Wayne State University MIT 5700 Industrial Robots Modeling and Simulation
Modeling and Validation of a Fanuc LR Mate 200iC M. C. Sabarense; W. S. Fonseca
1. Introduction
The Fanuc LR Mate 200iC is a six degrees of freedom electric servo-driven robot. It has multiple mounting options as floor, tabletop, inside machines, angle and invert, which maximizes flexibility for small and narrow workspaces. For these reasons it that can be used for a wide variety of applications as machine tending, material handling, assembly, picking and packing, part washing, dispensing, testing and sampling, education and entertainment.
Figure 1 – Fanuc LR Mate 200iC.
It is much important to study and to determine the kinematics of a robot because this knowledge can avoid accidents and singularities. A singularity can be defined as a situation that occurs when the robot is moving in a world frame (Cartesian space) and its axes are redundant (more axes than necessary to cause the same motion) or when the robot is in certain configurations that require extremely high joint rates to move at some nominal nominal speed in Cartesian space space [3]. The singularity conditions can be determined by the determinant of the Jacobian matrix of the robot and the region of singularity can be showed using Matlab® or another graphic software [1]. The purpose of this report is to obtain the forward kinematic and the Jacobian matrix for the Fanuc LR Mate 200iC robot and validate the model using Workspace LT® for simulation. These information can be use in the future design and production of the robot to make it faster and more accurate.
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Wayne State University MIT 5700 Industrial Robots Modeling and Simulation
Figure 2 – Standard dimensions and workspace of Fanuc 200iC and similar models.
2. Reference Papers
I.
OLASZ, Attila. SZABÓ, Tamás. Kinematic Analysis of Robot and Manipulator Arms. Advanced Logistic Systems , vol.6, nº1, 2012. This paper aims to determine the angles of the joints of the robot and the manipulator for the control system of a Fanuc LR Mate 200iC robot for a work cycle. The prescribed motions of the robot and the manipulator were simulated by computer. The results show that the curves computed are similar but not equal for the first three joints of the robot and the manipulator.
II.
JACOB, M. G.; LI, Y.; WACHS J. P. A Gesture Driven Robotic Scrub Nurse.
In this paper a Fanuc LR Mate 200iC robot is used as a gesture driven robotic scrub nurse (GRSN) reducing the workload of a human scrub nurse. The accuracy of the robot was determined experimentally and in 95% of the times it recognized and repeated the correct gestures and it is only 0.83 seconds slower than the average of the human performance. 2 December/2014
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III.
SILVA, S. R. X. et al. Modelagem Matemática da Cinemática direta do Robô Fanuc LR Mate 200iC com Simulação no Matlab. Congresso Brasileiro de Educação em Engenharia. 2012.
The authors determined the forward kinematics of a Fanuc LR Mate 200iC robot to analyze the behavior of the position and orientation of the robot. The validation of the results was performed using Matlab simulation. The authors also analyzed and proved the D-H parameters notation. IV.
CURKOVIC, P.; JERBIC, B. STIPANCIC, T. Coordination of Robots with Overlapping Workspaces Bases on Motion Co-Evolution.
Modern robotics systems development focus on the level of autonomy. And when robots are supposed to work together their workspaces are shared meaning that the robots are dynamic obstacles to each other. This paper presents a solution for the problem of motion coordination of two robots with overlapping workspaces. The process is evaluated in a simulation environment created on Matblab. V.
VALERA, A. et al. Industrial Robot Programming and UPnP Services Orchestration for the Automation of Factories. International Journal of Advanced Robotic Systems. 2012.
The authors describe and analyse the Plug-and-Play architecture in some robots as the Fanuc LR Mate 200iC. The validation was made through a test bed specially designed for this experiment. VI.
NUBIOLA, Albert. BONEV, Ilian A. Absolute Robot Calibration with a Single Telescoping Ballbar. Precision Engineering . 2014.
In this paper a new six degrees of freedom measurement system is introduced, using a telescoping ballbar and two custom-made fixtures, one attached to the robot base and one attached to the end-effector. This method is used to calibrate the robot completely. The robot used is the Fanuc LR Mate 200iC and the experiment showed an improvement in the absolute positioning error. 3 December/2014
Wayne State University MIT 5700 Industrial Robots Modeling and Simulation
3. Forward Kinematics
The forward kinematics involves the calculation of the position and orientation of the end-effector in terms of the joint variables. One easy way to calculate the forward kinematics is to use the D-H parameters. This method uses four parameters: link length (a), link twist ( α), link offset (d) and joint angle ( θ) to describe the kinematic model[4]. For the Fanuc LR Mate 200iC the D-H parameters and the kinematic structure are showed in Table ! and in Figure 3, respectively.
Table 1 – D-H parameters of Fanuc LR Mate 200iC.
Joint
d i
θ i
a i
α i
1
330
θ1 = 0º
75
-90º
2
0
θ2 = -90º
300
-180º
3
0
θ3 = 180º
-75
90º
4
-320
θ4 = 0º
0
-90º
5
0
θ5 = 0º
0
90º
6
-80
θ6 = 180º
0
180º
Figure 3 – Kinematic Diagram of Fanuc LR Mate 200iC [1]
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Wayne State University MIT 5700 Industrial Robots Modeling and Simulation
−
Using the D-H parameters and knowing that all joints are rotational (θ variable) it is possible to determine the six homogeneous matrices ( ) using Equation 1.
(1)
0 75 0 0 =00 100 00 753301 =00 100 00 32010 0 300 0 0 =0 0 10 3000 =0 10 0 00 0 0 0 0751 0 6 060 01 0 =00 010 00 7501 6 =006 00 6 100 8001 The Forward kinematics model is obtained by the multiplication between the 6 homogeneous matrices.
6 =. . . . . 6
(2)
Where:
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4. Jacobian Matrix
The Jacobian matrix is used to determine the singularity conditions for the robots through its determinant. Knowing these regions of singularities the paths of the robot can be optimized. In this paper the vector method was used to calculate the Jacobian matrix, as described in Equation 3.
× × × … × − − =[ … − ] − (−) 75 300 =75 75330 =3000 =750 =00 6 = 00 = 00 320 0 80 0 0 = =0 10 0 0 10 0 (3)
The first step of calculation is to determine the position matrices ( rotational matrices :
and the
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0 = 0 01 0 0 6 6 6 = 06 0 6 10
0 = 0 0 10 0 = 0 0 1 0
The rotational and the position matrices related to the base frame were obtained from the Equations 4 as detailed in Equations 5 and 6:
=. ... .− 1 , 1 1 , 2 1 , 3 = 23,,11 23,,22 23,,33 = 12,,44 3,4 =. 0 =01 . s i n + =0 =0 =.sin+ + . s i n cos . . . . =.coscos .
(4)
(5)
(6)
The next step is to determine z i, according to Equation 