the strength and intelligence to complete this book.
Mechanism
Design
with
COSMOSMotion
ii i
About the Author Dr. Kuang-Hua Chang is a Williams Companies Foundation Presidential Professor at the Univer sity of Okla hom a (OU), Norm an, OK. He received his diploma in Mechanic al Engineeri ng from the National Taipei Institute of Tech nolo gy, Taiwa n, in 1980 ; and a M.S . and Ph.D. in Mechan ical Engin eeri ng from the Universi ty of Iow a in 1987 and 1990, res pectivel y. Si nce then, he has joi ne d the Cente r for Compute rAid ed Des ign (CC AD ) at Iow a as a Res earc h Scientist and CAE Technica l Manager . In 1996, he joi ned Nort her n Illinois Universit y as an Assist ant Profess or. In 1997, he joi ned OU. Dr. Chang teaches mechanical design and manufacturing, in addition to con ducting research in comp uter -aid ed mod elin g and simula tion for design and manuf actur ing of mech anic al syst ems as well as bioengineering applications. His research work has been published in more than 100 articles in internatio nal jour nals and confe rence procee ding s. He has been invited to deliver talks an d offer short courses for US and foreign companies and universities. He has also served as a technical consultant to US industry and foreign companies. Dr. Cha ng won aw ards in both teac hing and researc h in the past few years . He is a recipie nt of the SAE Ralph R. Teetor Award (2006), Outstanding Asian American Award sponsored by Oklahoma Asian Amer ican Association (2003), and Public Employe e Awa rd of OK C Mayo r' s Commi ttee Award on Disability Concerns (2002). In addition, he received several awards from OU, including the OU Alumni Teaching Award (Spring 2007 and Fall 2007), Regents' Award on Supe rior Research and Creative Activities (2004), BP AMOCO Good Teaching Award (2002), and Junior Faculty Award (1999). Dr. Chang was named Williams Companies Foundation Presidential Professor in 2005 by OU President Dav id L. Bor en for meeting the highest standards of excellence in scholarship and teaching.
About the Cover Page The pictur e display ed on the cover page is the mot ion mode l of an assistive device de signed and built by engine ering students at the Universi ty of Okl aho ma (OU) during 2007- 2008 . Go Sooners ! Thi s device was cr eated for the purpos e of enha ncing expe rience a nd encour aging childr en with physical disabilities to participate in a soccer game. This is a special mechanism that can be mounted on a wheelchair to mimic soccer ball-kicking action while being operated by a child sitting on the wheelchair with limited mobility and hand strength. This example was extracted from an undergraduate student design project that was carried out in conjunction with a local children hospital. This device was int ended primarily to be used in the summer camp sponsored by the children hospi tal. This device has been employed as the application example to be discussed in Lesson 8 of this book. In addition to the soccer ball kicking device, students at OU have been involved in developing many other assistive devices. Currently, an Undergraduate student team is developing a transporting device that will help a local resident with only functional right hand move from her wheelchair to her bed and vise versa independently. Students were also involved in developing special baby c rib, pediatric assistive walk ing device , and modification of a child walke r, etc., in the past. All these projects requi re cust omiz ed features to mee t special needs . Th ese projects have been supp orted by Hon ors Co llege of OU, Schlumberger, and private donations. All supports are sincerely appreciated.
Mechanism
iv
Design
with
COSMOSMotion
Table of Contents Preface
i
Acknowledgments
11
Abo ut the Auth or
iii
Abo ut the Cover Page
iii
Table o f Contents
Lesson
1:
1.1 1.2 1.3 1.4 1.5
Introduction
i v
to
COSMOSMotion
Ove rv iew of the Le ss on Wh at is COSMOSMotion? Me cha nis m Desi gn and Mot ion Analys is COSMOSMotion Capabilities Mo ti on Ex am pl es
1-1 1-1 1-3 1-5 1-16
Lesson 2: A Ball Throwing Example
2.1 2.2
Over view of the Les son The Ball Thr owi ng Exa mpl e
2.3 2.4
Using COSMOSMotion Resu lt Verificat ions
Exercises
2-1 2-1 2- 3 2-12 2-14
Lesson 3: A Spring Mass System
3.1 3.2 3.3 3.4
Over view of the Less on The Spri ng-M ass Syst em Using COSMOSMotion Result Verifications
Exercises
3-1 3-1 3- 3 3-10 3-15
Lesson 4: A Simple Pendulum
4.1 4.2 4.3 4.4
Over view of the Les son The Simple Pe ndu lum Exa mpl e Using COSMOSMotion Resul t Verifications
Exercises
4-1 4-1 4- 2 4-5 4-9
Mechanism
Design
with
COSMOSMotion
v
Lesson 5: A Slider-Crank Mechanism
5.1 5.2 5.3 5.4
Ove rvi ew of the Les son The Slide r-Cr ank Exa mpl e Using COSMOSMotion Resul t Verificat ions
Exercises
5-1 5-1 5- 4 5-13 5-17
Lesson 6: A Compound Spur Gear Train
6.1 6.2 6.3
Ove rvi ew of the Less on The Gear Train Exa mpl e Using COSMOSMotion
Exercises
6-1 6-2 6- 6 6-9
Lesson 7: Cam and Follower
7.1 7.2 7.3
Over view of the Less on The Ca m and Foll ower Exa mpl e Using COSMOSMotion
Exercises
7-1 7-1 7- 6 7-10
Lesson 8: Assistive Device for Wheelchair Soccer Ga mes
8.1
Ove rv ie w of the Le ss on
8.2 8.3 8.4 8.5
The Assist ive Devi ce Using COSMOSMotion Result Disc ussi on Co mm ent s on COSMOSMotion Capabilitie s and Limit ations
8-1 8-2 8-7 8-20 8-20
Appe ndix A: Defining Joints
A-l
Appe ndix B: The Unit Systems
B-l
Appendix C: Importing Pro/ENGINEER Parts and Assemblies
C- l
Notes:
The pu rpos e of this lesso n is to provide you with a brief over view on COSMOSMotion. COSMOSMotion is a virtual prototyping tool that supports mechanism analysis and design. Instead of buildi ng and testing physic al proto types of the mech anis m, yo u ma y use COSMOSMotion to evaluate and refine the mechanism before finalizing the design and entering the functional prototyping stage. COSMOSMotion will help you analyze and eventually design better engineering products. More specifically, the software enables you to size motors and actuators, determine power consumption, layout linkages, develop cams, understand gear drives, size springs and dampers, and determine how contacting parts beh ave , which woul d usuall y requi re tests of physic al prototypes . With such inform ation, you will gain insight on how the mechanism works and why it behaves in certain ways. You will be able to modi fy the design and often achieve better design alternatives using the more convenien t and less expensive virtual prototypes. In the long run, using virtual prototyping tools, such as COSMOSMotion, will help you become a more experienced and competent design engineer. In this lesso n, we will start with a bri ef intr oduc tion to COSMOSMotion and the various types of physical problems that COSMOSMotion is capa ble of solving. We will then discuss capabilities offered by COSMOSMotion for creating motion models, conducting motion analyses, and viewing motion analysis results. In the final section, we will mention examples employed in this book and topics t o learn from these examples. Note that materials presented in this lesson will be kept brief. More details on various aspects of mechanism design and analysis using COSMOSMotion will be given in later lessons. 1.2
Wh at is
COSMOSMotion?
is a computer software tool that supports engineers to analyze and design m e c h a n i s m s . COSMOSMotion is a mod ul e of the SolidWorks product family developed by SolidWorks Corporation. This software supports users to create virtual mechanisms that answer general questions in product design as described next. An internal combustion engine shown in Figures 1-1 and 1-2 will be used to illustrate some typical questions. COSMOSMotion
1.
Will the compon ents of the me cha nis m collide in operat ion? For example , will the connectin g rod collide with the inne r surface of the piston o r the inner surface of the en gine ca se du ring op eration ?
2.
Will the compone nts in the me cha nis m you design mo ve according to you r intent? For exam ple, will the piston stay entirely in the piston sleeve? Will the system lock up when the f iring force aligns vertically with the connecting rod?
3.
Ho w mu ch torq ue or force does it take to drive the me cha nis m? For example , what will be the minimum firing load to move the piston? Note that in this case, proper friction forces must be ad ded to simula te the resistance of the mec han ism before a realistic firing force can be calculated.
4.
Ho w fast will the comp onen ts mov e; e.g., the longitudinal mot ion of the pist on?
5.
What is the reaction force or torqu e gener ated at a conne ction (also called joint or constraint) betw een com pon ents (or bodie s) during motio n? For exampl e, what is the reaction force at the joi nt between the connecting rod and the piston pin? This reaction force is critical si nce the structural integrity of the piston pin and the connect ing rod mu st be ensur ed; i.e., they must be str ong and durable enough to sustain the load in operation.
The capabilities available in COSMOSMotion also help you search for better design alternatives. A better design alternative is very much problem dependent. It is critical that a design pr oblem be clearly defined by the designer up front before searching for better design alternatives. For the engine example , a better design alternative can be a design that reveals: 1. 2.
A smaller reacti on force applied to the connectin g rod, and No collisions or interference bet ween com pone nts .
In order to vary component sizes for exploring better design alternatives, the part s and assembly must be adequately parameterized to capture design intents. At the parts level, desig n parameterization implies creating solid features and relating dimensions properly. At the assembly level, design parameterization involves defining assembly mates and relating dimensions across parts. When a solid model is fully parameterized, a change in dimension value can be pr opagated to all parts affected automatically. Parts affected must be rebuilt successfully, and at the same time, they will have to maint ain proper position and orientation with respect to one another without violating any assembly mates or revealing part penetration or excessive gaps. For example, in this engine example, a change in the bore
diam eter of the en gin e case wi ll alter not only the geom etr y of the ca se itself, but all other parts affe cted, such as the piston, piston sleeve, and even the crankshaft, as illustrated in Figure 1-3. Moreover , they all have to be rebuilt properly and the entire assembly must stay intact through assembly mates.
1.3
Mech anis m Design and Moti on Analysis
A mechanism is a mechanical device that transfers motion and/or force from a source to an output. It can be an abstraction (simplified mod el) of a mech anic al s ystem. A linkage consi sts of links (or bodies), whi ch are conne cted by join ts (or connection s), s uch as a revol ute joint , to form open or closed chains (or loops, see Figure 1-4). Such kinematic chains, with at least one link fixed, become mecha nisms. In this book, all links are assumed rigid. In general, a mechanism can be re presented by its corresponding schematic drawing for analysis purpose. For example, a slider-crank mechanism repre sents the engine motion, as shown in Figure 1-5, which is a closed loop mechanism.
In genera l, there are two types o f mot ion probl ems that you will have to solve in order to answ er questions regarding mechanism analysis and design: kinematic and dynamic. Kine mat ics is the study of mot ion witho ut rega rd for the forces that cause the moti on. A kinema tic mechanism must be driven by a servomotor (or motion driver) so that the position, velocity, and acceleration of each link of the mec han ism can be analy zed at any given time . T ypically, a kine mati c analysis mus t be cond ucte d before dyn ami c behavio r of the mech ani sm can be simulate d proper ly. Dy nam ic analysis is the study of mot ion in resp onse to externally applied loads. Th e dynam ic behavior of a mech anism is g overne d by New ton 's laws of motion. The simplest dynam ic problem is the particle dynamics introduced in Sophomore Dynamics—for example, a spring-mass-damper system sho wn in Figu re 1-6. In this case, mo tion of the mass is go ver ned by the following equation deri ved from Newton's second law,
(1.1) whe re (•) appe aring on top of the physical quantities repr esents tim e derivativ e of the quantities , m is the total mass of the block, k is the spring constant, and c is the damping coefficient. For a rigid body, mass properties (such as the total mass, center of mas s, mo me nt of inertia, etc.) are take n into account for dynamic analysis. For example, m otion of a pendulum shown in Figure 1-7 is governed by the follo wing equa tion of moti on,
Y M d
= -mgl s i n 0 = 10 = m£ 0
(1.2)
2
w h e r e M is the external moment (or torque), inertia
/ of
is the
the
polar
pendulum,
moment m
is
of the
p e n d u l u m m a s s , g is the gravitational acceleration, and 6 is the angular acceleratio n of the pendu lum . Dyn am ic analysis of a rigid bod y system, suc h as the single piston engin e show n in Figu re 1-3, is a lot mor e comp lica ted than the single body probl ems . Usua lly, a sys tem of differential and algebrai c equation s gover ns the mot ion and the dyna mic behavi or of the system . New to n' s law mus t be obeyed by every single bod y in the syste m at all time. The mot ion of the sy stem will be deter min ed by the loads acting on the bodie s or joi nt axes (e.g., a torque dri ving the system) . Rea ction load s at the join t connections hold the bodies together. Note that in COSMOSMotion, you may create a kinematic analysis model; e.g., using a motion driver to drive the mechanism; and then carry out dynamic analyses. In dynamic analysis, position, velocity, and accelera tion results ar e identical to those of kine mati c analysis. H owe ver , the inertia of the bodies will be taken into account for analysis; therefore, reaction forces will be calculated between bodies.
1.4
COSMOSMotion Capabilities
Ground Parts
The overall proce ss of usin g for analyzing a mechanism COSMOSMotion consists of three mai n steps: mod el generat ion, analysis (or simulation), and result visualization (or post-processing), as illustrated in Figure 1-8. Key entities that constitute a motion model include ground parts that are always fixed, moving parts that are movable, joints and constraints that connect and restrict relative motion between parts, servo motors (or motion drivers) that drive the mechanism for kinematic analysis, external loads (force and torque), and the initial conditions of the mec han ism . Mor e details about these entities will be discussed later in this lesson. COSMOSMotion The analysis or simulation capabilities in employ simulation engine, ADAMS/Solver, whic h solves the e quatio ns of mot ion for your mecha nism . ADAMS/Solver calculates the position, velocity, acceleration, and reaction forces acting on each moving part in the mechanism. T ypical simulation problems, including static (equilibrium configuration) and motion (kinematic and dynamic), are supported. More details about the analysis capabilities in COSMOSMotion will be discussed later in this lesson.
The analysis results can be visualize d in various form s. Yo u ma y animate moti on of the mecha nis m, or generate g raphs for more specific information, such as the react ion force of a join t in time d omai n. Y ou may also query results at specific locations for a given time. Furthermore, you may ask for a report on results that you specified, such as the acceleration of a moving part in the time d omain. You may also convert the motion animation to an AVI for faster viewing and file portability. In addition to AVI, you can export animations to VRML format for distribution on the Internet. You can then us e Cosmo Player, a plug-in to your Web browser, to view VRML files. To download Cosmo Player fo r Windows, go to http://ovrt.nist.gov/cosmo/. Operation
Mode
is embedded in SolidWorks. It is indeed an add-on module of SolidWorks, an d transition from SolidWorks to COSMOSMotion is seamles s. All the solid mod els , mater ials, ass embl y mates, etc. defined in SolidWorks are automatically carried over into COSMOSMotion. COSMOSMotion can be accessed through menus and windows inside SolidWorks. The same assembly created in SolidWorks can be directly employed for creating motion models in COSMOSMotion. In addition, part geometry is essential for mass property computations in motion analysis. In COSMOSMotion, all mass properties calculated in SolidWorks are ready for use. In addition, the detailed part geometry supports interference chec king for the mecha nis m during mot ion simulatio n in COSMOSMotion. COSMOSMotion
User
Interfaces
User interface of the COSMOSMotion is identical to that of SolidWorks, as shown in Figure 1-9. SolidWorks users shoul d find it is straig htforward to man euv er in COSMOSMotion.
As shown in Figure 1-9, the user interface window of COSMOSMotion consists of pull -do wn me nus , shortcut buttons, the brow ser, the graphics screen, the message window, etc. When COSMOSMotion is active, an extra tab $ (the Motion button) is available on top of the browser . T his Motion button will allow you to access
COSMOSMotion.
The graphics screen displays the motion model with which you are work ing. The global co ordina te syst em at the lower left corner of the graphics screen is fixed and serves as the reference for all the physical parameters defined in the motion model. The pull-down menus and the shortcut buttons at the top of the scr een provid e typical SolidWorks functions. The assembly shortcut buttons allow you to assemble your SolidWorks model. The COSMOSMotion shortcut button s on top of the graphics screen shown in Figure 1-9 provide all the functions required to create and modify the motion models, create and run analyses, and visualize results. As you move the mouse over a button, a brief description about the functi onalit y of the butto n, s uch as the Fast Reverse button shown in Figure 1-9, will appear.
When you choose a menu option, the Message window, at the lower left corner shown in Figure 1-9, shows a brief descri ption about the option. In addi tion to these butto ns, a COSMOSMotion p u l l - d o w n menu also provides similar options, as shown in Figure 1-10. When you click the Motion button, the browser will provide you with a graphical, hierarchical view of mot ion mode l and allo w you to access all COSMOSMotion functionalities through a combination of drag-and-drop and right-click activated menus. For example, you may drag and drop connectingrod_asm-l Components, under the Assembly as shown in Figure 1-11 to Moving Parts Parts under the branch to define it as a moving part. You may also right click an entity and choose to define or edit its property. For example, you may right click the Springs n o d e u n d e r Forces branch in Figure 112, and choose Add Translational Spring to add a spring. Switching
back
and
forth
between
COSMOSMotion
straightforward. All you have to do is to click the Motion
J?
and
SolidWorks
assembly
or Assembly but ton s
^
mode
is
(on top of the
browser) when needed. When you click the Motion button
tabbe d dialog box an d a wiza rd that leads you throug h the proces s of conver ting an ass embl y mode l into a motion model, performing motion simulations, and viewing simulation results.
To use the IntelliMotion Builder, click the IntelliMotion Builder button or right-click the Motion Model nod e (the ro ot entity of the mot ion model) from the browser, and then select IntelliMotion Builder (see Figure 1-14). The first tab is Units, which brings up the Units p a g e . At the low er-le ft corne r of eac h page in the the Back an d Next IntelliMotion Builder are buttons, which help you move sequentially through the motion model creation, simulation, and animation process. You may also click a tab on top to jump to that page directly, for example Parts, to define ground and moving parts. For a new user, the COSMOSMotion IntelliMotion Builder is very helpful in terms of leadi ng you thr ough the steps of creatin g simulation s models , running simulations, and visualizing the simulation results. For a more experienced user, the drag-and-drop and right-click activated menus may be more convenient. Tab le 1-2 giv es a bri ef exp lan ati on of each tab ava ilab le in the IntelliMotion Builder.
Defining
COSMOSMotion
Entities
Th e basic e ntities o f a val id COSMOSMotion simul ation model cons ist of gro und parts, m ovi ng parts, constraints (includ ing joint s), initial condition s, an d forces and/or drivers. Eac h of the basic entities will be briefly discussed next. More details can be found in later lessons.
Ground Parts
(or
Ground Body)
A ground part, or a ground body, represents a fixed reference in space. The first component bro ught into the assembly is usually stationary; therefore, often becoming a ground part. You will have to ide ntify moving and non-moving parts in your assembly, and assign the non-moving parts as ground parts using either the IntelliMotion Builder or the drag-and-drop in the browser. Moving Parts
(or Bodies)
A moving part or body is an entity represents a single rigid component (or link) that moves relatively to other parts (or bodie s). A movi ng part may consist of a single SolidWorks part or an assembly com pos ed of multi ple parts. W he n an ass emb ly is assigne d as a mov ing part, none of its compo sin g parts is allowed to move relative to one another within the assembly. A mo ving part has six degrees of freedom, three translational and three rotational, while a ground part has none. That is, a rig id body can translat e and rotate along the Y-, and Z-axes of a coord inate system. Rotation of a rigid bod y is mea sur ed by referring the orientation of its local coord inate sy stem to the global coordi nate sys tem, whic h is shown at the lower left corner on the graphics screen. In COSMOSMotion, the local coordinate system is assig ned automatical ly, usually, at the mas s center of the part. Mas s propertie s, includ ing total mas s, inertia, etc., are calculated using part geometry and material properties referring to the local coordinate system. A moving part has a symbol (see Figure l-16a) attached, usually located at its mass center, as shown in Figure 1-15. Constraints
A constraint (or connection) in COSMOSMotion can be a joint , conta ct, or coupl er that connec ts two parts and constrains the relativ e mot ion betwee n them . Typica l join ts include a revolu te, cylindrical , spherical, etc. Each ind epen dent move me nt permitte d by a constraint is a free degree of freedo m (dof). The degr ees of freedom that a constraint allows c an be translatio nal or rotational along the three perpe ndicul ar axes. Th e free dof is reveale d by the sym bol of the constraint. Fo r exam ple, the sy mbol of cylindrical join ts, s uch as thos e defined in the engine exa mpl e show n in Figu re 1-15, sh ow two conce ntric cylinders im plyin g two free d of s, a translat ional and a rotationa l, both are along the co mm on axis, as illustrated in Figur e l- 16b . Als o, a revolu te joint , for exa mpl e the one betw een the propeller and the case shown in Figure 1-15, allows only one rotational dof, as depicted in a hinge symbol shown i n Figure 116c. Under stan ding the joi nt symbol s will enable yo u to read existing moti on mod els . Also , a joi nt produces equal and opposite reactions (forces and/or torques) on the bodies connected d ue to Newton's 3 Law . Mo re ab out join ts will be discussed in later lesson s and for a list of com mon ly em plo yed join ts, please refer to Appendix A. r d
COSMOSMotion automa tically conver ts assem bly mat es to join ts. For examp le, a concent ric mate
togeth er with a coincident mate will be conver ted to a revol ute joint. Som etim es, COSMOSMotion will simply car ry over the assemb ly mates to mot ion if there is no ad equat e joi nt to convert to, following the ma pp ed mat es establ ished internally. For a list of co mm on mapp ed mat es, pleas e refer to Appe ndi x A. Yo u ma y either stay with the joi nt set conver ted by COSMOSMotion or delete s ome o f the m to create your own. H owev er, it is strongly rec om me nde d that you stay with the converte d joi nt set before completing all the examples provided in this book. In all the examples presented in this book, mapped jo ints or m a t es ar e e m p l o y e d with out any modi fica tio n. Not e that instead of compl etely fixing all the mov eme nts , certain d of s (trans lational and/ or rotational) are left to allow designated movement. For example, a motion driver is defined at the rotation dof of the revolut e joi nt in the engine exa mple , as show n in Figu re 1-15. This mot ion driver will rotate the
propeller at a prescribed angular velocity. In addition to prescribed velocity, you may use the motion driver to drive the dof at a pres cribe d displac emen t or acceleration, bot h translation and rotational.
In addition to joints, COSMOSMotion provides contact and coupling constraints. The contact constraints help to simulate physical problems more realistically. COSMOSMotion supports four types of contact, point-curve, curve-curve, intermittent curve-curve, and 3D contact. Only the first two types of contact impose degree-of-freedom restrictions on the connected parts and are true co nstraints. The 3D contact is employed most frequently, which applies a force to separate the parts when they are in contact
and prevent them from penetrating each other. The 3D contact constraint will become active as soon as the parts are touching. Joint coupler s allow the mot ion of a revolu te, cy lindrical, or translati onal joi nt to be couple d to the mot ion of anoth er revol ute, c ylindrical or translationa l joint . T he two co uple d joi nts ma y be of the sa me or different different types . Fo r exampl e, a revolute join t ma y be coupled to a translati onal joint . T he cou pled mot ion ma y also be of the s ame or different type. F or exam ple, th e rotary moti on of a revolute joi nt may be cou pled to the rotary mot ion of a cylindrical joint, or the translational mo tio n of a transl ational joi nt ma y be coupled to the rotary moti on of a cylindrical joint . A coupler rem ove s one additi onal degr ee of freedom from the motion model. Degrees
of Freedom
As mentioned earlier, an unconstrained body in space has six degrees of freedom; i.e., three translati onal and three rotational. W he n join ts are added to connect bodies, con straints are imp ose d to restrict the relative motion between them. For exam ple, the revolu te join t defined in the engin e examp le restricts mov em ent on five d of s so that only one rotational motion is allowed between the propeller assembly and the engine case. Since the engi ne case is a gro und body, the propelle r assem bly will rotate along the axis of the revolut e joint, as illustrated in the symbol shown in Figure 1-16b. Therefore, there is only one degree of freedom left for the propeller assem bly. F or a given motio n mod el, yo u can deter mine its numb er of degre es of freedom using the Gruebler's count. COSMOSMotion uses the following equation to calculate the Gruebler's count:
(1.3)
D = 6M-N-0
w h e r e D is the Grueb ler' s count representing the total total degrees of freedom of the mechani sm, M i s the num ber of bodie s exc ludin g the gro und body, TV is the num ber of do f s restric ted by all join ts, and O is the num ber of mot ion drivers def ined in the sys tem. In general, a valid motion model should have a Gruebler's count 0. However, in creating motion models , s ome joints remo ve redundant do f s. Fo r example, two hinges, mo dele d using two revolute joints, support a door. Th e second revolu te joi nt adds five redu ndan t d of s. Th e Grueb ler 's count bec ome s: D = 6x1
-2x5 = -4
For kinematic analysis, the Gruebler's count must be equal to or less tha n 0. T h e ADAMS/Solver reco gnize s and deactivat es redunda nt constraints during analysis . For a kine mat ic analysis, if you create a model and try to animate it with a Gruebler's count greater than 0, the animation will not run and a n error message will appear. The singl e-piston engine s hown in Figu re 1-15 1-15 consists of three bodies (ex cludi ng the grou nd body ), one revolute join t and three cylindric al joint s. A revolute joi nt rem oves five deg rees of fr eedom, and a cylindrical join t remo ves four do f s. In addition, a motio n driver is adde d to the rotational d of of the revol ute joint. Therefo re, acco rding to Eq. 1.3, 1.3, the Gru eble r's co unt for the engine exa mple is
If the Gru ebl er' s count is less than zero, the solver will automa ticall y re mov e redundan cies . In this engin e exam ple, if the two of the cylindri cal join ts; be twe en piston and the piston pin, a nd betw een the conne cting rod and the cran k shaft shaft,, are replace d by revolute joint s, the Gru eble r's c ount bec ome s D
=
6x(4-l)-(3x5-1x4)
-
lxl
=
-2
To get the Grueb ler 's coun t to zero, it is often possi ble to replace join ts that rem ove a large num ber of constra ints with join ts that re mo ve a smalle r num be r of constrai nts an d still still restrict the me cha nis m motion in the same way. COSMOSMotion detects the redun danc ies an d ignores redu nda nt do f s in all analyses, except for dynamic analysis. In dynamic analysis, the redundancies lead to an o utcome with a possibili ty of incorre ct reacti on results, yet the motio n is correct. For comple te and accurate reactio n forces, it is critical that you eliminate redundancies from your mechanism. The challenge is to find the jo j o i n t s th a t wi ll i m p o s e n o n - r e d u n d a n t co ns t r a in t s a n d st il l a l l o w fo r t h e i n t e n d e d m o t i o n . E x a m p l e s includ ed in this book should give you some ideas in cho osin g prope r join ts. Forces
Forces are used to operate a mechanism. Physically, forces are pr oduced by motors, springs, dampers, gravity, tires, etc. A force entity in COSMOSMotion can be a force or torque. COSMOSMotion provi des three types of forces: ap plied forces, flexible connector s, and gravity. Applied forces are forces that cause the mechanism to move in certain ways. Applied forces are very general, bu t you mus t supply your ow n descripti on of the force by specifying a cons tant force value or express ion function, such as a har mo nic function. Th e applied forces in COSMOSMotion include actiononly force or moment (where force or moment is applied at a point on a single rigid body, and no re action forces are calculated), action and reaction force and moment, and impact force. The force and moment symbols in COSMOSMotion are shown in Figure 1-17 and 1-18, respectively.
Figu re 1-17 1-17 The For ce (or Transl ational Driver) Symbo l
Figu re 1-18 1-18 The Mo me nt (or Rotat ional Driver) Symbol
Flexible connectors resist motion and are simpler and easier to use than applied forces bec ause you only supply constant coefficients for the forces, for instance a spring constant. The flexible connectors include translational springs, torsional springs, translational dampers, torsional dampers, and bushings, which symbols are shown in Figure 1-19.
A magnitude and a direction must be included for a force definition. You may select a predefined function, such as a harmo nic function, to define the mag nit ude of the force or mom ent . Fo r spring and d a m p e r , COSMOSMotion automatically makes the force magnitude proportional to the di stance or velocity between two points, based on the spring constant and damping coefficient entered, r espectively. Th e direc tion of a force (or mo me nt ) can be defined by either alo ng an axis defin ed by an edge or along the line between two points, where a spring or a damper is defined. Initial
Conditions
In motion simulat ions, initial conditions cons ist of initial configuration of the mech ani sm an d initial initial veloci ty of one or mo re com pone nts of the mecha nis m. M oti on simul ation must start with a prope rly ass embl ed solid mod el that deter mines a n initial initial configurat ion of the mec han ism , com pos ed by positi on and orientation of individu al comp onen ts. The initial configuration can be completel y defined by ass embl y mat es. Ho wev er, o ne or mo re asse mbly mates will hav e to be suppress ed, if the assem bly is fully constrained, to provide adequate movement. I n COSMOSMotion, initial veloc ity is def ined as part of defin ition of a mo vi ng part. T he initial veloci ty can be translational or rotational along on e of the three axe s. Motion
Drivers
Mot ion driver s are use d to imp ose a particular mov em en t of a joi nt or part over time. A moti on driver specifies position, velo city, or accele ration as a function of time, and can control either tran slat iona l or rota tion al mot ion . The driv er symb ol is identical to tho se of Fig ure s 1-17 and 1-18, for translational and rotational, respectively. When properly defined, motion drivers wi ll account for the remaining dof s of the mechanism that brings the Gruebler's count to zero or less. In the engine ex amp le sh own in Figure 1-15, 1-15, a mot ion driver is defined at the revolute join t to rotate the propeller at a constant angular velocity. Motion
Simulation
The employed by is ADAMS/Solver COSMOSMotion capab le of solving typical engineer ing pro blem s, suc h as static (equilibrium configuration), kinematic, and dynamic, etc. Static analysis is used to find the rest position (equilibrium conditi on) of a mec han ism , in whic h none of the bodies a re mov ing . A simple exa mple of the static analysis is illustrated in Figu re 1-20, 1-20, in whi ch an equili brium positio n of the block is to be determined according to its own mass m , the two spring constants ki a n d k , and the gravity g. 2
As discu ssed earlier, kinem atic s is the study of mot ion witho ut rega rd for for the forces that cause the motion. A mechanism can be driven by a motion driver (e.g., a servomotor) for a kinematic analysis, whe re the position, veloci ty, an d acceler ation of each link of the mec han ism can be anal yzed at any given time . Figur e 1-21 1-21 show s a serv omot or drives a me cha nis m at a constan t angular velocity. Dynamic analysis is used to study the mechanism motion in response to loads , as illustrated in Figure 1-22. This is the most complicated and common, and usually a more time-consuming analysis.
Viewing
Results
I n COSMOSMotion, results of the motio n analysis can be reali zed usin g animati ons, graph s, repor ts, and queries. Anim atio ns sh ow the configurat ion of the mech ani sm in conse cutive time frames. Animations will give you a global view on how the mechanism behaves, for example, t he single-piston engine shown in Figure 1-23. You may also export the animation to AVI or VRML for various purposes.
In addition, you may ch oose a joi nt or a part to generate result graph s, for examp le, the positio n vs. time of the piston in the engin e exam ple s hown in Figur e 1-24. The se graph s give you a quantitative unders tanding on the characteris tics of the mecha nis m. You may also query the results by moving the cursor closer to the curve and leave the curs or for a short period. The result data will appear next to the cursor. In addition, you may ask COSMOSMotion fo r a report that inclu des a com ple te set of resu lts ou tput in the form of text ual data or a Microsoft® Exc el spreadsheet. In addition to the capabilities discussed above, COSMOSMotion allows you to check interference between bodies during motion (please see Lesson 5 for more details). Furthermore, the reaction forces calculated can be used to support structural analysis using, for example, COSMOSWorks.
1.5
Motio n Exam ples
Numerous motion examples will be introduced in this book to illustrate the step-by-step details of mod elin g, simula tion, and result visualiz ation capabilities in COSMOSMotion. In addition, an application exam ple will be introd uced to illustrate the steps an d princip les of usin g COSMOSMotion for support of mechanism design. We will start with a simple ball-throwing example in Lesson 2. This example will give you a quick run-through on using COSMOSMotion. Lessons 3 thro ugh 7 focus on mod eli ng and analysis of basic mec han ism s and dyna mic sys tems. I n these lesso ns, you will learn variou s joi nt types , including revolute, planar, cylindrical, etc.; forces and connections, including springs, gears, c am-followers; drivers and forces; various analyses; and graphs and results. Lesson 8 is an application lesson, in which an assistive soccer ball kicking device that can be mounted on a wheelchair will be introduced to show you how to apply what you learn to real-world applications. All examples and main topics to be discussed in each lesson are summarized in the following table.
2.1
Ove rvi ew of the Les son
The purp ose of this lesso n is to provide you a quick run-thr ough on using COSMOSMotion. This example simulates a ball thrown with an initial velocity at an elevation. Due to gravity, the ball will t ravel following a parabolic trajectory and bounce back a few times when it hits the ground, as depicted in Figure 2-1. In this lesson, you will learn how to create a motion model to simulate the ball mo tion, run a simulation, and animate the ball motion. Simulation results obtain ed from COSMOSMotion can be verified using particle dynamics theory that was learned in high school Physics. We will review the equati ons of moti on, ca lculate the position an d veloci ty of the ball, and com par e our calculations with results obtained from COSMOSMotion. Validating results obtained from computer simulations is extremely important. COSMOSMotion is not foolproof. I t req uir es a certain level of exp eri enc e and expertise to master the software. Before you arrive at that level, it will be in dispensable to verify the simulation results, whenever possible. Verifying the simulation results will increase your confidence in using the software and prevent you from being occasionally fooled by the erroneous simulations produ ced by the software. Note that very often the erroneous results are due to modeling errors. 2.2
The Ball Thro wing Exam ple
Physical
Model
The physica l mode l of the ball exam ple is very simple. The ball is made of Cast Alloy Steel with a radius of 10 in. The units system employed for this example is IPS (inch, pound, second). The gravitational acceleration is 386 i n / s e c . Note that you may check or change the units system by choosing from the pull-down menu 2
Tools
>
Options
and choose the Document Properties tab in the System Options - General dialog box, click the node, and then pick the units system you prefer, as shown in Figure 2-2.
Units
The ball and ground are assumed rigid. The ball will bounce back when it hits the ground. A coefficient of restitution C = 0.75 is specified to determine the bounce velocity (therefore, the force) when the impact occurs. For this example, C = V/V , w h e r e V% and are the velo citi es of the ball befo re and after the impact . Th at is, the bou nce veloci ty will be 75 % of the inco min g velocity, a nd certainly, in the opposite direction. Note that in order for COSMOSMotion to capture the moment when the ball hits the ground, we will define a 3D contact constraint between the ball and the g round, and use the true geom etry of the parts for a finer interference cal culation dur ing the simulation. R
R
t
SolidWorks
Parts
and Assembly
For this lesson, the parts and assembly have been created for you in SolidWorks. There are four files created, ball.SLDPRT, a nd ground. SLDPRT, Lesson2. SLDASM, You can find Lesson2withresults.SLDASM. these files at the publisher's web site ( h t 1 p : / /w w w . s c h r o f f l x o m / ). We will start w i t h Lesson2.SLDASM, in which the ball is fully assembled to the ground; i.e., no movement is allowed. In addition, the Lesson2withresults.SLDASM assembly file consists of a comp lete si mulatio n mo del with si mulati on results, in which som e of the assembly mates were suppressed in order to pro vide ade quate de grees of freedo m for the ball to move. You may want to open this file to see how the ball is supposed to move. Since the gravity is defined in the negative 7-direction of the global coor dinate s ystem as default, all parts and assembly are created for a motion simulation that complies with the default setting. The assembly Lesson2.SLDASM consists of two par ts: the ball (ball.SLDPRT) and the ground (ground.SLDPRT). The ball is fully assem bled with the gr oun d by three a ssem bly mates of three pairs o f reference planes. They are Front (ball)/ F ront (ground), Right (ball)/ ' Right (ground), and Top (ball)/7b/? (ground), as shown in Figure 2-3. The distance between the reference planes Top (ball) and Top (ground) is 100 in., whic h defines the initial positi on of the ball, as s ho wn in Fig ure 2-4 . Th e rad ius of the ball is 10 in., and the ground is modeled as a 30*500*0.04 in. rectangular block. 3
Not e that the 7-axis of the glo bal coordinate system (located at the low er left corne r of the SolidWorks graphics screen, as shown in Figure 24) is pointing upward, which is consistent with the default direction of the gravity, but in the opposite direction. Motion
Model
In this example, the ball will be the only movable body. Two assembly m a t e s , Distancel a n d Coincident^, as shown in Figures 2-3a and 2-3c, will be suppressed to allow the ball to move on the X-Y plane A s mentio ned earlier, the ball will be thrown with an initial velocity of VQ = 150 in/sec.
R
2
.
4
T
h
e
S
o
l i
d
W o
r
k
s
A s s e
mbly
A gravitational acceleration -386 i n / s e c is defined in the 7-dir ection of the global coordi nate system. The ball will reveal a parabolic trajectory due to gravity. A 3D contact constraint will be added to characte rize the impa ct bet wee n the ball and the ground . As di scuss ed earlier, a coefficient of restitution C = 0.75 will be specified to determine the force that acts on the ball when the impact occurs. In this example, no friction is assumed. 2
R
Using COSMOSMotion
2.3
Start SolidWorks
and
open
assembly
file
Lesson2.SLDASM.
W h e n COSMOSMotion is active, the browser has an extra tab (the Motion button) for the Motion (see the buttons on top of the browser shown in Figure 2-5). This browser provides you with a graphical, hierar chical view of the moti on mode l and allows you to access all COSMOSMotion functionalities throug h a comb inat ion of drag- and-d rop and right click menus. Switch back and forth between COSMOSMotion an d SolidWorks assembly mode is straightforward. All you have to do is to click the Motion Motion
a nd Assembly button
to
buttons
enter
when needed. When you click the
COSMOSMotion,
a different
set of entiti es
will be listed in the browser, in addition, an additional toolbar is added to SolidWorks, located at the top of the gr aphics screen, as sho wn in Figure 2-6. This toolbar provides settings, simulation and post processi ng features. Especially, the Play Simulation button is hand y whe n you finish running a simulation and ready to animate the motion. Click some of the but ton s an d try to get famili ar with their functio ns. In this lesson, we will use the IntelliMotion Builder for mo st of the steps . Th e IntelliMotion Builder is the primary interface in COSMOSMotion. It is a tabbed dialog box and a wizard that leads you through
Before we start, we will suppress two assembly mates to allow the ball to move on the X-Y plane. Choose the button on top of the brows er, a nd expan d the but ton in f ront of it. Mates branch by clicking the small
Assembly
Choose press the Distance 1 (Ground< 1 >, ball<1>), right mouse button, and choose Suppress. Repeat the same fo r Both mates will Coincident3(Ground,ball). become inactive. If you mo ve the c ursor to the root node, Lesson2 (Default), in the browser, you should see a rectangular box appears in the graphics screen, which is simply the bounding box for the assembly (see Figure 2-8). Click the Motion button COSMOSMotion. enter Start
the
IntelliMotion
on ton of the bro wse r to
Builder
To use the IntelliMotion Builder, right click the Motion Model node from the browser, and then select IntelliMotion Builder (see Fig ure 2- 5). Th e first tab of the IntelliMotion Builder is Units, w h i c h brings up the Units page. As shown in Figure 2-9, the IPS units system has been chosen. No action is needed.
At the lower-left corne r of each pag e in th e IntelliMotion Builder are the Back a n d buttons, which help you move Next sequentially through the motion model creation, simulation, and animation process. C h o o s e Next or click the Gravity tab. T h e Gravity page (Figure 2-10) shows that the default acceleration is 386.22 i n / s e c and is acting in the negative 7-direction. This is what we want, and no action is needed. C h o o s e Next or click the Parts tab.
2
Defining
Bodies
The first step in creating a motion model is to indicate which components from your SolidWorks assembly model participating in the motion model. In an assembly that does not yet have any motion parts defined, all of the ass embl y compo nen ts are listed und er the Assembly Components branch (right colu mn) of the Parts page, as shown in Figure 2-11. We will move ball-1 to Moving Parts (left column) a nd Ground-1 to Ground Parts by using the drag-and-drop method. Click ball-1 and drag it by holding down the left-mouse button, moving the mouse until the cursor is over the Moving Parts node, and then releasing the mouse button. Part ball-1 is now added to the motion model as moving parts (can move). Repeat the same steps to move ground-1 to the Ground Parts n o d e . Now, the part Ground-1 is added to the motion model as a ground part (cannot move). Note that you may select multiple components by holding Ctrl key and selecting each component. You may select multiple components by selecting the first component, pressing and holding Shift key, and then selecting the last comp onent . All of the comp one nts betw een the first and seco nd selected components will be selected. Or you can drag-select by pressing the left-mouse button and moving the
mouse so that the selection rectangle intersects the components. In this case, any components within the selection rectangle will be selected.
Any time a component (a part or an assembly) is added to the motion model, COSMOSMotion looks at all of the ass embl y mat es that are attache d to that com pone nt. If an assem bly mate bet wee n the new ly added component and another component that is already participating in the motion m odel is found, a mot ion joi nt that map s to the ass emb ly mat e is generated. This allows yo u to take a fully ass embl ed model and quickly build a simulation-ready motion model by indicating which components from the ass embl y participa te in the motio n model. A list of map pin gs betwe en the assem bly and mot ion join ts that are frequently encountered can be found in Appendix A. Take a few minutes to review Appendix A to be com e mor e familiar with the mapp ing an d the join t types suppo rted in COSMOSMotion. U n d e r s t a n d i n g j oin ts a nd the m a p p i n g wi ll he lp y o u as s e m ble parts adequ ately fo r m ot i o n m o de l s , a voiding u nne ce s s ar y model editing and confusion. Defining
Initial
Velocity
We will add an initial velocity Vo =150 in/sec to the x
ball. Click ball-1 from the Parts page, press the right mouse button, and choose Properties (see Figure 2-12), the Edit Part dialog box will appear. Click the IC's tab and enter 150 fo r X Velocity, as shown in Figure 2-13. Click Apply. The initial velocity has been defined. Defining
Joints
C h o o s e Next or click the Joints tab. The Joints p a g e allows you to modify joints that were automatically created from assembly mates. You may add additional jo in ts to the m o ti on m o d e l if adequate. This p a ge conta ins a single tree that lists all of the joi nts i n the mo ti on mode l. As sh own in Figu re 2-14, there is only one joi nt listed, Coincident!, which mates Front Plane of ball to th e Front Plane of the g rou nd to allow a pla nar mot ion for the ball.
On the right, you will see a list of joint types you can choose to add to your motion model. The first j o i n t Revolute is selec ted by default. As indica ted in the mess age , a revol ute join t rem ove s five d egrees of freedom, three translation al and two rotational. Ho weve r, for this ball-thro wing examp le, the joi nt carried over from SolidWorks; i.e., Coincident2, is exactly what we want; therefore, no action is needed for the time being.
Running
Simulation
Click the Next button three times or click the Simulation tab directly (no spring or driver is needed for this example; therefore, we are skipping the Spring and Motion tabs). As shown in Figure 2-15, the simulation duration is 1 secon d and the num ber of frames is 50 as defaults. We will stay with these default values for the time being. Click Simulate to run a simulation.
After a few seconds, the ball will start moving. As shown in Figure 2-16 the ball will fall through the gro und , whi ch is not realistic . No te that the trace path that indica tes the trace o f the ce nte r of the ball is turned on in Figure 2-16. We will learn how to do that later. For the time being we will have to add a 3D Contact constraint between the ball and the ground in order to make the ball bounce back when it hits t he ground. The 3D Contact constraint will create a force to prevent the ball from penetrating the ground. This cons traint will be only activated if the ball com es i nto contact with the ground . Defining
a
3D
Contact
Constraint
T h e 3D Contact constraint cannot be created in the IntelliMotion Builder. We will have to use the browser or the pull down menu. Before creating a 3D Contact constraint, close the IntelliMotion Builder, and delete the simulation result by clicking the Delete Results but ton JIL
at the bot tom of the brow se r (see Figur e 2-17 for the location of the delete button ). No w, the ball sho uld return to its initial position. Also, save your model before moving forward. From the pull-down menu, choose COSMOSMotion
>
Contacts
>
3D Contact
or from the browser, right click the Contact branch, and then select Add 3D Contact, as shown in Figure 2-17. The Insert 3D Contact dialog box will appear (Figure 2-18).
COSMOSMotion calculates whether the parts' bounding boxes (usually the rectangular box, similar to thai
of Figu re 2- 8, but for individual par ts) interfere. If they interfere, COSMOSMotion performs a finer interference calculation between the two bodies. At the same time, ADAMS/Solver computes and applies an impact force on both bodies. From the browser, select Ground-7, the ground part will be listed in the first container (upper field), as show n in Figu re 2-18. Click the Add Container for contact pairs button (in the middle), and pick ball-1 The part ball-1 will be listed in Container 2 (lower field). Click the Contact tab to define contact parameters. Note that we will define a coefficient of restitution for the impact. In the three sets of para mete rs appe arin g in the dialog box (Figure 2-19) . turn off the Use Materials (deselect the entity) and Friction (click None). C h o o s e Coefficient of Restitution I in the middle), and enter 0.75 fo r Coefficient Restitution, as shown in Figure 2-19. Click Apply to accept the 3D Contact. T h e 3D Contact constraint should appear in the browser, as shown in Figure 2-20. You will have to expand the Constraints branch and then the Contact branch to see the contact constraint. Rerun
the
Simulation
Before we rerun the sim ulation, we will have to adjust some of the sim ulation param eter s. Especially we will ask COSMOSMotion to use precis e geomet ry to check contact in each fra me o f simulation. Right click the Motion Model node from the browser and choose Simulation Parameters. In the COSMOS Education Edition Options dialog box appearing (Figure 2-21), choose Use Precise Geo/?;, for 3D Contact, and enter 3 seconds for Duration a nd 500 fo r Number of Frames. Note that we increase the number of frame so that we will see smooth graphs in various result displays. Increasing the number of frame will certainly increase the simulation time. However, the increment i s insignificant for this simple example. Click OK io accept the definition and close the dialog box.
Right click the Motion Model node from the browser and choose Run Simulation. After a few seconds, the ball starts moving. As shown in Figure 2-22 the ball will hit the ground and bounce back a
few times before the simulation ends. The ball did not fall through the ground this time due to the addition of the 3D Contact constraint. Displaying
Simulation
Results
COSMOSMotion allows you to graphically display the path that any point on a ny moving part
follows. This is called a trace path. N ote that the trace path of the ball was dis playe d in both Figur es 2-16 and 2-22. We will first learn how to create a part trace path. From the browser, right click the Results node, and choose Create Trace Path (see Figure 2-23) to bring up the Edit Trace Path dialog box, as shown in Figure 2-24. Note that Assem2 should be listed in t h e Select Reference Component text box, which serves as the default reference frame for the trace path. The default referenc e frame is the global refere nce f rame inclu ded as part of the grou nd body . No change is needed.
To select the part used to generate the trace curve, select the Select Trace Point Component text field (should be highlighted in red already), and then select one moving part; i.e., the ball, fro m the graphics screen. The part ball-1 will be listed in the Select Trace Point Component text field, and balll/DDMFace2 is listed in the Select Trace Point on the Trace Point Component text box. Click Apply button, you should see the trace path appears in the graphics screen, similar to that of Figure 2-22. Nex t, we will creat e a gra ph for the 7-po siti on of the ball usin g the XY Plots. Plots. From the browser, right click ball-1 (under Parts, Moving Parts) and choose Plot > CM Position > Y. T h e XY Plot for the CM (Cente r of Mas s) posit ion of the ball in the 7-direction will appe ar, similar to that of Figur e 2-2 5. No te that you may adjust properties of the gr aph, for instance the axis scales, following steps similar to those of Microsoft® Exce l s preads heet graphs . The graph shows that the ball was thrown from Y= 100 in. and hits the ground at Y= 10 in. (CM of the ball) and time about t— 0.6 seconds. The ball bounces back and moves up to an elevation determined by the coefficient of restitution. The mo tio n continue s until reachi ng the end of the s imulation.
Note that you may click any location in the graph to bring up a fine red vertical line that correlates the gra ph wit h the posi tio n of the ball in anima tion . As sh ow n in the gr aph of Fi gur e 2.25, a t t = 1.4 seconds, the ball is roughly at Y= 44 in. T he sn aps hot of the ball at that specifi c time an d 7-loc ation is shown in the graphics screen.
tur ned off all friction for the 3D Contact constraint earlier, therefore, no energy loss due to contact. Figu re 2-27 sho ws 7-velocity of the ball. The ball move s at a linear veloc ity due to gravity. The 7velocity is about -263 in/sec at t = 0.67 seconds. You may see this data by moving the cursor close to the corner point of the cu rve a nd leave the curso r for a short period. The data will appear. You may also convert the XY Plot data to Microsoft® Excel spreadsheet by simply moving the cursor inside the graph and right click to choose Export CSV. Open the spreadsheet to see more detailed simulation data. From the spreadsheet (Figure 2-28), the 7-velocity right before and after the ball hits the ground are -264 a n d 198 in/sec, respectively. The ratio of 198/264 is about 0.75, wh ic h is the coef ficient of rest ituti on we define d earlier . In addition, you may use the Export A VI button on top of the gr aphi cs sc ree n to creat e an AVI movie for the motion animation. In the Export A VI Animation File dialog box (Figure 2-29); simply click the Preview button to review the AVI animation. Leave all default data for Frame a n d Time. Click OK to accept the definition. An AVI file will be created in your current folder with a file name, Lesson2.avi. You may play the A VI animation using, for example, Window Media Player. Be sure to save your mo del before exiting from COSMOSMotion. 2.4
Resu lt Verif icatio ns
In this section, we will verify analysis results obtained from COSMOSMotion using particle dynamics theory you learned in high school Physics. There are two assumptions that we have to make in order to apply the particle dynamics theory to this ballthrowing problem: (i) (ii)
The ball is of a conce ntra ted mas s, and No air fric tion is pre sen t.
Equation
of Motion
It is well-known that the equations that describe the positi on and velocity of the ball are, re spectiv ely,
w h e r e P a n d P are the X- and 7-positions of the ball, respecti vely; V an d V are the X- and 7-velocities, x
y
x
y
respectively; P an d P y are the initial positions in the X- and 7-directions, respectively; 0x
0
V a nd Vg ar e 0x
y
the initial velocities in the X- and 7-directions, respectively; and g is the gravitational acceleration. These equations can be implemented using, for example, Microsoft® Excel spreadsheet shown in Figure 2-30 , for nume rica l solutions. In Figu re 2-30, Co lum ns B and C show the results of Eqs. 2.1a and that when the a ball the ground, 2.1b, Note respectively; with timehits interval from 0 we to 3will seconds and increment of 0.01 seconds. Columns D have to reset the velocity to 7 5 % of that at the prior and E show the results of Eqs . 2.2a and 2.2b, respect ively. time step and in the opposite direction. Data in column C is graphed in Figure 2-31. Columns D and E are graphed in Figure 2-32. C ompa ring Figur e 2-31 w ith Figure 2-25 and Figu re 232 with Figures 2-26 and 2-27, the results obtained from theory and COSMOSMotion are very close, which -:eans the dynamic model has been created properly in JSMOSMotion, a n d COSMOSMotion does its jo b a nd gives us good results. Note that the solution spreadsheet am be found at the publisher's website (filename: . on2.xls).
1.
Use the sam e mot ion mod el to condu ct a simula tion for a different scenario . This tim e the ball is thrown at an initial velocity of from an elevation of 750 in., as shown in Figure E2-1. (i)
Create a dyna mic simulation mod el usin g COSMOSMotion to s imu late the traject ory of the ball. R epor t position, vel ocity, a nd acceleration of the ball at 0.5 seconds in both vertical and horizontal directions obtained from COSMOSMotion.
(ii)
Deri ve and solve the equation s that describ e the position and veloc ity of the ball. Com par e your solutions with those obtained from COSMOSMotion.
(iii) Calcula te the time for the ball to reac h the gro und and the distan ce it travels . C omp ar e your calculation with the simulation results obtained from COSMOSMotion. 2.
A 1 "xl "xl" blo ck slides from top of a slope (due to gravity) without friction, as shown in Figure E2- 2. The materi al of the block and the slo pe is AL2014. (i)
Create a dyna mic simulation mod el usin g COSMOSMotion to anal yze mo tio n of the block. Repo rt position, velocity, a nd acceleratio n of the block in both vertical an d horizo ntal directions at 0.5 seconds obtained from COSMOSMotion.
(ii)
Crea te a LimitDistance mat e to stop the blo ck when its front lower ed ge reach es the e nd of the slope. You may want to review COSMOSMotion help menu or preview Lesson 3 to learn more about the LimitDistance m a t e .
(iii) Der ive and solve the equation of mot ion for the syst em. Com par e your solutions with thos e obtained from COSMOSMotion.
3.1
Overv iew of the Lesso n
In this lesson, we will create a simple spring-mass system and simulate its dynamic responses u nder vario us sce narios. A schem atics of the sy stem is sh own in Figu re 3- 1, in which a steel block of V'xV'xl" is sliding along a 30° slope wit h a spr ing conn ect ing it to the top en d of the sl ope. Th e bl ock will slide back and forth along the slope under three different scenarios. First, the block will slide due to a small initial displacement, essentially, a free vibration. For the second scenario, we will add a frict ion between the block and the slope face. Finally, we will remove the friction and add a sinusoidal force p(t) therefore, a forced vibration. Gravity will be turned on for all three scenarios. In this lesson, you will learn how to create the spring-mass model, run a motion analysis, and visualize the an alysis results. In addition, yo u will learn ho w to add a friction to a joint , in this case, a planar (or coincident) joint. T he
9
analysis results of the spr ing-m ass ex amp le can be verified usin g particle dyn amic s theory. Similar to Lesson 2, we will formulat e the equati on of motio n, solve the differential equations, grap h posit ions of the block, and compare our calculations with results obtained from COSMOSMotion. Specifically, we will focus on the first and the last scenarios; i.e., free and forced vibrations, respectively. 3.2
The Spring- Mass System
Physical
Model
Note that the IPS units system will be used for this example. The spring constant and unstretched length (or free length) are k = 20 lbf/in. and U = 3 in., respectively. As ment ion ed earlier, the first scen ario ass umes a free vibration, where the block is stretched 1 in. downward along
the
30°
slope.
Friction
will
be
imposed
for
Scenario 2, in which the friction coefficient is assumed jU = 0.25. In the third scenario, an external force p(t) = 10 cos 360t l b is applied to the block, as shown in Figure f
3-1. All three scenarios will assume a gravity of g = 386 in/sec
2
in the negative 7-direction. All three scenarios
will be simula ted usin g SolidWorks
Parts
COSMOSMotion.
and Assembly
For this lesson, the parts and assembly have been created for you in SolidWorks. There are six files created, block. SLDPRT, ground. SLDPRT, Lesson3. SLDASM, Lesson3Awithresults. SLDASM, an d Lesson3Cwithresults.SLDASM. You can find these files at the Lesson3Bwithresults.SLDASM, publisher's web site ( h t t p : / / w w w . s c h r o f f l . c o m / ). We will start with Lesson3.SLDASM, in which the block
is assembled to the ground and no motion entities have been added. In addition, the assembly files and Lesson3Awithresults. SLDASM, Lesson3Bwithresults. SLDASM, Lesson3Cwithresults. SLDASM contain the complete simulation models with simulation results for the three respective scenarios. In the assembly models, there are three assembly mates, a nd as Coincident3(ground,ball), LimitDistancel(ground,ball),
Coincidentl(ground,block),
s hown
in
Figu re
3-2. m
The bloc k is allowed allowed to to mo mo ve ve alo alo ng ng the the slope slope face. face. If I f yo yo uu choose choose the the Move button component Move Component Component button on The bloc k is top of the grap s creen, block m the graph ics sscreen, creen, you sshhould ould be able to mov graphhics ics scr een, aannd d drag the bloc k in graphics movee the block on the slope face, but not beyond the slope face. This is because the third mate is defined to re strict the block block to to move the move between between the the lower lower and and upper upper limits. limits. We We will will take take aa look look at at the the assembly assembly mate mate LimitDistancel. 1. LimitDistance
on
From the browser, righ-click the third mate, LimitDistance 1, and choose Edit Feature. The mate is brought back for reviewing or editing, as shown in Figure 3-3. Note that the distance between the two faces (Face<2>@block-l Face@ground-l, a nd se e Figure 3-2c) is 3.00 in., which is the neutral position of the block when the spring is undeformed. The upper and lower limits of the dist ance are 9.00 a n d 0.00 in., respec tively. The le ngth of the slo pe face is 10 in., therefore, the upper limit is set to 9.00 in., so that the block will stop when its front lower edge reaches the end of the slope face. Not e that you will have to cho ose Advanced Mates in order to access the limit fields. Motion
Model
A spring with a spring constant k = 20 lb /i n. a nd an unstretched length U = 3 in. will be added to connect the b l o c k (Face<2>, as shown in Figure 3-2c) with the ground (Face). f
By default, the ends of the s pring will conne ct to the center of the co rres pondi ng squar e faces (see Figure 3-4). No reference points are needed. This model is adequate to support a free vibration simulation under the first scenario. Note that we will move the block 1 in. downward along the slope face for the simulation. This can be accomplished by changing the distance from 3 to 4 in. in the LimitDistancel assembly mate. Note that before entering COSMOSMotion we will suppress two assembly mates, Coincident^ a n d LimitDistancel, and only keep Coincident 1 in order fo r to impose a planar (or COSMOSMotion coincident) joint between the block and the slope face. You may unsuppress these mates when you want to make a change to the assembly, for example, moving the block back to its initial position. As mentioned earlier, a friction force will be added between the block and the slope face for Scenario 2. In addition, a sinusoidal force p(t) = 10 cos 360t will be added to the block for the 3rd scenario. Gravity will be turned on for all three scenarios. Using COSMOSMotion
3.3
Start SolidWorks Before LimitDistancel.
choose
entering From
Suppress.
LimitDistancel.
and
open
assembly we
COSMOSMotion,
the Assembly browser, The
Save
mate
your
Coincident3
file will
Lesson3.SLDASM.
suppress
expand will
the
become
two
Mates
assembly branch,
inactive.
mates,
right
Repeat
Coincident3
click Coincident3,
the
same
to
and and
sup press
model.
From the browser, click the Motion button
on top to enter
COSMOSMotion.
In this lesson, instead of usin g IntelliMotion Builder (as in Lesson 2), we will use the browser, and basic drag-and-drop and right click activated menus to create and simulate the block motion. Before creating any entities, always check the units system. Similar to Lesson 2, choose from the null-down menu
Choose
t h e Document Properties tab
in
the System
Options -
General d i a l o g b o x ,
click the
Units
n o d e . Y o u s h o u l d s e e t h a t t h e IPS units system has been chosen. In this units system, the gravity is 386 i n / s e c in the negativ e 7-dir ection of the global coo rdinat e syste m by default. No change is neede d. 2
Defining
Bodies
From the browser, expand the Assembly Components branch (right underneath the Motion Model nod e) by clic king the small + but ton in front of it. You shou ld see tw o par ts listed, block-1 a n d ground-7,
as shown in Figure 3-5. Also expand the Parts branch; you should see Moving Parts a n d Ground Parts listed. We will move block-1 to Moving Parts a nd ground-1 to Ground Parts by using the drag-and-drop method. Click block-1 and drag it by holding down the left-mouse button, moving the mouse until the cursor is over the Moving Parts node, and then releasing the mouse button. Part block-1 is now added to the motion model as moving parts. Repeat the same steps to move ground-1 to the Ground Parts node. Now, the part ground-1 is added to the motion model as a ground part (completely fixed, as shown in Figure 3-6). Expand the Constraints branch, and then the Joints branc h. Y ou shoul d see that only one joint, is listed. Expa nd the Coincident1, Coincident! branch to see that the assembly mate is defined between a nd Since this ground-! block-1. coinci dent join t restricts the block to mo ve o n the slop e face of the gr oun d, it is ther efor e a planar joint. A planar j oi n t s ym bol s hould appea r in the motion model, as shown in Figure 3-4. Defining
Spring
From the browser, right click the Spring node and choose Add Translational Spring (see Figure 3-7). In the Insert Spring dialog box (Figure 3-8), the Select 1st Component field is highlighted in red and re ady for yo u to pick. P ic k the face at top rig ht of the g ro und (see Fi gur e 3-9), th e Select 2nd Component field should now highlight in red, and ground l/DDMFace4 should appear in the Select Point on 1st Component field, whi ch indic ates that the spri ng will be conn ect ed to the cente r poi nt of the fac e. Rotate the view, and then pick the face in the block, as shown in Figure 3-9. Now, block-1 and block-l/DDMFace3 should appear in the Select 2nd Component field and Select Point on 2nd Component field, respectively. Also, a spring symbol should appear in the graphics screen, connecting the center points of the two selected faces.
Defining
Initial
Position
We would like to stretch the spring 1 in. downward along the slope face as the initial position for the block. The block will be released from this position to simulate a free vibration; i.e., the first scenario. We will go back to the Assembly m o d e , u n s u p p r e s s LimitDistancel, change the distance dimension from 3 to 4 in., and then sunnress the mate before returning to COSMOSMotion. Go back to Assembly by clicking the Assembly button
on top o f the brow ser.
Expand the Mates branch listed in the browser, right click and choose Unsuppress. Right click the same assembly mate and choose Edit Feature. You should see the definition of the as sem bly mate in the dialog bo x like that of Figu re 3-3 . C han ge the distance from 3.00 to 4.00 in., and click the checkmark on top to accept the change. In the graphics screen, t he block should m o v e 1 in. downward along the slope face. Click the checkmark again to close the assembly mate box. Right click L i m i t D i s t a n c e l ( z r o u n d < l > , b a l l < l > ) again and choose Suppress.
Go back to COSMOSMotion by clicking the Motion button (y . Click the Motion Model node, press the right mouse button and select Simulation Parameters. Enter 0.25 for simulation duration and 500 fo r the num ber of frames. Click the Motion Model node again, press the right mouse button and select Run Simulation. Y o u may also click the Run Simulation button |J|] right below the browser to run a simulation. You should see the block start movi ng bac k and forth along the slope face. We will g raph the positio n of the bloc k in terms of the mag nit ude (instead ofX- or 7 -com ponen t) next.
Displaying
Simulation
Results
Since there is no position graph defined for the block, we will have to create one. We will create a graph for the distance between the two faces that were selected to define the spring. From the browser, expand the Results branch, right click the Linear Disp node, and choose Create Linear Displacement (Figure 3-10). In the Insert Linear Displacement dialog box (Figure 3-11), the Select First Component field should be highlighted in red and ready for you to pick. This dialog box is ver y s imilar to the u ppe r half of the Insert Spring dialog box (Figure 3-8). We will select exactly the same two faces shown in Figure 3-9 for this displacement. Similar to the spring, pic k the face of the Figure 3-9). Rotate the view, and then pick the block, as shown in Figure 3-9. A straight line that center points of thes e two faces appear s, as show n 12. Click Apply button to accept the definition.
gr oun d (see face in the connects the in Figu re 3-
Next , we will create a graph for the displac emen t of the block using the XY Plots option. This position graph should reveal a sinusoidal function as we have seen in many vibration examples of Physics. From the browser, right click LDisplacement > Plot > Magnitude (see Figu re 3-13) . A grap h like that of Fig ure 3- 14 should appear. From the graph, the block moves along the slope face between 2 and 4 in. This is because the unstretched leng th of the s pri ng is 3 in. and we stretched the spring 1 in . to start the motion. Also, it takes about 0.04 seconds to complete a cycle, which is small. The small vibration period can be attributed to the fact that the spring is fairly stiff (20 lb /in ). f
Note that you can also export the graph data, for example, by right clicking the graph and choosing Open the Export CSV. spreadsheet and exam the data. The time for the block to move back to its initial position; i.e., when the distance is 4 in., is 0.037 seconds. We will carry out calculations to verify these results later in Section 3.4. Before we do that, we will work on two more scenarios: with frict ion and with th e ad dition o f an exte rnal force. Save your model before moving to the next scenario. You may save the model under different name and use it for the next scenario. Scenario
2:
With
Friction
We will ad d a friction force to the plana r joi nt {Coincident 1) between the block and the ground. The friction coeffic ient is ju = 0.25. Before making any chan ge to the definition of the s imulatio n model, we will have to delete existing simulation results. Click the button to delete the results.
Delete
Results
at the bot tom o f the brow ser
Note that for calculating friction effects, COSMOSMotion mod els a planar joi nt as one block sliding and rotating on the surf ace of anothe r block, as illustrated in Figure 3-15, where L is the length of the top (sliding) r ectan gular block, W is the width of the top recta ngular block, and R is the radi us of a circle, cen ter ed at the ce nter of the
top block face in contact with the bottom block, which circu mscr ibes the face of the s liding block.
Expand the Constraints branch and then the Joints branch. Right click the Coincident! node and c h o o s e Properties. In the Edit Mate-Defined Joint dialog box, choose the Friction tab, click the Use Friction, enter 0.25 fo r Coefficient (mu), and enter Joint dimensions, Length: 1, Width: 1 , a n d Radius: 1.414, as shown in Figure 3-17. Click Apply button to accept the definition. Run a simulation (with the same simulation parameters as th ose of Scenario T). Graph the disp lacem ent of the block; you sh ould see a graph similar to that of Figur e 3-18. The ampl itude of the graph (that is, the distance the block travels) is decreasing over time due to friction. Save your mode l. We will move into Scenario 3. You may save the model again under different name and use it for the next scenario.
In this scenario we will add an external force p(t) = 10 cos 360t at the ce nter of the end face of the block in the downward direction along the slope. At the same time, we will remove the friction in order to simplify the problem. Before creating a force, we will delete the simulation results and remove the f riction. Delete the results by clicking the Delete Results button
at the bottom of the brows er.
Right click the Coincidentl node and choose Properties. In the Edit Mate-Defined Joint dialog box, choose the Friction tab, and deselect the Use Friction by clicki ng the small bo x in front of it. All parameters and selections on the dialog box should become inactive. Click Apply button to accept the change. The force can be added by expanding the Forces branch, right clicking the Action Only node, and choosing Add Action-Only Force, as shown in Figure 3-19. In the Insert Action-Only Force dialog box (see Figure 3-20), the Select Component to which Force is Applied field will be active (highlighted in red) and ready for you pick the component. Pick the end face of the Component to which Force is and the Select Direction fiel ds. in the direction that is normal
block, as sh own in Figure 3- 21. The part block-1 is now listed in the Select Applied field, and block-l/DDMFace8 is listed in both the Select Location T hat is, the force will be appl ied to the cent er of the s elec ted end face and to the selected face.
Now in the Insert Action-Only Force dialog box, the Select Reference Component to orient Force field is active (highlighted in red) and is ready for selection. We will pick the ground part for reference. Pick any place in the ground part, ground-1 will now appear in the Select Reference Component to orient Force field.
Click the Function tab (see Figure 3-22), choose Harmonic, and enter the followings: Amplitude: Frequency: Phase Shift:
10 360 -90
Note that the -90 degrees entered for Phase Shift is to convert a sine function (default) to the desired cosine function. Click the graph button (right most and circled in Figure 3-22); the sinusoidal force function will appear like the one in Figure 3-23. This is indeed the cosine function p(t) = 10 cos 360t we wanted to define. Close the graph and click Apply button to accept the force definition. You should see a force symbol added to the block, as shown in Figure 3-4. From the browser, right click the Motion Model node, and choose Simulation Parameters. Change the simulation duration to 0.5 seconds (in order to see a graph later that covers a larger time span). Note that the 0.5- second duration is half the harm oni c function peri od of the force applie d to the block. From the browser, right click the Motion Model node again, and choose Run Simulation. After 2 to 3 seconds, the block starts moving. Not e that in some oc casio ns, the bloc k ma y slide out of the slope face during the sim ulation, a s shown in Figure 3-24. When this happens, simply unsuppress the assembly mate; for example, Coincident3, to restricts the block to stay on the slope face.
After unsuppressing Coincident3, the planar joint will become a translational joint (converted by COSMOSMotion) comp osed of two assemb ly mates, Coincident 1 a n d Coincident^. Please refer to the assembly file the Lesson3Cwithresults.SLDASM for translat ional join t emp loy ed for this exam ple. Rer un a simulation if necess ary. As soo n as the simula tion is compl eted, a graph like that of Figur e 325 should appear. From the graph, the block m o v e s along the slope face roughly for 2 in. back and forth (since friction is turned off). The vibration amplitude is enveloped by a cosine function due to the external force p(t). Also, it takes about 0.04 seconds to complete a cycle, which is unchanged from the previous case. We will carry out calculations to verify these results later. Save your model.
Figure 3-25
The Displace ment Graph: Scenario 3
In this section, we will verify analysis results of Scenarios 1 and 3 obtained from COSMOSMotion. We will assume that the block is of a concentr ated mass so that the particle dynamics theory is applicable. We will start with Scenario 1 (i.e., free vibration with grav ity), a nd then so lve the equations of moti on for Scenario 3 (forced vibration, no friction). Equation
of
Motion:
Scenario
1
From the free-body diagram shown in Figure 3-26, applying Newton's Second Law and force equili brium alon g the X-direct ion (i.e., along the 30° slope), we have
w h e r e m is the mas s of the block, U is the unstr etche d length of the s pring, x is the distance between the ma ss c enter of the bloc k and the top right end of the sl ope, me asu red from the top right end. The double dots on top of x represent the second derivative of x with respect to time. Rearrange Eq. 3.2, we have (3.3)
mx + kx = mgsin 0 + Uk
where both terms on the right are time-independent. This is a second-order ordinary differential equation. It is well kn ow n that the gen eral so lution of the differential equation is
dete rmi ned with initial condition s. No te that the mass of the steel block is 0.264 l b . This can be obtain ed from m
SolidWorks by opening the block part file, and choosing,
from the pull-down menu, Tools > Mass Properties. F r o m the Mass Properties dialog box (Figure 3-27), the mass of the block is 0.264 pounds (pound-mass, lb ). Note that there are 2 decimal points set in SolidWorks by default. You may increase it through the Document Properties - Units dialog box (choose from pull-down menu, Tools > Options). m
Note that the pound-mass unit lb is not as common as slug that we are more familiar with. The corr espon ding force unit of l b i s l b i n / s e c according to Newton's Second Law. m
2
m
m
Equation 3.7 can be implemented into Microsoft® Excel spreadsheet, as shown in Figure 3-28. Column B in the spread sheet sho ws the results o f Eq. 3.7, which is gra phed in Figure 3-29. Comparing Figure 3-29 with Figure 3-14, the results obtained from theory and COSMOSMotion agree very well, which means the motion model has been properly defined, and COSMOSMotion gives us good results. Equation
of
Refer
Motion:
to
the
Scenario
free-body
3
diagram
shown
in
Figure 3-26 again. For Scenario 3 we must include the force p = fo cos (cot) along the X-direction for force equilibrium; i.e.,
whe re the right -hand side consists of consta nt and time-d epen dent terms. For the constant term s, the particular solution is identical to that of Scenario 1\ i.e., Eq. 3.5. For the time-dependent term, p = f 0
cos (cot), the particular solution is
Note that terms grouped in the first brac ket of Eq. 3.12 are identical to thos e of Eq . 3. 7; i.e., Scenario 1. The second term of Eq. 3.12 g rap hed in Figu re 3-30 repre sents the contr ibution of the exter nal force p(t) to the block motion. The graph shows th at the amplit ude of the blo ck is kept within 1 in., but the pos iti on of the block varies in time. The vibration amplitude is enveloped by a cosine function. The overall solution of Scenario 3; i.e., Eq. 3. 12, is a com bin ati on of gra phs shown in Figures 3-29 and 3-30. In fact, Eq. 3.12 has been implemented in Column C of the spre adsheet. The data are grap hed in Figure 3-31. Comparing Figure 3-31 with Figure 3-25, the results obtained from theory and COSMOSMotion ar e very close. Note that the spreadsheet shown in Figure 3-28 can be found at the publisher's website lesson3.xls). (filename:
Exercises:
1.
Sh ow that Eq. 3.12 is the corr ect solu tion of Scenario 3 governed by Eq. 3.8 by simply plugging Eq. 3.12 into Eq. 3.8.
2.
Rep eat the Scenario 3 of this lesson, except cha ngin g the external force to p(t) = 10 cos 9798. Ot l b . f
Will this external force chan ge the vibrat ion amplit ude of the syst em? Ca n you sim ulate this resonance scenario in COSMOSMotion! 3.
Ad d a dam per with dam pin g coefficient C = 0.01 l b sec/in. and repeat the Scenario 1 simulation f
using
COSMOSMotion.
(i)
Calcula te the natura l freq uency o f the system and comp are your calculation with that of COSMOSMotion.
(ii)
Deri ve and solve the equations that descri be the positi on and veloci ty of the mas s. C omp ar e your solutions with those obtained from COSMOSMotion.
4.1
Ove rvi ew of the Les son
In this lesson, we will create a simple pendulum motion model using COSMOSMotion. The pe ndu lum will be released from a positio n slightly off the vertical line. Th e pendu lum will then rotate freely due to gravity. In this lesson, yo u will learn how to create the pen dul um moti on model, run a dyna mic analys is, and visualiz e the analysis results. Th e dynami c analysis results of the simpl e pend ulum example can be verified using particle dynamics theory. Similar to Lessons 2 and 3, we will formulate the equat ion of mot ion; calculate the angula r position, velocit y, and accelerat ion of the pendul um; anc compare our calculations with results obtained from COSMOSMotion. 4.2
The Simple Pen dulu m Exam ple
Physical
Model
The physical model of the pendulu m is com posed of a spher e and a ro d rigi dly conn ecte d, as s how n in Figur e 4-1 . Th e radiu s of the sphere is 10 mm. The leng th and radiu s of the thin rod are 90 mm and 0.5 mm , respectiv ely. T he top of the rod will be connect ed to the wall with a revolute joint. This revolute joint allows the pendulum to rotate. Both rod and sphere are ma de of Alu nim um. Not e that from the SolidWorks material library the Aluminum Alloy 2014 has been selected for both sphere and rod. The MMGS units system is selected for this example (millimeter for length, Newton for force, and second for time). Note that in the MMGS units system, the gravitational acceleration is 9,806 m m / s e c . 2
The pendulum will be released from an angular position of 10 degrees measured from the vertical positi on about the rotational axis of the revol ute joint. The rotation angle is intentionally kept small so that the particle dynamics theory can be applied to verify the simulation result.
You can find these files at the publisher's web site ( http://www.schroffl.com/) . We will start with Lesson4.SLDASM, in which the pendulum is fully assembled to the ground. In addition, the assembly f ile Lesson4withresults.SLDASM consists of a complet e s imulati on mo del with sim ulation results.
4- 3
Fr om top of the bro wser , cl ick the Motion button
to
enter
COSMOSMotion.
Fr om top of the bro wser , click the Motion but ton $ to enter COSMOSMotion. Before crea ting any entities, alway s check the units system. Ma ke sure that MMGS is chosen. Defining
Bodies
From the browser, expand the Assembly Components branch (right underneath the Motion Model node) by clic king the small H butt on in front of it. You sho uld see two parts listed, ground-1 a nd pendulum-7, as shown in Figure 4-4. Also expand the Parts branch; you should see Moving Parts and Ground Parts listed. Go ahead to move pendulum-1 to Moving Parts a nd ground-1 to Ground Parts by using the drag-and-drop method. Expand the Constraints branch, and then the Joints branch. You should see a Revolute joint listed, as shown in Figu re 4-5 and a revol ute join t symbol s hould appear in the graphics screen (see Figure 4-3).
Setting
Gravity
We would like to make sue the gravity is set up properly. From the browser, right-click the Motion Model
node
and
select
System
Defaults.
In
the
Options
dialog
box
(Figure
4-6),
enter
9806 fo r
Acceleration (mm/sec**2) which should appear as default already, and make sure the Direction is set to
-7 for Y. Click OK to accept the gravity setting. Defining
and
Running
Simulation
Click the Motion Model node, press the right mouse button and select Simulation Parameters. Enter 1.5 for simulation duration and then 300 for the nu mbe r of frames. Click the Motion Model node again, press the right mouse button and select Run Simulation. Y o u shoul d see the pen dul um start movi ng back and forth about the axis of the revolu te joint. We will graph the position, velocity, and acceleration of the pen dul um next. Displaying
Simulation
Results
The results o f angula r position , velocity, and accelerat ion of the pen dul um can be directly obtained by right clicking the moving part, pendulum-7, from the browser.
The results o f angula r position , velocity, and accelerat ion of the pen dul um can be directly obtained by right clicking the moving part, pendulum-7, from the browser. From the browser, expand the Parts node and the then Moving Parts node. Right-click pendulum-7, and choose Plot > Bryant Angles > Angle 3. Note that the Bryant angles are also known as X-Y-ZEuler angles or Cardan angles. They are simply the rotation angles of a spatial object along the 7-, and Z-axes of the refere nce coord inate system. Angle 3 is measured about the Z-axis. A graph like that of Figur e 4-7 sho uld appear. F ro m the graph, the pe ndu lum sw ings ab out the Z-axis b e t w e e n -10 a nd 10 degrees, as expected (since no friction is involved). Also, it takes about 0.6 seconds to complete a cycle. Note that you can export the graph data, for example, by right clicking the graph and choosing Export CSV. Open the spreadsheet and exam the data. From the spreadsheet, the time for the pendulum to swing back to its original position; i.e., -10 degrees., is 0.64 second, as shown in the spread sheet of Figu re 4-8. We will carry out calculations to verify these results later. Before we do that, we will graph the angula r velocit y and acceleration of the pendu lum .
and choose Angular Acceleration > Z Component. Yo u should see gr aphs like those of Figur es 4-9 and 410. Figure 4-9 shows that the angular velocity starts at 0, which is expected. The angular v elocity varies between roughly -100 a n d 100 degrees/sec. Also, the angular acceleration varies between roughly -1,000 a nd 1,000 d e g r e e s / s e c . Ar e these results corr ect? We will carry out calculation s to verify if these g raphs 2
are accurate.
4.4
Resu lt Verifi cations
In this section, we will verify the analysis results obtained from dynamics theory.
COSMOSMotion using particle
There are four assumptions that we have to make in order to apply the particle dynamics theory to this simple pendulum problem: (i) (ii) (iii) (iv)
Mas s of the rod is negligible (this is wh y the diamete r of the pen dul um rod is very smal l), The sphere is of a conce ntrat ed mas s, Rotat ion angle is small (rem emb er the initial conditio ns we defined?), and No friction is pre sent .
The pendulum model has been created to comply with these assumptions as much as pos sible. We expect that the particle dynamics theory will give us results close to those obtained from simulation . Two appro aches will be pres ente d to formulate the equatio ns of mot ion for the pendul um: energ y conservat ion and Newton's law. Energy
Conservation
Referr ing to Figu re 4- 11 , the kinetic en ergy and potential ener gy of the pend ulu m can be written, respectively, as
T=- J 0
(4.1)
2
wh er e J is the po lar mo me nt of inertia, i.e., J = m£ \ an d U=mg/(l-<:os
6)
According
to
the
energy
conservation
theory,
the
total
mecha nica l energy, whi ch is the sum of the kinetic energ y and potential energy, is a constant with respect to time; i.e.,
From equil ibriu m
the
free-body
equation
diagram
of mo men t
shown at the
(normal to the paper) can be written as:
in
origin
Figure
4-12,
abo ut the
the
Z-axis
Not e that the sam e equatio n of mot ion has been derived fro m two different appro ache s. T he linear ordinary second-order differential equation can be solved analytically. Solving the Differential Equation
The above equations represent angular position, velocity, and acceleration, of the revolute joint. Thes e equations can be implemented into, for example, Excel spreadsheet shown in Figure 4-13, for numerical solutions. Columns B, C, and D in the spreadsheet show the results of Eqs. 4.9a, b, and c, respe ctively , betwe en 0 and 7.5 seconds with an increments of 0.005 seconds. Data in these three columns are graphed in Figures 4-14, 15, and 16, respectively. Comparing Figures 4-14 to 16 with Figures 4-7, 4-9, and 4-10, the results obtained from theor y and simula tion are ver y close. The motio n model has been properly defined, and COSMOSMotion gives us good results. Note that in the calculation, the angula r positi on of the pend ulu m is set to zero wh en it aligns with the vertical axis; therefore, the pendulum swings between -10 a n d 10 degrees.
However, even though graphs obtained from COSMOSMotion and spreadsheet calculations are alike these results are not identical. This is because that the COSMOSMotion model is not really a simple pen dul um since ma ss of the rod is non-z ero . If you reduc e the diame ter of the rod, the COSMOSMotion results should approach those obtained through spreadsheet calculations.
Exercises:
1.
Create a spring-da mper-m ass system, as shown in Figure E4- 1, u s i n g COSMOSMotion. Note that the unstretched spring length is 3 in. T he radi us of the ball is 0.5 in. and the material is Cast Alloy Steel (mass density: 0.2637 l b / i n ) . 3
m
2.
(i)
Find the spring length in the equilibrium condition usin g COSMOSMotion.
(ii)
Solve the same probl em using New ton 's laws. Compare you r results with thos e obtaine d from COSMOSMotion.
If a force p = 2 l b is applied to the ball as shown in Figure E4f
1, repeat both (i) an d (ii) of Pr obl em 1.
5.1
Ove rvi ew of the Les son
In this lesson, you will learn how to create simulation models for a slider- crank mechanism and cond uct three analyse s: kinem atic s, interference, and dynami cs. Mo re join t types will be introduc ed in this lesson. You will learn how to select assembly mates to connect parts in order to cre ate a successful motion model. We will first drive the mechanism by rotating the crank with a constant ang ular velocity; therefore, conducting a kinematic analysis. After we complete a kinematic analy sis, we will turn on interferenc e checki ng and repeat the analysis to see if parts collide. It is very imp ortan t to mak e sure no interference exists between parts while the mechanism is in motion. The final analysis will be dynamic, where we will add a firing force to the piston for a dynamic analysis. This lesson will sta rt with a brief overview about the slider-crank assembly created in SolidWorks. At the e nd of this less on, we wi ll verify the kinematic simulation results using theory and computational methods employed for mechanism design. 5.2
The Slider-C rank Exam ple
Physical
Model
The slider-crank mechanism is essentially a four-bar linkage, as shown in Figure 5-1. They are commonly found in mechanical systems; e.g., internal combustion engine and oil-well drilling equipment. For the internal combustion engine, the mechanism is driven by a firing load that pushes the piston, converting the reciprocal motion into rotational motion at the crank. In the oil-well drilling equipment, a torque is applied at the crank. The rotational motion is converted to a recip rocal mot ion at the piston that digs into the ground. N ote that in any case the length of the cran k mus t be small er than that of the rod in order to allow the mech ani sm to operate. This is c omm onl y refe rred to as the G ra sh of s law. In this exa mpl e, the leng ths of the cr ank and rod are 3" an d 8", respectively. Note that the units system chosen for this example is A l u m i n u m , 2014 Alloy. subassemblies).
No
friction
is
ass ume d bet wee n
IPS (in-lbj-sec).
any pair
of the
All parts are made of comp one nts
(parts
or
SolidWorks
Parts
and Assembly
The slide r-crank syste m consists of five parts and one suba ssem bly. T hey are beari ng, crank, rod, pin, piston, a nd roda ndpi n (subass embly , consis ting of rod and pin). A n explod ed vie w of the mech ani sm is shown in Figure 5-2. SolidWorks parts and assembly have been created for you. They are a nd bearing.SLDPRT, crank. SLDPRT, rod.SLDPRT, pin.SLDPRTpiston.SLDPRT, rodandpin.SLDASM. In addition, there are three assembly file s, and Lesson5.SLDASM, Lesson5Awithresults.SLDASM, LessonSBwithresults.SLDASM. Yo u can find these files at the publ ish er' s we b site. We will start with LessonS. SLDASM, in which all components are properly assembled. In this assembly the bearing is anchored (ground) and all other parts are fully constrained. We will suppr ess one assembly mate in order to allow for movement. Same as before, the assembly file an d LessonSAwithresults. SLDASM (with firing Lesson5Bwithresults.SLDASM force) consist of comp lete s imulation mode ls with simulation results. You may want to open these files to see the mot ion anim ation of the mechanism. In these assembly files with complete simulation results, a mate has been suppressed. You can also see how the parts move by moving the cursor to the graphics screen and press the right mouse button. In the menu option appearing next, choose Move Component, and drag a movable part, for example drag the crank to rotate it with respect to the bearing. The whole mechanism will move accordingly. There are eight assembly mates, including five coincident and three concent ric, defined in the assembly. You may want to expand the MateGroupl bra nch in the bro wse r to see the list of mate s. Mo ve you r cursor on any of the mate s; yo u should see the entities selected for the ass embl y mate highlig hted in the graphics screen. The first three mates (Concentric 1, Coincident 1, a nd Coincident!) assemble the crank to the fixed bearing, as shown in Figure 5-3a. As a result, the crank is c ompletely fixed. Note that the mate Coincident! orients the crank to the upright position. This mate will be suppressed before entering COSMOSMotion. Suppressing this mate will allow the crank to rotate with respect the bearing. COSMOSMotion will convert these two mates, Concentricl an d Coincident 1, to a revolute joint. The next two mates (Concentric2 and Coincident^) assemble the rod to the crank, as shown in Figure 5-3b. Unlike the crank, the rod is allowed to rotate with respect to the crank, leading to another revolute joint in COSMOSMotion. The next two mates (Concentric3 an d Coincident4) assemble the piston to the pin, allowing the piston to rotate about the pin. As a result, a revolute joint (or a concentric j o i n t in som e cas es) wil l be a dd e d be tw e e n th e piston a nd the pin . T he fi na l m a t e (CoincidentS) eliminates the rotation by mating two planes, Right Plane of the pi sto n and the Top Plane of the ass embly , as sho wn in Figure 5-3c. COSMOSMotion will add a translatio nal joi nt betw een the piston and the grou nd. Since the translational joi nt is comp ose d of Coincident5 a n d Coincident4, Concentric3 will be carried over to COSMOSMotion as it is. T herefore , in stead of a revol ute joint, a cylindrical join t appears in the mot ion model.
Simulation
Model
In this example, after suppressing Coincident COSMOSMotion converts assembly mates to four jo in ts : Concentric3 (directly carry ing over from ass embl y mat e), Revolute, Revolute2, a nd Translational, as sh own in Figure 5-4. T he total num ber of degre es of fre edom of the slid er-crank mech ani sm can be calculated as follows: 3 -
(bodies) 1
=
x6
(concentric)
18-19
=
(dofs/body) x4
(dof
-
2
(revolute)
X 5
(dofs/revolute)
-
1
(translational)
X 5
(dofs/translational)
s/concentric)
-1
Appar ently , there are two redu ndant do f s embe dde d in the motio n mod el. Ki nema tical ly, this mec han ism is identical to that of the single pisto n engine pres ente d in Lesson 1. In Lesson 1, instead of defining two revolut e join ts, on e concentric joint , and one translat ional join t, the engine exa mpl e emplo ys three cylindrical join ts and one translati onal joint, resul ting one free degr ee of freedom. Sinc e COSMOSMotion will autom atical ly detect and re mov e redund ant dof s duri ng mot ion simu lation, we will not ma ke any change s to the join ts conver ted from the as sem bly mates. Since the mechanism has one free degree of freedom, either rotating the crank or the rod (ab out the axis of the revolute join ts), or mo vin g the piston horizon tally (alo ng the translat ional joint ) will be sufficient to unique ly determ ine the position , velocity, and accelera tion of any parts in the mech ani sm. The mechanism will be first driven by rotating the crank at a constant angular velocity of 360 degrees/sec. Gravity will be turned off. This will be essentially a kinematic simulation. This model will also serve for interference check. It is very important to make sure no interference exists between parts while the mechanism is in motion. The simulation results are included in LessonSAwithresults.SLDASM. The next and final analysis will be dynamic, where we will add a firing force to the piston for a dynamic simulation. The results are included in LessonSBwithresults. SLDASM.
5.3
Using COSMOSMotion
Start SolidWorks
and
open
assembly
file
Lesson5.SLDASM.
Before entering COSMOSMotion, we will suppress the third assembly mate, Coincident2. In this lesson, we will use dra g-an d-dr op as well as right-click activate d me nus , inste ad of the IntelliMotion Builder. From the Assembly browser, expand the Mates branch, right click Coincident2, and choose Suppress. The mate Coincident2 will become inactive. Save your model.
Befor e creating any entities, alway s check the units system. Mak e sure IPS units system is chosen for this example. Defining
Bodies
From the browser, click bearing-1 and drag and drop it to the Ground Parts node. Click the first part under the Assembly Components n o d e (should be crank-1), press the Shift key, and click the last part listed under the Assembly Components node (should be All three rodandpin-1). components will be selected. Drag and drop them to the Moving Parts n o d e . Expand the Constraints branch, and then the Joints bran ch. Y ou shoul d see that four join ts, a nd Concentric3, Revolute, Revolute2, Translational, are listed (Figure 5-6). All join t symbols should appear in the graphics screen, similar to that of Figu re 5-4. Exp and all join ts in the browser and identify the parts they connect. Tak e a loo k at the joi nt Revolute (connecting crank to bearing), where we will add a driver next. Driving
Joint
From the browser, expand the Constraints node and then the Joints node. Right click the Revolute node and choose Properties (see Figure 5-7). In the Edit Mate-Defined Joint dialog box (Figure 5-8), under the Motion tab, choose Velocity fo r Motion Type, choose Constant fo r Function, and enter 360 degrees/sec for Angular Velocity (should appear as defaults), as shown in Figure 5-8. Click Apply to accept the definition. We are ready to run a simulation. Turning
Off Gravity
Running
Simulation
We will use all default simulation parameters for the kinematic analysis. Click the Motion Model node, press the right mouse button and select Run Simulation. After a few seconds, you should see the mechanism starts moving. The crank rotates 360 degrees as expected and the piston moves a complete cycle, similar to that of Figur e 5-10, s ince the default simulation duratio n is 1 second. Saving
and
Reviewing
Results
We will create four graphs for the mechanism: Ap position, X-velocity, an d X-a cce ler atio n of the pis ton; and angular velocity of Revolute2 (between crank and rod).
Fig ure 5-10 Mo ti on Ani ma tio n
From the browser, expand the Parts branch and then the Moving Parts branch. Right click the piston-1 node, and choose Plot > CM Position > X( s ee Figur e 5-11). The grap h should be similar to that of Figur e 5-12. Not e that fr om the graph, the piston mov es bet wee n about 5 and 11 in. horizontally, in reference to the global coordinat e system, in whi ch the origin of the coor dinate sy stem coincid es with the center point of the hole in the bearin g. At the starting point, the crank is at the upright position, and the piston is located at
7.42 in. (that is,
V8 - 3 ) to the right of the or igin of the glob al coord inate system . No te that the lengths of the cr ank and 2
2
rod are 3 and 8 in., respectively. When the crank rotates to 90 degrees counterclockwise, the position b e c o m e s 5 (which is 8-3). When the crank rotates 270 degrees, the piston position is 11 (which is 8+3).
Re pe at the sam e steps to creat e grap hs for the velo cit y direction. The gra phs sh ould be similar to those of Figur es 5-13 piston-1 node in the browser, you should see there are three Position -X-piston-1, an d CM Velocity-X-piston-1, as shown in
and accele rati on of the pis ton in the in and 5-14, respective ly. I f you exp and the entities listed, CM Accel - X-piston-1, CM Figure 5-15.
The graph of the angula r velocity of the joi nt Revolute2 can be created by expanding the Constraints branch and then the Joints branch, right clicking Revolute2 and selecting Plot > Angular Velocity > ZComponent. Th e grap h sho uld be si mila r to tha t of Fig ur e 5-16. An entity, Angular Vel - Z-Revolute2, is added under the joint Revolute2 in the browser. Interference
Check
Next we will learn how to perform interference check. COSMOSMotion allows you to check for interference in your mec han ism as the parts move. Y ou can check any of the comp one nts in your
SolidWorks ass embl y mod el for possib le interference, reg ardless of whe the r a com pone nt participat es in
the motion model. Using the interference detection capability, you can find:
(1)
All the interferen ce that occur betw een the selected com pone nts as the me cha nis m mo ves through a specified ran ge of motio n, or
(2)
The place whe re the first interference occurs bet wee n the selected com pone nts . The assemb ly is moved to the position where the interference occurred.
Make sure you have completed a simulation before proceeding to the interference check. Right clic k the Motion Model node in the browser and then select Interference Check. T h e Find Interferences Over Time dialog box appears (Figure 5-17). To select the parts to include in the interference check, select the Select Parts to test text field and then pick all four components from the graphics screen (or from the browser). The Start Frame, End Frame, a nd Increment allow you to specify the motion frame used as the starting position, final position, and increment in between for the interference check. We will use the default numbers; i.e., 1, 51, a n d 2, for the Start Frame, End Frame, a n d Increment, respec tively. C lick the Find Now button (circled in Figure 5-17) to start the interference check. After pressing the Find Now button, the mechanism starts moving, in which the crank rotates a complete cycle. At the same time, the Find Interferences Over Time dialog box expands. The list at the lower half of the dialog box sho ws all interference condition s detected. T he f rame, simul ation time, parts that caused the interference, and the vol um e of the interfere nce detect ed are listed.
Close the dialog box and save your model. After saving the model, you may want to save it again under a different name and use it for the next simulation.
Creating
and Running
a
Dynamic
Analysis
A force simulating the engine firing load (acting along the negative X-direction) will be added to the piston for a dyna mic simulat ion. It will be more realistic if the force can be applied when the piston starts moving to the left (negative X-direction) and can be applied only for a selected short period. In order to do so, we will have to define mea su re s that mo nit or the posi tio n of the pist on for the firing loa d to be activated. Unfortunately, such a capability is not available in COSMOSMotion. Therefore, the force is simplified as a step function of 3 l b along the negative X-direction applied for 0.1 seconds. The force will be defi ned as a poi nt force at the ce nter poin t of the en d face of the pist on, a s sh ow n in Fig ure 5- 21 . f
Bef ore we add the force, we will turn off the an gula r vel oci ty driv er define d at the jo int Revolute2 in the previous simulation. We will have to delete the simulation before we can make a ny changes to the
From the browser, expand the Constraints branch, and then the Joints branch. Right click Revolute to bring up the Edit Mate-Defined Joint dialog box (Figure 5-22). Pull-down the Motion Type and choose Free. Click Apply to accept the change. Not e that if you run a simula tion now, no thing will happen since there is no motion driver or force defined (gravity has been turned off). Now we are ready to add the force. The force can be added from the browser by expanding the Forces branch, right clicking the Action Only node, and choosing Add Action-Only Force, as shown in Figure 523. In the Insert Action-Only Force dialog box, the Select Component to which Force is Applied field (see Figure 5-24) will be active (highlighted in red) and ready for you to pick the component. Pi ck the en d face of the pisto n, as s ho wn in Fig ure 5-21. The part piston-1 is now listed in the Select Component to which Force is Applied field, and piston1/DDMFacelO is listed in both the Select Location an d the Select Direction fields. That is, the force will be app lied to the center of the e nd face and in the di rect ion that is normal to the face; i.e., in the positive X-direction.
Now in the Insert Action-Only Force dialog box (Figure 5-24), the Select Reference Component to orient Force field is active (highlighted in red) and is ready for selection. We wil l pick the bearing you should see As semi appear in the Select Reference Component to orient Force field. Click the Function tab (see Figure 5-25), choose Step for function, and enter the followings: Initial Final
Value: Value:
-3 0
Start Step Time: End Step
Time:
0 0.1
Note that the negative sign for the initial value is to reverse the force direction to the negative Xdirection. Click the graph button (right most, as shown in Figure 5-25), the step function will appear like the one in Figure 5-26. Note that this is a smoothed step function with time extrapolated to the negative domain. The force varies from -3 at 0 second to 0 at 0.1 seconds. During the simulation, the force will be activated at the beginning; i.e., 0 second. Close the graph and click Apply button to accept the force definition. You should see a force symbol added to the piston, as shown in Figure 5-4. Before running a simulation, we will increase the number of frames in order to see more refined results and graphs. From the browser, right click th e Motion Model node, and choose Simulation Parameters. Cha nge the nu mbe r of frames to 500. Accept the change and then right click the Motion Model node, and choose Run Simulation. T he mechanism will move and the crank will make several turns befo re reach ing the en d of the simulation duration; i.e., 1 second by default. Graphs created in previous simulation, such as the piston position, etc., should appear immediately at the end of the simu lation. As s how n in Figu re 5-27, the piston mo ve s along the.neg ative X-direc tion for about 0.15 seconds before reversing its direction. It is also evident in the velocity graph shown in Figur e 5-28 that the velocity changes signs at two instances (close to 0.15 a nd 0.48 seconds). Recall that the force was applied for the first 0.1 seconds. Had the force application lasted longer, the piston could be continuously pushed to the left (negative X-direction) even when the piston reaches the left end a nd tries to m ov e to the right (due to inertia) . As a resul t, the cran k wo ul d ha ve been osci llati ng at the left of the center of the bearin g; i.e., bet ween 0 a n d 180 degrees about the Z-axis, without making a complete turn.
Graph the reaction force for the applied force at the piston by expanding the Forces branch, then the Action Only branch, right clicking the ForceAO, and choosing Plot. The reaction force that represents the actual force applied to the piston appears, as shown in Figure 5-29. The graph shows that the force of 3 lbf was ap plied at the beginn ing of the simulat ion. T he force graduall y decrease s to 0 in the 0.7-second period, which is what we expected and is consistent with the force function, as seen in Figure 5-26. Graph the reaction force at the joint Revolute (between crank and the ground) along the X-direction; you sho uld see a graph like that of Figu re 5-30. T here are three peaks in Figure 5-30 repre sentin g when the largest reaction forces oc cur at the join t, whi ch occur s at close to 0.15, 0.48, a n d 0.8 seconds; i.e., when the piston reverses its moving direction. The results make sense.
5.4
Resu lt Verifi cations
In this section, we will verify the motion analysis results using kinematic analysis theory often found in mechanism design textbooks. Note that in kinematic analysis, position, velocity, and acceleration of given points or axes in the mechanism, are analyzed. In kinematic analysis, forces and torques are not involved. All bodies (or links) are assumed massless. Hence, mass properties defined for bodies are not influencing the analysis results. The slider-crank mechanism is a planar kinematic analysis problem. A vector plot that represents the positi ons of join ts of the planar mech an ism is sho wn in Figure 5- 31. The vecto r plot serves as the first step in com puti ng position, velocit y, and acceleration s of the mecha nis m. The positio n equations of the sy stem can be described by the following vector summation,
The real and imag inary parts of Eq. 5.1, c orre spon ding to the X and / com pone nts of the vector s, ca n be written as
In Eqs. 5.2a and 5.2b, Zj, Z , a nd 6 are given. We are solving for Z a n d 6 . Equations 5.2a and 2
A
3
B
5.2b are non-linear. Solving them directly for Z a nd 0 is not straightforward. Instead, we will calculate s
Z first, using trigonometric relations; i.e., 3
B
where two solutions ofZ repr esent the two possible configur ations of the mec han ism sh own in Figu re 53
32. Note that point C can be either at C or C for any given Z an d 0 . 1
A
Figure 5-32 Two Possible Configurations
Similarly, 0 has two possi ble solutions, cor resp ondin g to vecto r Z j . B
Taki ng derivative s of Eqs. 5.2a and 5.2b with respect to time, we hav e
relatively. In Figure 3-37, the angular velocity 0
B
is the a ngular veloci ty of the rod referring to the
ground. Therefore, it is zero when the crank is in the upright position. Not e that the accele rations of a given join t in the mec han ism ca n be form ulated by taking one mor e derivative of Eqs. 5.5a and 5.5b with respec t to time. The resulti ng two coupl ed equations can be solved, using Excel spreadsheet. This is left as an exercise.
Exercises:
1.
Deri ve the acceleration equations for for the slider-crank mec han ism , by taking derivatives of Eqs, 5.5a 5.5a and 5.5b with respect to time. Solve these equati ons for the linear acceleration of the piston and the angula r acceler ation of the joi nt Revolute2, using a spreadsheet. Compare your solutions with those obtained from COSMOSMotion.
2.
Us e the same slider-cr ank mod el to condu ct a static analysis using COSMOSMotion. The static analysis in COSMOSMotion should give yo u equili brium configur ation(s) of the mech ani sm due t o gravity (turn on the gravity). Sh ow the equil ibrium configu ration(s ) of the mech ani sm and use the the energy method you learned from Sophomore Statics to verify the equilibrium configuration(s).
3.
Cha nge the length of the crank from 3 to 5 in. in SolidWorks. Repeat the kinematic analysis discussed in this lesson. In addition, change the crank length in the spreadsheet {Microsoft Excel file, lesson5.xls). Gener ate positi on and velocit y graph s from b oth COSMOSMotion and the spre adshee : Do they agree with each other? Does the maximum slider velocity increase due to a longer crank? I s there any interference occurring in the mechanism?
4.
Down load five SolidWorks parts from the publisher's web site to your computer (folder name Exercise
(i)
5-4).
Use these five parts, i.e., bear ing, crankshaft, connect ing rod, piston pin, and piston (see Figure E5-1), to create an assembly like the one shown in Figure E5-2. Note that the crankshaft mus: orient at 45° CCW, as shown in Figure E5-2.
(ii)
Crea te a mot ion mo del for kine mati c analysis. Cond uct mot ion analysis by defining a dri va that drives the crankshaft at a constant angular speed of 1,000 r p m .
Figure E5-1
Five SolidWorks Parts
Figure E5-2
Asse mble d Configuration
6.1
Ove rvi ew of the Less on
In this lesso n we will disc uss ho w to sim ulat e mot io n of a spur gea r train . A gear trai n is a set or syste m of gears ar rang ed to transfer torq ue or energy from one part of a mec hani cal s ystem to another. A gear train consists of driving ge ars that are moun ted on the input shaft, driven gears m oun ted on the output shaft, and idler gears that interpose between the driving and driven gears in order to maintain the dir ecti on of the out put shaft to be the s am e as the inpu t shaft or to incr eas e the dis tanc e betw ee n the dri ve and driven gears. Ther e are different kind s of gear trains, s uch as simp le gear train, comp oun d gear train, epicylic gear train, etc., depending on how the gears are shaped and arranged as well as the fuct ions they intend to perform. The gear train we are simulating in this lesson is a compound gear train, in which two or more gears are used to transmit torque or energy. All gears included in th is lesson are spur gears; therefore, the shafts that these gears mounted on are in parallel. In COSMOSMotion, gear pair is defined as a special coupler constraint. Joint couplers allo w the mot ion of a revolu te, cylindrical, or translational join t to be coupl ed to the motio n of another revolu te, cylindrical or translati onal joint. The tw o coupl ed join ts ma y be of the s ame o r different types . Fo r exam ple, a revolu te joi nt ma y be coupled to a translati onal joint. The c ouple d moti on may also be of the same or different type. For exa mple , the rotary motio n of a revol ute joi nt may be coupled to the rotary mot ion of a cylindrical joint, or the transla tional mot ion of a translational join t may be coupl ed to the rotary mo tion of a cylindrical joint . T o create a gear pair, we will be coupl ing two revol ute join ts. Usual ly a concentric an d a coincid ent mates will lead to a revolu te joint , as see n in prev ious les sons. Coup ling two revol ute joi nts for a gear pair will be carrie d out in SolidWorks using the advance assembly mate option, whe re two axe s that pass thr ough the respect ive revolute join ts (or gears) are pick ed for the gear mate. The ge ar mate will be mapp ed to a gear mate join t in COSMOSMotion. In fact, neither SolidWorks n or COSMOSMotion cares about the detailed geo metr y of the ge ar pair; i.e., if the gear teeth me sh adequa tely. Y ou may sim ply uses cylinder s or disks to repre sent the gears. No detailed tooth profile is nece ssar y for any of the comp utati ons invo lved. App aren tly, force and mom en t bet wee n a pair of teeth in contact will not be calculated in gear train sim ulations . Ho weve r, there ar e other important data being calculated by COSMOSMotion, such as reaction force exerting on the driven shaft (for a dynamic analysis), which is critical for mechanism design. In any case, pitch circle diameters are essential for defining gear pair and gear trains in COSMOSMotion. Gear ratio of the gea r train, whi ch is defined by the ratio of the ang ular velocities of the out put and input gears , is deter mine d by the pitch circle diame ters of the indiv idual gear pairs in the gear train. Although cylinders or disks are sufficient to model gears in SolidWorks, we will use more realistic gears throughout this lesson. All gears in the example are shown with detailed geometry, including teeth. In addition, detailed parts, including shafts, bearing, screws and aligning pins are included for a realistic gear train system, as shown in Figure 6-1. In this gear train simulation, we will focus more on graphical
animat ion, less on co mput atio ns of physic al quantities. We will add a mot ion driver to drive the input shaft. 6.2
The Gear Train Exam ple
Physical
Model
The gea r train exa mpl e we are using for this less on is part of a gearbox de signe d for an experim ental lunar rover. T he gea r train is loc ated in a gear box whi ch is part of the trans missi on sys tem of the rover, driven by a mot or powe red by solar energy. The pur pose of the gear train is to convert a high-sp eed rotation and small torque generated by the motor to a low speed rotation and large torque output in order to drive the whee ls of the rover. The ge ar train consists of four spur gears mou nte d on three parallel shafts, as shown in Figure 6-1.
The four spur gears form two gear pairs: Pinion 1 an d Gear 7, and Pinion 2 and Gear 2, as depicted in Figure 6-1 and 6-2. Note that Pinion 1 is the driving gear that connects to the motion driver; e.g., a motor. The motor rotates in a clockwise direction, therefore, driving Pinion 1. Gear 1 is the driven gear of the first gear pair, which is mounted on the same shaft as Pinion 2. Both rotate in a counterclockwise direction. Gear 2 is driven by Pinion 2, and rotates in a clockwi se direc tion. No te that the dia meter s of the pitch circles of the four gears are: 50, 120, 60, and 125 mm , respective ly; an d the numbe rs of teeth are 25, 60, 24, and 50, respectively. Therefore, the circular pitch P the diametral pitch P , and module m of the first gear pair are, respectively C9
d
num ber of teeth of the four respective ge ars. The ge ar ratio of the gear train sh own in Figu re 1 is 1:5; i.e., the angular velocity is reduced 5 times at the output. Theoretically, the torque output will increase 5 times if the re is no loss due to; e.g., frict ion. No te that we will us e MMGS units system for this lesson. SolidWorks
Parts
and Assembly
In this lesson, SolidWorks par ts of the gea r train hav e been cre ate d for you . T her e are six files created, gbox housing.SLDPRT, gbox input.SLDPRT, gboxjniddle.SLDPRT, gbox_output.SLDPRT, Lesson6.SLDASM, an d Lesson6withresults.SLDASM. You can find these files at the publisher's web site ( http://www.schroffl.com/) . We will start with Lesson6.SLDASM, in which the gears are assembled to the housing. In addition, the assembly file Lesson6withresults.SLDASM consists of a comp lete simulat ion model with simulation results. Note that the housing part in SolidWorks was converted directly from Pro/ENGINEER part. The three gear parts in SolidWorks were converted from respective Pro/ENGINEER assemblies. There were nine, nine, and six distinct parts within the three gear assemblies, respectively. These three Pro/ENGINEER assemblies (and associated parts) were first converted to SolidWorks as assemblies. Parts in each assembly were then merged into a single gear part in SolidWorks. The detailed part and assembly conversions as well as merging multiple parts into a single part in SolidWorks can be found in Appendix C. In the SolidWorks assembly models Lesson6.SLDASM (and Lesson6withresults.SLDASM), there are nine assembly mates. The first three mates, Concentric1, Coincidentl, an d Coincident2 assemble the input gear to the housing. The input gear is fully constrained. Note that before enter ing COSMOSMotion, we will suppress Coincident2 in order to allow rotational degree of freedom for the input gear about the Z-axis (see Figures 6-3a, b, and c). Similarly, the next three mates, Concentric2, Coincident^ a n d Coincident4 assemble the middle gear to the housing. Again, we will suppress Coincident4 to allow the mi dd le gear to rot ate abo ut the Z-axis ( see Figu res 6- 3d, e and f). The thir d set of mat es , Concentric3, Coincident5, a nd Coincident6 does the same for the output gear (see Figures 6-3g, h and i). Simil arly, Coincident6 will be suppressed to allow for rotation. Note that the three suppressed mates are created to properly orient the three gears, so that the gear teeth mesh well between pairs.
As mentioned earlier, one important factor for the animation to "look right" is to mesh the gear tee th properly. You may want to use the Front vie w and zoom i n to the tooth me sh area s to chec k if the two pairs of gears mes h well (see Figu re 6-4). T hey shou ld me sh well, whic h is accomp lish ed by the three coincident mates that will be suppressed before entering COSMOSMotion. Note that the tooth profile is repr esen ted by straight lines, instead of mo re popu lar ones s uch as involut es, jus t for simplicity.
Figure 6-4 Gear Teeth Properly Meshed If yo u tur n on the a xis d ispl ay (View > Axes), axes that pass thr ough the cen ter of the gea rs a bout the Z-axis are defined for each gear. These axes are necessary for creating gear mates. Simulation
Model
The gear housing will be defined as the ground part. All three gears will rotate with respect to their respective axes. The four gears will be meshed into two gear pairs; Pinion 1 with Gear 7, and Pinion 2 with Gear 2, as discussed earlier. In SolidWorks, gear pairs are created by selecting two axes of respe ctive gears (or cylinder s) usi ng Advanced Mates capability. Before the gear mates can be created, we will suppress the three coincident mates that help properly orient the gears; i.e., Coincident2, Coincident4 a n d Coincident6, in order to allow desired gear rotation motion. When these mates are suppressed, revol ute join ts will be created bet wee n the hous ing and the three gear parts in COSMOSMotion, as shown in Figure 65. The revolute joint between the housing and the input gear will be driven at a constant a ngular velocit y of 360 degrees/sec. We will basically conduct a kinematic analysis for this example.
6. 3
U s i n g COSMOSMotion Start SolidWorks and
open
the
assembly
file Lessond. SLDASM.
Note that when you open the assembly, you will see a message window, as shown in Figure 6-6, indicating that SolidWorks is unable to locate gbox input, sldasm. SolidWorks is trying to locate the assembly from which the input gear part was created. Since the input gear assembly and its associated parts are not available in the Lesson 6 folder, SolidWorks is unable to locate it. It is fine to click No an d not to locate gbox_input.sldasm. Not locating the assembly file for the input gear part will not affect the motion simulation in this lesson. After clicking No, SolidWorks will ask you to locate the middle gear assembly and output gear assembly. Choose No for both. The assembly files that SolidWorks is looking for are actually located in the subfolder under Lesson 6 as well as the Appendix C folder. You may choose Yes from t he mess age win do w and locate the miss ing files in one of these two folders. Before entering COSMOSMotion there are two things need to be done. First, we will suppress three assembly mates, Coincident2, Coincident4 an d Coincident6. Second, we will create two gear mates for the two gear pairs, respectively. From the Assembly browser, expand the branch, right-click a nd Mates Coincident2, c h o o s e Suppress. The mate Coincident2 will become inactive. Repeat the same to suppress Coincident4 an d Coincident6. Save your model. Next, turn on the axis view by choosing from the pull-down menu, View > Axes. All three axes, one for each gear, will appear in the graphics screen. We will create two gear mates. Choose from the pull-down menu Insert > Mate. In the Mate dialog box (overlapping with the browser), the Mate Selections field will be active (in red), and is ready for you to pick entities. Pick the axes of the input and middle gears from the graphics screen. Choose Advanced Mates, click Gear, a nd enter 50mm and 120mm fo r Ratio, as shown in Figure 6-7. Click the checkmark button on top to accept the mate definition, and click the same button one more time to close the dialog box. Not e that if the axe s of the two gears a re pointin g in the opp osite dire ction, you will have to click Reverse (right below the Ratio text field in the Mate dialog box) to correct the rotation direction. In this example, all three axes are pointing in the same direction. Therefore, do not choose Reverse. Rep eat the same steps to define the sec ond gear mate . Th is time, pick the axes of the midd le and output gears, and enter 60mm a nd 125mm fo r Ratio. Two new mates, Gear Mate 1 (gbox_input, gbox_middle) GearMate2(gbox_middle,gbox_output), and are now listed unde r Mates.
Now we are ready to enter COSMOSMotion. Click the Motion button
enter
COSMOSMotion.
Now we are ready to enter COSMOSMotion. Click the Motion button
#
enter
COSMOSMotion.
Similar to previous lessons, we will use the browser, and basic dra g-and-drop and right-clicl^ methods to create and simulate the gear train motion in this lesson. Before creating any entities, always check the units system. Make sure the units syste m chosen is Defining Bodies MMGS. From the browser, expand the Assembly branch. You should see four parts Components gbox housing-1, gboxjnput-l, gboxmiddlelisted, 1, a n d gbox_output-l, as shown in Figure 6-8. Also expand the Parts branch; you should see Moving Parts a n d Ground Parts listed. Go ahea d to Ground Parts and move m o v e gboxjiousing-l to the three gears to Moving Parts by using the dragand-drop method. Expand the Constraints branch, and then the Joints branch. You shoul d see two ge ar mat es and three revolute joint s listed, as sho wn in Figu re 6-9. In addition, you should see the revolu te join t symbols ap pear in the gra phics screen, similar to those o f Figu re 6-5. Exp and all joint s in the browser and identify the parts they connect. Take a look at the joint Revolute2 (connecting the input gear to the gear housing), where we will add a driver next. Note that you may see a different r evolute joint connecting the input gear to the gear housing. Make sure you pick the right one. Driving
Joint
From the browser, expand the Constraints node and then the Joints node. Right-click the Revolute2 node and c h o o s e Properties. In the Edit Mate-Defined Joint dialog box (Figure 6-10), under the Motion tab (default), choose Rotate Z fo r Motion On, choose Velocity fo r Motion Type, c h o o s e Constant fo r Function, and enter 360 degrees/sec for Angular Velocity (should appear as defaults). Click Apply to accept the definition. A motion driver symbol should appear at Revolute2, as shown in Figure 6-5. We are ready to run a simulation. We will use all default simulation parameters.
Running
Simulation
Click the Motion Model node, press the right mouse button and select Run Simulation. After a few seconds, you should see the gears start turning. The input gear rotates 360 degrees as expected since the default simulation duration is 7 second. Saving
and Reviewing
Results
We will gra ph the angul ar veloci ty of the out put gear. From the browser, expand the Parts branch and then the Moving Parts branch. Right-click the ghox_output-l node, and choose Plot > Angular Velocity > Z Component (Figure 6-11). The graph shoul d appea r and is similar to that of Figu re 6-12, wh ich sh ows that the output velocity is a constant of 72 degree s/sec. N ote that this mag nitu de is on e fifth of the input velocity since the gear ratio is 7:5 . Bo th the input (Pinion 7) and output gears (Gear 2) rotate in the same direction. COSMOSMotion gives good results. Save your model.
Exercises:
1.
The sam e gear train will be use d for this exercise. C reate a consta nt torq ue for the input gear (gboxinput.SLDPRT) about the Z-axis. Turn on friction for all three axles (Steel-Dry/Steel-Dry). Define and run a 2-second dynamic simulation for the gear train. (i)
Wha t is the mini mu m torq ue that is requ ired to rotate the input gear, and therefore , the entire gear train?
(ii)
If the tor que appl ied to the inpu t gear is 100 mm N, wha t is the output angu lar velocity of the gear train at the en d of the 2-s econd s imulati on? Verify the simula tion result usin g your own calculation.
(iii)
Create a grap h for the reaction mom en t bet wee n gears of the first gear pair {GearMatel) due to the 100 mm N torque. What is the reaction moment obtained from simulation?
7.1
Ove rvi ew of the Less on
In this lesson, we will learn cam and follower, or cam-follower. A cam-follower is a device for conver ting rotary motio n into linear moti on. The s implest form of a cam is a rotating dis c with a varia ble radius, so that its profile is not circular but oval or egg-shaped. When the disc rotates, its edge (or side face) pushes against a follower (or cam f ollower), w hic h may be a small whe el at the end of a lever or the end of the lev er or ro d itself. T he fol lowe r will thu s rise and fall at exactl y the s am e amo un t as the variatio n in radius. By profiling a cam approp riately, a desired cyclic pattern of straight-line motio n, in terms o f position, veloc ity, and accelerati on, can be prod uced . We will learn to create a motion model and simulate the contr ol of open ing an d closing of an inlet or exhausti ve valve, usually found in internal combustion engines, using cam-follower connections. In a design such as that of Figure 7-1, the drive for the camshaft is taken from the crankshaft through a timing chain, which keeps the cams synch roniz ed with the mov em en t of the piston s o that the valves are opened or closed at a precise instant. The mech anis m we will be work ing with consists of bushings, camshaft, pushrod, rocker, valve, valve guide and spring, as shown in Figure 7-1. The cam-follower connects the camshaft and the pushrod. When the cam on the camshaft pushes the pushrod up, the rocker rotates and pushes the valve on the other side downward. The spring surrounding the valve gets compressed, and opens up the inlet for air to flow into the combustion chamber. 7.2
The Ca m and Follow er Exa mpl e
Physical
Model
The camshaft an d the rocker will rotate abou t the axes of their respe ctive revol ute join ts conn ecting the m to their respe ctive bearin gs (define d as gr ound body). The cam shaft is driven by a mot or of constan t velocity of 600 rpm (or 10 rev/se c). The profile of the ca m consists of two c ircular arcs of 0.25 an d 0.5 in . radii, respectively, as shown in Figure 7-2. The lower arc is concentric with the shaft, and the center of the upper arc is 0.52 in. ab ove the center of the shaft. Wh en the camshaf t rotates, the c am mou nte d on the shaft pushes the pushrod up by up to 0.27 in. (that is, 0.52+0.25-0.5 = 0.27). As a result, the rocker will rotate and push the valve at the other end downward at a frequency of 10 times/sec. The valve will move again up to 0.27 in. downward since the pushrod and the valve are positioned at an equal distance from the rotation axis of the rocker. Wh en the camshaf t rotates wh ere the larg er circular arc (0.5 in. radius) of
the cam is in contact with the follower (in this example, the pushrod), the push rod has room to move downward. At this point, the rocker will rotate back since the spring is being uncompressed. As a result, the valve will move up, and therefore, close the inlet. The valve will be open for about 120 degree per cycle, based on the cam design shown in Figure 7-2. The unit system chosen for this example is IPS and all parts are ma de up of steel. SolidWorks
Parts
and Assembly
The cam- follow er system consists of seven parts, bushin g (two), valve guide, camshaft, pushrod, rocker, and valve, as shown in Figure 7-1. In addition, there are two assembly files, Lesson7.SLDASM Lesson7withresults.SLDASM that an d you may download from the publisher's web site. We will start with Lesson 7. SLDASM, in which the parts are adequately assembled. In this assembly the first bushing is anchored (ground) and the second busing and the valve guide are fully constrained. These three parts will be assigned as ground parts. The remaining four parts will be defined as movable parts in COSMOSMotion. Same as before, the assembly file contains a complete Lesson 7withresults. SLDASM simulation model with simulation results. You may want to open the ass embl y to see the mot ion anim ation of the mechanism. In the assembly where a motion model is completely defined, a mate has been suppressed to allow movement between components. You can also see how the parts move by right clicking in the graphics screen, c h o o s i n g Move Component, and dragging any movable parts; for example the camshaft to rotate with respect to the second bushing. The whole mechanism will move accordingly. There are eighteen assembly mates, including four coincident, three concentric, seven distance, two parallel, one tangent, and one cam-mate-tangent, as listed in the browser (see Figure 7-3). You may want to expand the Mates branch in the browser to review the list of ass emb ly mate s. M ov e the cursor over any of the mat es; you should see the entities selected for the assembly mate highlighted in the graphics screen. As mentioned earlier, the first bushing, bushing, shown in the browser is anchored to the assembly. The second bushing (bushing<2>) and the valve guide (valve guide) were fully assembled to The first three mates, bushing. Coincident 1, Distance 1, a nd Distance2, were employed to assemble bushing<2> to bushing. And the next three distance mates assemble the valve guide to bushing.
Note that the distance mates are essentially coincident mate with distance bet ween entities. The distance mates were created to properly position the second bushing with respect to the first bush ing. All three parts will be defined as the ground part in COSMOSMotion. The next two mates, Concentric 1 a nd Coincident!, assemble the rocker {rocker) to the first b u s h i n g (hushing), allowi ng a rotatio n degree of freedo m about the Z-axis, as sh own in Figu res 7-4a and b. COSMOSMotion will ma p a revolute joi nt betw een the rocke r and the first bushi ng. The next part assembled is the pushrod (pushrod). The pushrod was assembled to the rocker u s i n g Tangent/, Distance6, and Coincident3 mates, as shown in Figures 7-4c, d, and e, respectively. As a result, the pushrod is allowed to move vertically at a distance of 1.25 in. from the Right pla ne of the first b u s h i n g (Distanced), at the sa me time, mai ntain ing tang ency betw een the top of the cylindrical surface of the push rod and the soc ket surface of the rocker .
(c) Pushrod: Tang entl
(d) Pushrod: Distance6
(e) Pushrod: Coincident3
Figure 7-4 Asse mbly Mates Defined for the Mech anis m
The next part is the camshaft (cam_shaft). The camshaft was first assembled to the second b u s h i n g (bushing<2>), and then to the pushrod. Concentric2 aligns the camshaft and the second bushing. Coincident4 mat es the ce nter plane of the cam shaft to that of push rod, as show n in Figures 7-4f and g. As a result, the camshaft is allowed to rotate about the Z-axis. In addition, the CamMateTangentl defines a ca m and follower betwe en the cam surface of the camshaf t and the cylindri cal surface at the bot tom of the pushro d. No te that all su rroun ding surfaces on the ca m and follower mus t be selecte d for the cam- follow er joint. In this case, four surfaces are s elected for the cam (mounted on the camshaft) and one surface is included on the follower, as shown in Fig ure 74h. Note that the assembly should have overall one degree of freedom at this point. You may either rotate the camshaft, the rocker , or mov e the pus hro d vertically to see the relative motion of the ass embly. Use
Apparently, this result implies that there are redundant dofs created in the system. This is fine since COSMOSMotion filters out the redundant dofs. You may want to check the redundancy by choosing, from the pull down menu, COSMOSMotion > Show Simulation Panel, as discussed in Appendix A. You may want to revi ew App end ix A for mo re informa tion about defining join ts and calculating degrees of freedom. The fina l motio n model is s hown in Figur e 7-6, whe re the Z-rotation of the concent ric joint, Concentric2, between the camshaft and the second bushing is driven by a constant angular velocity of
3,600 degrees /sec; i.e., 600 rpm, a bout the Z-axis of the global coor dinate sys tem. In addition, a spring surrounding the valve will be created in order to provide a vertical force to push the rocker up, therefore, close the valve. The spring has a spring constant of 10 lbf/in and an unstretched length of 1.25 in. The spring is create d bet wee n the bottom face of the rocke r and top face of the valv e guide. Using COSMOSMotion
7.3
Start SolidWorks and
open
assembly
file Lesson 7. SLDASM.
From the browser, click the Motion button
if to enter COSMOSMotion. 1
Again, always check the units system. Make sure that IPS units system is chosen for this example. Defining
Bodies
From the browser, expand the Assembly Components branch. You should see Bushing-1, Bushing-2, cam_shaft-1, pushrod-1, rocker-7, valve guide-1, an d valve-1, 7-7. Also expand the Parts branch; you should see Moving Parts and Ground Parts Bushing-1, Bushing-2, a nd valve guide-1 to Ground Parts and the remaining four by using the drag-and-drop method.
seven entities listed, as shown in Figure listed. We will move parts to Moving Parts
From the browser, click Bushing-1. Press the Ctrl key and click Bushing-2 a nd valve guide-1. three parts should be selected. Drag and drop them to the Ground Parts n o d e .
Al l
Repeat the same to select the remaining four parts under the Assembly Component branch. Drag and drop them to the Moving Parts n o d e . Expand the Constraints branch, and then the Joints bran ch. Yo u should see that ten join ts are listed (see Figur e 7-5). All join t symbo ls s hould appear in the graphics sc reen, s imilar to that of Figu re 7-6. Ex pan d all joint s in the brows er and identify the parts the y connect. Tak e a look at the joi nt Coincident2 (connecting camshaft to Bushing-2), where we will add a driver next.
Driving
Joint
Right click the Concentric2 node and choose Properties (see Figure 7-8). In the Edit Mate-Defined Joint dialog box (Figure 7-9), under the Motion tab (default), choose Rotate Z for Motion On, choose Velocity fo r Motion Type, choose Constant fo r Function, and enter 3600 degrees/sec for Angular Velocity, as shown in Figure 7-9. Click Apply to accept the definition. Defining
Spring
From the browser, expand the Forces branch, right click the Spring node and choose Add Translational Spring (see Figure 7-10). In the Input Spring dialog box (Figure 7-11), the Select 1st Component field should be highlighted in red and ready for you to pick. Rotate the view and pick the bot tom face of the rocker (see Fig ure 7- 12), the Select 2nd Component field should now highlight in red, a nd rocker-1/DDMFace 19 should appear in the Select Point on 1st Component field, which indicates that the s pring will be conn ecte d to the center poin t of the face sele cted. In case you picked a wrong entity, simply select the entire text in the respective text field in the dialog box, and press the Delete key to delete the text. The text field will turn back to red and will be ready for you to pick another entity. Rotate the view back, and then pick the top face in the valve guide, as shown in Figure 7-12. Now, valve guide-1 a nd valve guide-l/DDMFace20 should appear in the Select 2nd Component field and Select Point on 2nd Component field, respectively. Also, a spring should appear in the graphi cs screen, c onnec ting the center points of the two faces. Enter the followings: Stiffness:
10
Length: 1.25 (Note that you have to deselect the Design b o x
to the right before entering this value) Force: 0 Coil Diameter: 0.75 Number of coils: 8 Wire Diameter: 0.1 Click Apply to accept the spring definition and close the Insert Spring dialog box. Defining
and
Running
Simulation
Click the Motion Model node, press the right mouse button and select Simulation Parameters. Enter 0.5 fo r simulation duration and 500 for the nu mb er of frames. Click the Motion Model node again, press the right mouse button and select Run Simulation. Y o u should see that the camshaft starts rotating, the pushrod is moving up and down, which drives the rocker,
and then the valve. The camshaft rotates 5 times in the 0.5-second simulation duration. We will graph the position, veloc ity, a nd acceleratio n of the valve next.
As shown in Figure 7-14, the flat portion on top indicates that the valve stays completely closed, which spans about 0.066 seconds, approximately 240 degrees of the camshaft rotation in a complete cycle. Therefore, the valve will open for about 0.034 seconds per cycle, roughly 120 degrees. Gra ph the 7- velocity and 7-ac celeratio n of the valve by choosi ng Plot > CM Velocity (and Acceleration) > Y Component. The gra phs of the velocity and accelerati on are sho wn in Figur es 7-15 16, respectively. As shown in Figure 7-15, there are two velocity spikes per cycle, representi ng that valve is pushed downward (negative velocity) for opening and is being pulled back (positive velocity) closing, respectively. The valve stays closed with zero velocity.
CM
and the for
Figure 7-16 reveals high accelerations when the valve is pushed and pulled. Note that suc h a high acceleration is due to high-speed rotation at the camshaft. This high acceleration could produce large inertial force on the valve , yieldin g high contact force betwe en the top of the valve and the socket surface in the rocker. We woul d like to che ck the reacti on force bet wee n the top of the valve an d the rocker. The
grap h of the reactio n force can be created by expand ing Constraints and Joints branches, right clicking Concentric2 (between the valve and the rocker), and choosing Plot > Reaction Force > Y Component. The reacti on force graph (Fig ure 7-17) s hows that the reactio n force bet wee n the top of the valve and the s ocket face of the rock er is abo ut 0.4 l b , which is insignificant. Note that this small reaction force can f
be attribut ed to the sm all mas s of the valv e. If you o pen the valve part and acqu ire its ma ss ( from pull down menu, choose Tools > Mass Properties), the ma ss of the val ve is 0.03 l b . Therefore, the inertia for the valve at the peak accelerations is about 0.03 \b x5,600 i n / s e c = 168 l b i n / s e c = 168/386 l b = 0.44 lbf, wh ic h is consis tent to pea ks fo und in Fi gur e 7-17. I f yo u are no t quit e sure ab out why this 386 is factored in for force calculation, please refer to Appendix B for mass and force un it conversions. Save your model. m
2
m
2
m
f
Exercises:
1.
Redes ign the cam by redu cing the small arc radius from 0.25 to 0.2 and reducing the center distance of the sm all arc from 0.52 to 0.40, as shown in Figure E7-1. Repeat the dynamic analysis and check reaction force between the valve and the rocker. Does this redesigned cam alter the reaction force?
2.
If we cha ng e the Parallel! mate between the Right plan e of the valv e an d the Right pla ne of the first bushing to a distance mate, will the mechanism move? What other changes must be made in order to create a valid and movable mechanism similar to that was presented in this lesson?
8.1
Ove rvi ew of the Les son
This is an application lesson. We will apply what we learned in previous lessons to a real-world application. This application involves designing a device that can be mounted on a wheelchai r to mimic soccer ball-kicking action while being operated by a child sitting on the wheelchair with limited mobility and hand strength. Such a device will provide more incentive and realistic experience for children with physical disabilities to participate in soccer games. This example was extracted from an undergraduate student design project that was carried out in conjunction with a local children hospital. This device was intended primarily to be used in the summer camp sponsored by the children hospital. The focus of this less on is slightly different from pr evio us ones . In stead of focusing on discuss ing how to use COSMOSMotion to create motion entities, we will focus on how to use COSMOSMotion to support design. In order to narrow down the design options to be more manageable, we w ill assume all major components are designed with dimensions determined. More specifically, we will use COSMOSMotion to help choos e a spring, as well as de term ine if the requir ed operating force is accepta ble. Since the users of this device are childr en with limite d physic al hand strength, the operating force must be minimized in order to make the device useful. The exa mple s we hav e discusse d in prev ious less ons are simpl e enoug h so that some of the simulation results can be verified by hand calculations (for example, using a spreadsheet). However, most of the real- world applic ations, includ ing the examp le of this lesson, are too complic ate to verify by han d calculations. When we are dealing with such applications, two principles are helpful in leading to successful simulations. First, the simulation model you created has to be physically meaningful a nd is as consistent to the physical conditions as possible. Second, very often you will have to make assumptions i n order to simplify the problems so that the simulations can be carried out. This is because that the simula tion mode ls mus t compl y with the ability of the softwar e you are using. In order to effectively use the simulations to support design, you will have to understand the physical problems very well; in the me an time, b e familiar with the capabiliti es an d limitations of the s oftware you are using. Since mo st of yo u will be often learning the softwa re as you are tacklin g sim ulation an d/or design problems, it is strongly recommended that you employ the principle of spiral development to incrementally build up your simulation model. In another word, you may want to start from a simplified model with simple scenarios by making adequate assumptions to your simulation model. Make the simplified model works first, then relax the assumptions and add motion entities to make your model closer to the real situation. Repeat the process until you reach a simulation model and simulation scenarios that answer you questions and help you make design decisions. In each step, make sure tha t the simulation model does what you expect it to do before bringing it to the next level. In this lesson, we will employ the spiral development principle. We will assume that all component s and their physical dimensions are determined. The design is essentially narrowed down to the selection of
a spring, including both spring constant and free length, and to ensure that the re quired force is small enough for a child to easily operate the device. We will try our best to check and hopefully verify the simulation model in each step. Note that COSMOSMotion is very sensitive to s ome of the condit ions a nd parameters, such as the initial condition (that is, the handle bar orientation), spring constant, etc. S ome of the conditions simulated are physically meaningful and yet COSMOSMotion gives unrealistic simulation results due to its limitations. Again, COSMOSMotion is not foolproof. One cannot blindly accept the simulation results. When a result is determined unrealistic after reviewing animation, graphs, etc., the best way to proceed is to compose a simpler simulation model and/or try a different (more idealized) scenario until the simulatio n result is physically meaningf ul based on you r educated jud gme nt. Yo u will see trialsand-errors in this lesson and many other real-world applications in the future. 8.2
The Assis tive Devi ce
Physical
Model
This assistive device for soccer gam es consists of five major comp onen ts: the clam per, handl e bar, plate, kicking-rod, and spring, as illustrated in Figure 8-1. In reality the se five components will be ass embl ed first and clam ped to the lowe r frame of the wheel chair for use.
The han dle bar is mo unt ed to the plate at the pivot pin of the plate a nd linked to the middle pi n of the kicking rod. The kicking rod is inserted into the two lower brackets mounted on the plate. When the hand le (on top of the handle bar) i s pulled backwa rd, the hand le bar rotates a bout the pivot pin; therefore, drives the kicking rod to move forward along the longitudinal direction through the link between the bot tom slot of the handl e bar and the middl e pin of the kickin g rod. T he for ward move me nt of the kicki ng rod produces momentum to "kick" the soccer ball. A spring is added between the upper brac ket and the handle bar to restore the handle bar to its neutral position after pulling. The spring also helps the user to pull the handle bar with a lesser force.
Th e focus of this l esson is to use COSMOSMotion to simulate the posi tion and velocity of the kicking rod for a given force that can be comfortably provided by a child with limited physic al strength. Lots o f factors contribut e to the operatin g force of the mech anis m. For exam ple, one of the critical para meter s is the locatio n of the pivo t pin. The lo wer the pivot pin is located the lesser force is requi red to operate the mechan ism. Howe ver , the purpos e of this lesson is not necessarily to determin e the final design of the d evice, b ut illustrate the proces s of usin g COSMOSMotion to assist the design. Therefore, as men tio ned earlier, the scope of the desi gn has been narr owe d down to the selection of the spri ng and to det ermi ne if the force is smal l eno ug h for a chil d to oper ate the devi ce. SolidWorks
Parts
and Assembly
The asse mbly of the mecha nis m consists of eight parts and one sub assemb ly. Thes e parts are handle.SLDPRT,
plate. SLDPRT,
collar. SLDPRT, rod.SLDPRT
In
an d
wheelchair.SLDPRT.
The
foot.SLDPRT,
subassembly
is
clamper. SLDPRT, kickingjrod.SLDASM which
joint.SLDPRT,
consists
of
m& foot.SLDPRT.
addition,
there
are
Lesson8TaskTwo.SLDASM, SLDASM,
rod.SLDPRT,
six
assembly
files,
Lesson8. SLDASM,
Lesson8TaskThreeNoFriction.SLDASM,
mdLesson8TaskThreeLargeFriction. SLDASM.
Yo u
can
Lesson8TaskOne.SLDASM,
Lesson8TaskThreeSmallFriction.
dow nlo ad these
files
from
pu bli sher 's
web site. Same as before, the assembly files, with the exception of Lesson8.SLDASM,
consist of compl ete simulati on models wit h
simulation results under respective simulation scenarios. You may want to open these files to see the motion animations of the mechanism. In these assembly files, a mate (Anglel) has been suppressed. You can also see how the parts move by right clicking
in
the
graphics
screen,
choosing Move
Component,
and dragging any movable parts; for example dragging the handle to drive the kicking rod. There
are
fifteen
assembly
mates,
including
four
coincident, three concentric, four distance, two parallel, and one angle, defined in the assembly, as listed in the browser (see Figure 8-2). You may want to expand the Mates branch in the browser to see these assembly mates. Move your cursor ove r any of the mat es ; you sho uld see the entities cho sen for the assembly mate highlighted in the graphics screen. The
first
nine
mates
assemble
the
clamper
to
the
wheelch air, the joi nt to the clamper and the wheelchair, a nd then the plate to the joint part. Note that the joint is a SolidWork part that connects the plate and the clamper rigidly.
These nine mates are pretty standard. All these parts are fully constrained and are fixed to the wheelchair. The next two mates, Concentric3 an d Distance4, assemble the handle bar to the plate at the pivot pin, allowing the handle bar to rotate at the pivot pin, as shown in Figure 8-3a. COSMOSMotion will conver t these mates to a revolu te join t. Th e distance mate provide s an adequate clea rance between the handle bar and the plate, as shown in Figure 8-3b.
The next three mates, CamMateTangentl, Coincident3, a n d Coincident4, assemble the kicking rod to the plate and the han dle bar. Firs t, the middl e pin of the kicki ng rod is ass emb led to the inner surface o f the bot tom slot of the hand le bar using CamMateTangentl, as shown in Figure 8-3c. As a result, the pin can only move within the slot, which is desirable. Second Coincident3 mat es the bot tom face of the kicki ng rod to the inner bot tom face of the firs t lower brac ket of the plate, as s how n in Figure 8-3d. Similarly Coincident4 ma te s the rear face of the kick ing ro d to the inner side fac e of the fi rst low er brack et of the plate, as sho wn in Figu re 8-3e. T hese tw o mate s restrict the kickin g rod to slide along the longitudin al directi on, whi ch will be conver ted to a translatio nal joi nt by COSMOSMotion. The final mate, Anglel, orients the vertical pl ane of the hand le bar {Right Plane) respect to that of the plate {Right Plane). This mate will help determine an initial condition for motion simulations. Note that the Anglel mate to orient the handle, it will has to be suppressed to allow the handle bar to rotate
Bas ed on the geo met ry of the mech ani sm and dimens ions of its constituent comp onen ts, the kicking rod is able to travel a total of 12.2 in. along the longitudinal direction (Z-direction). The kicking rod can m o v e 6.82 in. forward (positive Z-direction with respect tot the middle pin) until its middle pin becomes in contac t wit h the inne r face at the low er end of the slot, as s ho wn in Fi gur e 8-4a. Simil arly , the kic king rod moves 5.34 in. bac kwa rd until the side face of the handl e bar bec ome s in contac t with the front end face of the first low er bra cke t, as s how n in Fig ure 8-4 b. At the same time, the handle will travel a total of 18.6 in., 9.98 b a c k w a r d a n d 8.6 in. forward, as shown in Figures 8-4c and 8-4d, respectively. Note that these measurements shown in Figure 8-4 can be obtained by using the Measure option in SolidWorks. To access the Measure option, simply choose from the pull-down menu Tools > Measure. Simulation
Model
In this motion model, the only moving parts are the handle b ar and the kicking rod. After suppressing the mate Angle1, COSMOSMotion will ad d a revolu te joi nt to the mot ion mode l betwe en the handle bar and the plate at the pivot pin, as shown in Figure 8-5. The handle bar is allowed to rotate ab out the X-axis of the global coordi nate s ystem at the pivot pin. In addition, a translatio nal joi nt is crea ted by COSMOSMotion bet wee n the kick ing rod and the first lower bracket. This joi nt constrains the kick ing rod to translate alo ng the longitudina l direction; i.e., the Z-direction. The third and final joi nt is the CamMateTangent be tw ee n the oute r surface o f the mi ddl e pin and the inn er surfac e of the s lot at the bot tom of the hand le bar. This join t restricts the pin to mo ve in side the slot. In addition to joints, a spring is added between the upp er bracke t of the plate and the ho ok on the side of the handle bar. This spring, as shown in Figure 8-5, is added to restore the handle bar to a neutral position after pulling. Since the free spring length is set to a slightly larger value so that the handle bar will be oriented at a negative 5~/0-degree angle (about the X-axis). Therefore, the user will have to push the handle forward before pulling it back to kick the ball. A larger spring free length will p ush the ha ndle leaning further backward (toward the user), providing additional pulling force that helps the users to pull back the handle bar. Note that the pulling action will push the kicking rod forward (positive Z-direction) to "kick" the soccer ball. There is one contact constraint added to the motion model. The contact constraint is defined between the oute r side face of the han dle ba r and the f ront end face of the first lower bracket. This contact constraint will prevent the handle bar from moving further backward and penetrating through the brackets. In this contact constraint, a restitution coefficient of 0.5 is assumed. Finally, an impulse force of 5-65 l b in a time span of 1.0 second will be added to the handle bar along the Z-direction, as shown in Figure 8-5, to simulate the operating force. Note that the impulse force must first push the handle bar about 10 degrees forward before pulling it back, as illustrated in Figure 8-6. f
In this example, we will turn on the gravity, which is acting in the negative 7-direction (vertically dow nwa rd) ; i.e., the default setting. We will first ass ume no friction in any joint s. This ass umpt ion will greatly simplify the simulation model and help set up the motion model correctly. We will use this model to choos e a spring, including the selection of spring constant and free length. T he simul ation results of this non-friction model have been created in the assembly files Lesson8TaskOne.SLDASM and Lesson8TaskTwo. SLDASM. The friction force will be turned on for both the revolute and translational joints to determine the required force for operating the mechanism. In addition, the operating force, modeled as an impulse force will be added to the mechanism. Note that the friction is not added to the CamMateTangent joint between the middle pin and the slot since such a capability is not currently supported by COSMOSMotion. Results of these simula tions c an be found in Lesson8TaskThreeNoFriction.SLDASM, Lesson8TaskThreeSmallFriction.SLDASM, Lesson8TaskThreeLargeFriction.SLDASM. a nd 8. 3
U s i n g COSMOSMotion
In this example, we will start with a valid simulation model defined in the assembly Lesson8.SLDASM. The unit system is IPS. When you open this assembly file, you should see a properly assembled model with fifteen mates, as shown in Figure 8-2, where the last c onstraint, Angle1, should have been suppressed. Note that the mate angle is set to positive 10 degrees for the time being, and the handle bar is leaning forward (toward the Z-direction), as shown in Figure 8-7. Note that this angle is what we assume for Task One simulations. If yo u e nter COSMOSMotion and expand the Parts a n d Constraints branches in the browser, you should see the existing motion entities, as shown in Figure 8-8. There are four parts under the Ground Parts branc h. O nly handle bar and kick ing rod are mov abl e. I n addition, there are three join ts defined, CamMateTangentl, Revolute, a nd Translational, as discussed earlier. In the Contact branch under the Constraints, there is one contact joint, Contact 3D, defined to prevent the kicking rod from penetrating into the brackets. Due to the contact constraint and the restitution coefficient defined, the handle bar will bou nce ba ck wh en it hits the f ront edge of the first lower bracket.
There are three major tasks we will carry out in this design. In Task One we will run s imulation to chec k the function of the 3D contact constraint. We hope to ensure that all joint s are adeq uatel y defined, and the restitution coefficient we assumed in the contact constraint gives us reasonable results. In Task Two, we will add the spring. We will adjust the spring constant and its free length unti l we reach an equilibrium configuration that we can work with. Note that a desired free length should bring the handle bar backward a negative 5-10 degree angle ( ab ou t the X-axis) . After the spring is deter mined, we will add an operating force at the handle in Task Three. Note that the force will first push the handle bar forward about 10 degrees (positive, about the X-axis) before pulling it backward in order to provide enough travel distance for the kicking rod, and hopefully, sufficient momentum to kick the ball. In Task Three, we will start with a non-friction case, and then turn on friction in both the revolute and translational join ts. Fr om the friction cases, we will det ermi ne if the ope ratin g force is sufficient to push the handle forward about 10 degree s before pulling it back ward . We will vary the fricti on coefficients to simula te different scenario s and then dete rmin e the mag nit ude of the opera ting forces accor dingly. The magni tude o f the force will answer the critical question: if the design is accep table. We hope to keep the maximum force magnitude under 20 lbf. Task
One:
Determining
Contact
Constraints
We will carry out simulations for the motion model defined in Lesson8.SLDASM. In the assembly, the handle is leaning forward 10 degrees (see Figure 8-7), the contact joint Contact 3D is defined, and the gravity is turned on. You may want to open the Contact3D constraint by right clicking Contact3D from the browser and choosing Properties. In the Edit 3D Contact dialog box, you should see that the plate and hand le are included in the first and second containers, res pectively , as s how n in Figu re 8-9. If you choo se the Contact tab, you should see that the Coefficient of Restitution is 0.5, as shown in Figure 8-10. Note that no friction is imposed for this constraint. Close the dialog box by clicking the Apply button.
Also, we would like to make sure that the gravity is set up properly. From the browser, right click th e Motion Model node and select System Defaults. In the Options dialog box (Figure 8-11), you should see the acceleration is 386.22 i n / s e c , and the Direction is set to -1 fo r Y. Click OK to accept the gravity 2
setting.
Click the Motion Model node from the browser, press the right mouse button and select Simulation Parameters. Enter 2 for simulation duration and the 200 for the number of frames, as shown in Figure 8-
12. Make sure the Use Precise Geometry for 3 D Contacts is selected in order for detect contact during simulation.
COSMOSMotion to
Click the Motion Model node again, press the right mouse button and select Run Simulation. Y o u should see that the handle bar start moving forward and the kicking rod moving backward due to gr avity. When the handle bar and the first lower bracket is in contact, the handle bar bounces back slightly due to the contact constraint we defined. Next, w e will graph the position and velocity of the kickin g rod a lo ng the Z-direction. From the browser, expand the Parts node and then the Moving Parts node. Right click kickingjrod7, and choose Plot > CM Position > Z, and Plot > CM Velocity > Z Component. Tw o graph s like those of Figur es 8-13 and 8-14 sho uld appear. Not e that the vertical sc ales of the graph s have been adjusted for clarity. Th e position graph s hows that the mas s center of the kickin g rod was located at Z = 21.6 in. initially. The mass center moves to the right to Z = 17.8 in., where the handle bar is in contact with the first lower bracket. The handle bar, therefore the kicking rod, bounces back , and the ce nter mass of the kickin g rod reaches to Z = 18.6 in. before it slides to the right again due to gravity. After about 1.5 seconds, the kicking rod rests and stays in contact with the bracket. The velocit y graph (Figu re 8-14) shows that the bounc ing velocity is half of the inc omin g velocity in the opposite direction. This is certainly due to the 0.5 restitution coefficient defined at the contact constraint. From these two graphs, we conclude that the motion model has been defined correctly. Save your model. You may want to save the model under different name and use it for Task Two simulations.
Task
Two:
Adding
Spring
In Task Two, we will add a spring to the mechanism. We will adjust the spring constant and its f ree length until we reach an equilibrium configuration that we can work with. Note that the free length we specify will have to bring the handle bar backward about 5-10 degrees (that is, negative 5-10 degrees about the X-axis).
Delete the simulation result. From the browser, right click the Spring node and choose Add Translational Spring, the Insert Spring dialog box will a ppear (F igure 8-15). Pic k the cent er hole of the upper bra cket and the hoo k of the handle bar, as shown in Figure 8-16. Enter the followings: Stiffness: Length: Force:
30 5 0
Coil Diameter: Number
of coils:
Wire Diameter:
1 10 0.25
Note that the actual distance between the hole and the hook under the current configuration is about 4.34 in., which can be obtained by clicking the Design bo x to the righ t of the Length field. The number we enter, 5, is larger than the actual distance. Agai n, the purpos e of entering a larger free spr ing length is to make the handle bar lean backward at equilibrium. Click the Apply button to accept the spring. In the current configuration, the spring is compressed since the handle is leaning 10 degrees forward. Run a simulation. You should see that the handle bar start moving backward and the kicking rod moving forward due to the stre tchin g of the spr ing. Wh en the simulatio n is comple ted, the position and velocit y graphs of the kicking rod will appear, similar to Figures 8-17 and 8-18. Both the position and velocity graphs reveal a sinus oidal type curve. This is due to the fact that no friction has been applied to the joints. Also, the handle bar is not colliding with the brack et. The gr aphs sho w that the perio d of one vibration is jus t unde r 0.5 seconds.
No w we will add a graph to sh ow the rotation angle of the handle bar . Del ete the simul ation result. From the browser, right click the handle-1 and choose Plot > Bryant Angles > Angle 7; i.e., about the Xaxis. Rerun the simulation, the angle graph should appear, similar to Figure 8-19. The grap h shows that the handle bar is oscillating between 10 a nd -9 degree s. T he angle of the handle ba r at equilibr ium (assuming friction is added to dissipate energy) will be roughly the average of 10 and -9; i.e., less than 1 degree, which is far less than the desired angle (negative 5-10 degrees). Delete the simulation result, change the free length to 5.5 in., and rerun the simulation. The angle graph shown in Figure 8-20 indicates that the handle bar oscillates between 10 and -25 degrees, and the mean angle is about -7 degrees, which is desired.
No te that a softer spring will inc rea se the oscillati on angle. If the spr ing cons tant is too sm all, sa y 2 lbf/in, the handle bar ma y reach a dead lock positio n with the middle pin of the kicki ng rod, similar to wh at wa s sho wn in Fig ure 8-4a, wh ic h is not desi rab le. O n the othe r han d, if the sp ring is too stiff, the
force required to push the handle bar forward may be excessive. Currently, the spring constant is set t o 30 lbf/in. This parameter will be revisited later in Task Three. Save you model before moving to Task Thre e. Task
Three:
Determining
the
Operating
Force
In Task Three, we will determine the operating force. The force must be small enough to allow children with limited physical strength to operate the mechanism. We will add a force at the handle, and use simulation results to determine the required operating force. The force to be determined is supposed to push the handle forward about 10 degrees, as shown in Figure 8-6, and then pull it backward to push out the kicking rod. Then, we will turn on friction at both translational and revolute joints, and determine the operating force again. We will adjust the friction coefficient (assuming different physical conditions) in order to determine a rang e of the oper ating force. In the simulat ion, we will start with a configuration where the handle bar is set to -7 degrees; i.e., in its neutral position, as determined in Task Two. Save the model under a different name, say Task3. Delete the simulation result, and go back to SolidWorks a s s e m b l y m o d e by clicking clicking the the Assembly buttons % on er. Assembly buttons on top top of o f the the brows bro wser. e
First unsuppress the mate AngleL Anglel. Then, right click the Anglel mate and choose Edit Feature. In the Anglel w i n d o w (Figure 8-21), change the angle to 7, click the Flip direction button (to deselect it), and click the checkmark button on top to accept the definition. The handle bar should rotate to a 7-degree position backward in the graphics screen, as shown in Figure 822. This is the initial configuration for Task Three simulations. Next we will create a force at the handle. The force can be added from the browser by expanding the Forces branch, right clicking the Action Only node, and choosing Add Action-Only Force. In the Insert Action-Only Force dialog box, the Select Component to which Force is Applied field (see Figure 8-23) is active (highlighted in red) and ready for you to pick the entities. Rota te the mo del and pick the face of the handle, as shown in Figure 8-24. The part handle-1 Select is now listed in the Component to which Force is Applied field, a n d handle- 1/DDMFace 10 is listed in both the Select Location and the Select Direction fields.
Figure 8-21
Now the Select Reference Component to orient Force field is active for selection. We will click the grou nd button to the right 01 the hel d. Alte r that, yo u should see Assem5 (representing the ground) appear in the text field. A force symbol will appear in the graphics screen pointing downwar d, which is not what we want. We will have to change the force direction. Now the Select Reference Component to orient Force field is active for selection. We will click the gro und but ton •
to the righ t of the field. After that, yo u should see Assem5 (representing the ground)
appear in the text field. A force symbol will appear in the graphics screen pointing downwar d, which is not what we want. We will have to change the force direction. Select all the text in the Select Direction field (press the let mouse button and drag to select all text), and press the Delete ke y to delet e the cur ren t selection . Pi ck the en d face of the foot, as s ho wn in Fig ure 8-24, to orient the force along the negati ve Z-direction. The ar row of the force sy mbol should now point to the negative Z-direction, which is normal to the face we picked.
Click the graph button (right most, as circled in Figure 8-25), the function graph will appear like the one in Figure 8-26. Note that internally will create a smooth spline COSMOSMotion function using the data entered. Close the graph and accept the force definition.
click Apply button
to
Run a simulation. The result graphs will appear at the end of the 2- seco nd simulat ion. The angle graph (Figure 8-27) shows that the handle bar starts at an orientation angle of -7 degrees as expected, and swing forward to a 13degree angle, which is desirable, due to the forward force. The handle then moves backward to about 26 degrees, and then oscillates.
The positi on graph in Figure 8-28 sho ws that the mas s center of the kickin g rod starts at about 24 in . It then travels to about 21.2 (backward) and then to about 26.8 in. forward due to the pulling force and stretch of the s pring. The over all distan ce that the kicki ng rod travels is about 5.6 in., which seems to be sufficient to produce enough momentum to kick the ball. Figur e 8-29 sh ows that the velocit y of the kickin g rod reac hes a bout 27 in/sec pus hed near the foremos t position. This velocity will pro duc e a mo me nt um of about seconds, as shown in Figure 8-30. To create a momentum graph you may simply right from the browser and choose Plot > Translational Momentum > Z Component. Note that mo me nt um are proportion al, with the mas s of the kicking rod as the scaling factor.
when the rod is 310 lbf-sec at 0.5 clic k kicking_rod-l the velocity and
The maximum force required to operate the device is determined to be 5 l b (maximum force value entered ), as sumi ng no friction at any join ts. Eve n thou gh the force data we entere d show a polyli ne in Figure 8-26, the actual force employed for simulation in COSMOSMotion is a spline curve generated f
Save you model. We will turn on friction and continue determining the required operating force. We will turn on friction at both the revolute and the translational joints. Friction for the CamMateTangent joi nt is curr ently unava ilabl e in COSMOSMotion. Delete the simulation result from the browser. Expand the Constraints and then the Joints branch. Right click Revolute and choose Properties. In the Edit Mate-Defined Joint dialog box (Figure 8-33), choose the Friction tab, click the Use Friction, and choose Aluminum Greasy for both Material 1 a nd Material 2. The Coefficient (mu) will show 0.03. Enter Joint dimensions, Radius: 0.26 and Length: 0.31. Click Apply butto n to accep t the definition. Not e that the di mens ions entere d are the diam eter of the pivot pin and the thickness of the hand le bar where the join t is located.
Sim ilar ly, turn on the friction for the trans lati onal joi nt. Ente r 7.25, 7, a nd 7, for Length, Width, an d Height, respec tively, as show n in Figur e 8-34. Not e that the length dim ensi on entered is the sum of both the lower brackets; i.e., 7 and 0.25 in. for the first and second lower brackets, respectively. The width and hei ght of the inner squ are of the brac ket s is 7 an d 7 in., res pect ivel y. Ru n a simulati on and chec k the ang le of the hand le bar. Even though the friction coefficient is small (ju = 0.03) for both join ts, the handl e bar hardl y move s. Therefore, the force magnitude must be increased. We will follow in general the overall force pattern, and increase the force magnitude to push the handle bar forward. Delete the simulation result. Expand the Forces and then the Action Only nod es from the brows er. Right click the ForceAO node and choose Properties. In the Edit Action-Only Force dialog box, choose the Function tab (see Figure 8-25), and enter the followings:
Click the graph button, the function will appear like the one in Figure 8-35. The maximum fo rce is n o w 12 lbf. No te that the first hal f of the for ce (neg ativ e part) is i ncr eas ed mo re tha n twi ce, and the positi ve portion remain s the sam e. T he positive part of the force is kept the same since the spring will contrib ute partially to the pulling force. The over all force pattern is simi lar to that of Figur e 8-26. T he force data enter ed are results of a few trials-and-er rors.
The momentum graph (Figure 8-37) shows that when the rod is pushed near the foremos t position the mom en tu m of the kicking rod is about 230 l b sec, which is less than the previous non-friction case. After reviewing the graphs, the 72-lb force seems to be acceptable. However, this small operating force, 12 lbf, is du e to a ve ry smal l frictio n for ce; i.e., f riction coef fici ent jU = 0.03. This result also indicates that the spring constant 30 lbf/in seems to be adequate. Next, we will increase the friction coefficient by changing the material from Aluminum Greasy to Aluminum Dry. r
f
Delete the simulation result. Expand the Constraints and then the Joints branch. Right click Revolute and choose Properties. In the Edit Mate-Defined Joint dialog box, choose the Friction tab, and choose Aluminum Dry for both Material 1 an d Material 2. T h e Coefficient (mu) will show 0.20. Repeat the same for the translation al joint. Run a simulat ion. T he handle bar is hardly move d. That is, the force will hav e to be increased again. Delete the simulation results. Right click the ForceAO node to enter the force data. Note that after several attempts, a force that is large enough to move the handle bar, therefore the kicking rod, is about 65 lbf. More specifically, the force data entered are:
Click the graph button, the function will appear like the one in Figure 8-38. Even though the maximum pushing force is now 65 l b . the pullin g force (positive portio n) rem ains the same, A r e : running a simulation, the angle and momentum graphs appear as in Figures 8-39 and 8-40, respectively Both seem to be reasonable. However, the large operating force, 65 lb , raises a flag. The mechanism requires too large a force for a child to operate. f
f
Note that the simulation engine, ADAMS/Solver, is very sensitive to the force data entered. You may encou nter pro blem s whil e carrying out some of the simula tions in Tas k Thre e. Wh en this happ ens, simply change the maximum force data, e.g., 65, to a slightly different value, e.g., 63, until a simulation can be completed. Save your model.
8.4
Resul t Discu ssio n
Apparently, the biggest concern raised in the simulations is the large operating force. The friction coefficient ju = 0.20, provided by COSMOSMotion fo r Aluminum-Aluminum contact without lubrication, seems to be physically reasonable. Although this friction coefficient represents an extreme cas e since in reality some lubricant would be added to the joints to reduce friction resistance. Nevertheless, the for ce is still too large. As revealed in simulations; i.e., Task Three, the maximum operating force increases fro m 5 lbf for non-friction, 12 lbf for sma ll friction (ju = 0.03) to 65 lbf for large friction (ju = 0.20). Reducing the frict ion force at join ts, especially the translation al joi nt betwe en the kicking rod and the two lower bracke ts on the plate, is critical for a successful device. Y ou can easily confirm that the translationa l joi nt contributes significantly to the friction encountered in the mechanism by conducting separate sim ulations whe re fr iction is on ly present in one of the two join ts. The flag raised by the simulation has been observed in the physical device, as shown in Figure 8-41, built by students following the design created in SolidWorks an d COSMOSMotion. The physical device confirms that the contact between the kicking rod and the two brackets produces a larg e friction force, resulting in a large operating force to operate the device. For children with limited physical strength, such a device is unattractive. In order to reduce the friction, four bearings are added to the device, as shown in Figure 8- 42. Two are adde d to the top surf ace of the kicking rod, a nd two a re underne ath the kicking rod. Wi th the beari ngs, the friction is significantly reduced. Therefore, a smaller force is required to operate the device. The actual operating force is less than 20 lbf.
8.5
Com men ts on COSMOSMotion Capabilities and Limitations
U s i n g COSMOSMotion does answer critical questions and help the design process, as demonstrated in this examp le. Ho wev er, from thi s examp le, a num ber of limitations in COSMOSMotion have also been encountered. Knowing these limitations will help you use COSMOSMotion more effectively. First, the simulation engine, ADAMS/Solver, whi ch solves the eq uations of mot ion for the mechanism, is not stable. Sometimes when you rerun the same simulation, you could see slightly differ ent results. This problem is more vivid when we ran the same simulation using different computers.
Moreover, the simulation engine produced results, such as the velocity or momentum (see Figures 8-37 and 8-40), with spikes, wh ich is not quite realistic. S ome of the spikes dis appea r or bec ome sm aller wh en we rerun the same simulation. Second, friction is not supported for a CamMateTangent joint. Therefore, an attempt was made to add a 3D contact joi nt betw een the m idd le pin and the slot of the hand le bar. A numb er of restitution coefficients were used, including 0.5, 0.75, etc. Yet, a dding a 3D contact joi nt significantly slow do wn the moti on of the handl e bar and the kickin g rod since lots of contact are en coun tere d bet wee n the outer surface of the midd le pin and the inner surface of the slot when the mec han ism is in motio n. M or e contact causes more energy dissipation. However, the slow-down is way too much to grant a physically reasonable simulation. In addition, more spikes appear in graphs, such as in velocity. However, the biggest issue with adding the 3D contact is that the simulation engine becomes extremely sensitive to the initial orientation angle of the handl e bar and the magn itu de of the oper ating force. For so me s imulatio ns, the solution engine encountered problems, for example, force imbalance at certain time steps during the simulation, and terminated the simulation prematurely. Overall COSMOSMotion is an excel lent too l wit h lots of nic e feature s and capabil ities for sup por t of mechanism design and analysis. However, as mentioned in this book numerous t imes, no software is foolproof. Before creating a simulation model, you always want to formulate your design questions and set up your simulation model and scenarios gearing toward answering these specific questions. You will have to ex am the simu lation results ver y carefully and challeng e yoursel f about the validity of the results since if yo u don' t som ebo dy else will do, usually in a less friendly way .
APPENDIX A: DEFINING JOINTS Degrees of Fre edom
Understanding degrees of freedom is critical in creating successful motion model. The free degrees of fre edom of the mec han is m repr esent the num ber of indep ende nt para mete rs req uired to specify the position, velocity , and acceler ation of each rigid bod y in the sys tem for any given time. A comple tely uncon stra ined body in space has six degrees of freedom , three translational and three rotational. I f you add a join t; e.g., a revolu te join t to the body , you restrict its mo ve me nt to rotation about an axis, and the free d egree s of freed om of the body are red uce d from six to one. For a given mot ion mode l, you can determ ine its numb er of degree s of freedo m using the Gru eble r's count. The mech anis m's Grue bler count is calculat ed usin g the mec hani sm' s total num ber of bodie s. As mentioned above, each movable body introduces six degrees of freedom. Joints added to the mechanism constrain the system, or remove dofs. Motion inputs, i.e., motion drivers, remove additional dof s. COSMOSMotion uses the following equation to calculate the Gruebler's count:
(A.1) w h e r e D is the Grueble r count repr esent ing the total free degree s of f reedom of the mech ani sm, M is the num ber of bodie s excl uding the gr ound body, TV is the numb er of d o f s restricted by all joint s, a nd O is the num ber of the moti on inputs in the system. For kinematic analysis, the Gruebler's count must be equal to or less t han 0. T h e ADAMS/Solver recognizes and deactivates redundant constraints during motion simulation. For a kinematic analysis, if you create a model with a Gruebler's count greater than 0 and try to simulate it, the simulation will not run and an error message will appear. If the Gru eble r's cou nt is less than zero , the solver will automati cally remo ve redund anci es, if possible. For example, you may apply this formula to a door model that is supported by two hinges mode led as revolute joints. Since a revolute joint removes five d of s, the Gru ebler' s count becom es:
The calculated degrees of freedom result is -4, which include five redundant dofs. Redundancy
Redu ndan cies are excess ive do f s . Wh en a join t constra ins the mod el in exactly the same wa y as anothe r joi nt (like the door exam ple) , the mod el contains excess ive do f s , also kn ow n as redu ndan cies . A j o in t b e c o m e s excessive w h e n it does n o t introduce a ny fu rt he r restr ic ti on on a bo dy' s m ot io n. It is important that you eliminate redundancies from your motion model while carrying out dyna mic analys es. If you do not rem ove redu ndan cies , you ma y not get accurat e values whe n you chec k join t reactions or load reactions. For exam ple, if you mod el a door using two revolut e join ts for the hinges , the se cond revolute join t does not contribute to constraining the door's motion. COSMOSMotion detects the redundancies and ignores one of the resolute join ts in its analysis . T he out com e may be incorre ct in react ion results, yet the
motion is correct. For complete and accurate reaction forces, it is critical that you eliminate re dundancies from your mechanism. For a kinematic simulation where you are interested in displacement, velocity, and acceleration, redu ndanc ies in you r mod el do not alter the perfo rman ce of the mecha nis m. You can eliminate or reduce the redundancies in your model by carefully choosing joints. These joints must be able to restrict the same dofs, but not duplicate each other, introducing redundancies. After you decide which joints you want to use, you can use the Gruebler's count to calculate the dofs and check redundancies. You may also ask COSMOSMotion to calculate the Gruebler's count for you. You can simply click the Show simulation control butt on
on top of the graphics screen to
bring up the dialog box, as shown in Figure A1. Note that the DOF field in the dialog box will sho w the Gru eble r's c ount if a simulation has bee n complet ed. If not, Yo u ma y click the Calculate button to ask COSMOSMotion to calculate the actual dof. In the message window appearing next (Figure A-2), COSMOSMotion identifies redundant dofs and recalculates the dof for the simulation model.
Before yo u select a joi nt to add to your mode l, yo u shoul d kn ow what mov em en t yo u wan t to restrain for the body and what movement you want to allow. The following table describes the co mmonly empl oyed joint types in COSMOSMotion and the degrees of freedom they remove.
The fo llowing provid es mor e details abou t the join ts listed in the table above . Revolute
Joint
A revolute join t, as d epicte d in Figure A- 3, allows the rotat ion of one rigid body with respect to anothe r rigid body about a comm on axis. The origin of the revolut e joi nt can be located anyw her e along the axis abo ut whi ch the bodie s can rotate with respect to each other. Th e joi nt origin is assigned by from SolidWorks. COSMOSMotion when you enter COSMOSMotion Orient ation of the revol ute join t defines the dire ction of the axis about whi ch the bodie s can rotate with respe ct to each other. The rotat ional axis of the revolu te joi nt is parallel to the orientation vector and passes through the origin.
Translational
Joint
A translational join t allows on e rigid bo dy to translate alon g a vecto r with respect to a second rigid body, as illustrated in Figure A-4. The rigid bodies may only translate, not rotate, w ith respect to each other. Th e locat ion of the or igin of a tra nsla tion al jo in t wit h res pec t to its rigid bodie s doe s not affect the mot ion o f the joi nt but does affect the reaction l oads o n the joint. The location o f the joi nt origin deter mine s where the join t symbol is located. The or ientation of the translati onal join t determ ines the direction of the axis along whi ch the bodies can slide with respe ct to each other (axis o f transla tion). The d irection of the mo tion of the translati onal j o i n t is pa ral lel to the or ie nt at io n v ec tor a nd pass es t h r o ug h t he or ig in . Cylindrical
Joint
A cylindrical join t allows bot h relative rotation and relative transla tion of one bod y with respect to anothe r body , as s how n in Figur e A-5 . Th e origin of the cylindrical joi nt can be located anyw her e along the axis about which the bodies rotate or slide with respect to each other. Orient ation of the cylindr ical joi nt defines the direc tion of the axis ab out which the bodie s rotate or slide along with resp ect to each other. T he rotational/t ranslation al axis of the cylindri cal join t is parallel to the orientation vector and passes through the origin.
Spherical
Joint
A spherical joi nt allows fre e rotatio n about a comm on point of one body with respec t to anoth er body, as depi cted in Figu re A-6 . Th e origin location of the spher ical joi nt determ ines the point about which the bodies pivot freely with respect to each other.
A universal join t allows the ro tation of one bo dy to be transferred to the rotation of another body , as shown in Figure A-7. This joint is particularly useful to transfer rotational motion around corners, or to transfer rotational motion between two connected shafts that are permitted to bend at the connection point (such as the drive shaft on an automobile). The or igin location of the univers al joi nt represents th e conne ction point of the two bodies . The tw o shaft axes identify the center lines of the two bod ies c onnec ted by the unive rsal joint. Not e that COSMOSMotion uses rotational axes parallel to the rotational axes you identify but passing throu gh the origin of the univ ersal joint.
A screw joi nt rem ove s one degre e of freedom. I t constrains on e body to rotate as it translat es with respect to another body, as shown in Figure A-8. Wh en defining a scr ew joint, y ou can define the pitch. The pitch is the a mou nt of translat ional displ acem ent of the two bodi es for each full rotation of the first bo dy. The d ispl acem ent of the first bo dy
relative to the seco nd body is a function of the bod y' s rotation abou t the axis of rotation. For eve ry full rotation, the d ispla ceme nt of the first bod y along the translation axis with resp ect to the se cond body is equal to the va lue of the pitch. Ver y often, the s crew join t is use d with a cylindrical joint. The cylin drical joi nt remov es two translat ional and two rotationa l degrees of freedom. The s crew join t rem ove s one more degr ee of free dom by constraining the translational motion to be proportional to the rotational motion. Planar
Joint
A planar joi nt allows a plane on one bod y to slide and rotate in the plane of anothe r body, as show n in Figure A-9. Th e orientation vector of the planar joi nt is perpend icula r to the joi nt' s plane of moti on. T he rotationa l axis of the planar joint, w hic h is norm al to the joi nt' s plane o f moti on, is paral lel to the orientation vector.
Figur e A-9 Plan ar Joint Sym bol Fixed
Figur e A-1 0 Fixe d Joint Sym bol
Joint
A fixed join t locks two bodies toget her so they cannot mov e with respect to each other. T he fixed j o i nt sy m b ol is s h o w n in F i gur e A - 10 .
Mapped
SolidWorks
Mates
After you bring an assembly from SolidWorks to COSMOSMotion and assign components to ground part and moving parts, COSMOSMotion automatically maps assembly mate s to joints. In most cases, these join ts wor k well for the mot ion sim ulation. A select ed set of the map pe d SolidWorks mates, which is commonly employed in assembly, is given in the next table for your reference.
Therefore, from Eqs. B.2 and B.3, we have 7 lb = 386 l b f
i n / s e c , and the force in l b 2
m
i n / s e c unit 2
m
is 386 ti mes smaller than that of l b that we are more used to. When you apply a 7 lb force to the same f
f
mass block, it will accelerate 386 i n / s e c , as shown in Figure B-lb. 2
On the other hand, we hav e the mas s unit, 7 l b
1/386 l b s e c / in . I t m e a n s that a 1 l b 2
m
f
m
mass block
is 386 tim es sm aller than that of a 7 l b s e c / i n bloc k. Therefore, a 1 l b s e c / i n bl o c k wil l w e i g h 386 l b 2
f
2
f
on earth. When applying a 1 lbf force to the mas s block, it will accele rate at a 7 in/ se c rate, as illustrated 2
in Figure B-lc.
f
APPENDIX C:
IMPORTING Pro/ENGINEER PARTS AND ASSEMBLIES
From time to time when you use COSMOSMotion for simulations, you may encounter the need for importing solid models from other CAD software, such as Pro/ENGINEER. SolidWorks provides an excellent capability that support importing solid models from a broad range of software and formats, including Parasolid, ACIS, IGES (Initial Graphics Exchange Standards), STEP (STandard f or Exchange of Pro duct data), SolidEdge, Pro/ENGINEER, etc. F or a compl ete list of suppor ted software and formats in SolidWorks, please refer to Figure C-1. You may access this list by choosing File > Open from the pull -do wn men u, a nd pull down the Files of type in the File Open dialog box. In this appendix, we will focus on Pro/ENGINEER importing parts and assemblies. Hopefully, methods and principles you learn from this appendix will be applicable to importing solid models from other software and formats. provides capabilities for importing both part and assembly. Users can choose two options in importing solid model. They are Option 1: importing solid features and Option 2: impor ting jus t geom etry. Im porti ng solid features may bring you a parametric solid model th at jus t like a SolidWorks part that you will be able to modify. On the other hand, if you cho ose to impor t geometry only, you will end up with an imported feature that you cannot change since all solid features are lumped into a single imported geometry without any solid features nor dimensions. SolidWorks
Importing geometry is relatively straightforward. In general, SolidWorks does a goo d jo b in bringing in Pro/ENGINEER part as a single impo rted geomet ry. In fact, several other translator s, such as IGES and STEP, support such geometric translations well. IGES and STEP are especially useful when there is no direct translation from one CAD to another. Importing solid models with solid features is a lot more challenging, in which solid features embedded in the part geometry, such as holes, chamfers, etc., must be identified first. In addition, sketches that were employed for generating the solid features must be recovered and the feature types, for instance revol ve, extr ude, s weep, etc., mus t be identified. With virtually infinite nu mb er of possibilities in creating solid features, it is almost certain that you will encounter problems while importing solid models with feature conversio n. Ther efore, if you do not anticipate mak ing desi gn changes in SolidWorks. it is highly recommend that you import parts as a single geometric feature. We will discuss the approache s of impor ting parts, and then impor ting assem blies. In each case, e will try both options; i.e., importing solid features vs. importing geometry. We will use the gear train example employed in Lesson 6 as the test case and as an example for illustrations.
sketches in the graphics screen by clicking their names listed in the browser. In addition, the back plate (Extrudel in the browser) is recognized incorrectly. Certainly, SolidWorks is capab le of impor ting s ome parts correctly and completely, especially, when the solid features are relatively simple (but not this gear housing part). If yo u take a clo ser lo ok at any of the successful solid features, for example ExtrudeS, you will see that the sketches (for example Sketch3 of ExtrudeS) of the solid features do not have complete dimensions. Usually a (—) symbol is plac ed in front of the sketch, i ndicating that the sketch is not fully defined. Apparently, this translation is not satisfactory. Unfortunately, this translation represents a typical scenario you will encou nter for the majority of the parts. In many cases, it may take only a small effort to repair or re-create wrong or unrecognized solid features. However, when you translate an assembly with many parts, the effort could be substantial. Option
2:
Importing
Geometry
Imp ortin g geome try is mor e straig htforward and has a high er successful rate than that of impo rting solid features. Repeat the same steps to open the gear housing part, gboxjiousingprt. In the Pro/ENGINEER to SolidWorks Converter dialog box (Figure C-8), choose Import geometry directly (default), and then Kniting (default) in order to im port solid mode ls instead of jus t surface mod els . No te that if you c hoose BREP (Boundary Representation), only boundary surfaces will be imported. Click OK.
The conversion process will start. After about a minute or two, the converted model will appear in the graphics screen, as shown in Figure C-9. In addition, an entity Importedl will appear in the browser (Figure C-9). As mentioned earlier, there will be no parametric solid feature with dimensions and sketch conve rted if yo u choose Option 2. However, the geometry converted seems to be accurate. All the geometric features in Pro/ENGINEER shown in Figure C-3 were included in this imported feature. This translation is successful. Since we do not anticipate making any change to the gear housing, this i mported part is satisfactory. The gear housing part, gbox housing, sldprt, employed in Lesson 6 was created by u s i n g Option 2.
We will import the input gear assembly (gbox_input.asm) shown in Figure C-10 using both options. We will try Option 1 first; i.e.. importing solid features. As shown in Figure C-10 {Pro/ENGINEER Model Tree window), there are 11 parts (and several datum features) in this assembly. SolidWorks will try to imp ort this asse mbl y as well as the 11 p arts from Pro/ENGINEER.
Impo rtin g geomet ry is also more s traightfo rward for assemb ly and has a high er rate of succes s. Repeat the same steps to open the input gear assembly, gbox input.asm. In the Pro/ENGINEER to SolidWorks Converter dialo g box (Figur e C-l 3), choos e Use body import for all parts (default), and then Kniting (default) in order to import solid mod els . Cho ose Overwrite fo r If same name SolidWorks fil e is and choose Import material properties a nd Import sketch/curve entities. Click Import. The found, conversion process will begin.
After about a minute or two, the converted assembly will appear in the graphics screen, as shown in Figur e C-l 4. The ass embl y and all 11 parts s eem to be correctly imported . If you expa nd any of the part branch, for example, the gear (wheel_gbox_pinion_ls), you will see an imported feature listed, as
dep ict ed in Fig ure C-1 4. Agai n, there is no solid feature con ver ted in any of the parts. In addit ion, the Mates branch is empty. Since we do not anticipate making any change to this input gear assembly, this imported assembly is satisfactory, except it does not have any assembly mates. Assemble all 11 parts (may be more for some cases) will take a non-trivial effort. Since we do not anticipate making change in how these parts are assembled, we will merge all 11 parts into a single part. In SolidWorks, you can joi n two or more parts to create a new part in an assembly . T he mer ge operation removes surfaces that intrude into each other's space, and merges the parts into a single solid volume. We will insert a new part into the assembly and merge all 11 parts into that new part. Choose from the pull-down menu Insert > Component > New Part. In the Save As dialog box, enter gbox Jnput for part name, and click Save. SolidWorks is expecting you to select a plane or a flat face to place a sketch for the new part. Click a plane or planar face on a component, for example pick the assembly Front plane from the browser, the Front plane will appear in the graphics screen (Figure C-15). The new part gboxinput will appear in the browser. In the new part, a sketch opens on the selected plane. Close the sketch. Be cau se we are creati ng a joi ned part, we do not need a sketch. Next, we will select all 11 parts and merge them into the new part. From the browser, click the first part wheel box_shaftinput, press the Shift key, and then click the last part, screw_setjip_6*6<2>. All 11 parts will be selected. From the pull-down menu, choose Insert > Features > Join. T h e Join window will appear (overlapping with the browser) as shown in Figure C-16. In the Join window, all 11 parts are listed. All you have to do is to click the checkmark on top to accept the parts. Save the assembly (and the par t), and then close the whole assembly. Now open the part gbox Jnput. Make sure you open gbox input, sldprt instead of gboxJnput. sldasm. The part gbox input will appear in the graphics screen. In addition, all entities belong to this part will be listed in the browse r, as sho wn in Figure C-1 7. Not e that there is an arro w symb ol -> to the right of the root entity, gbox Jnput. This symbol indicates that these entities enclosed in this part refer to other parts or assembly. Note that the Joinl branch has the same symbol. Expand the Joinl branch, you will see 11 parts listed, all with arrows, pointing to the actual parts currently in the same folder. When the link is broken; i.e., when the referring parts are removed from the folder, a question mark symbol will be added to the arrow. The three gear parts, gbox Jnput. sldprt, gboxjniddle.sldprt, a nd gbox output, sldprt, employed for Lesson 6 were created following the approach discussed. One axis in each part that passes through the center hole of the gear was created si mply by intersecting two plane s, for examp le, Top a n d Right planes for the axis in gbox Jnput. sldprt, as shown in Figure C-18. These axes are necessary for creating gear pairs, as discussed in Lesson 6.
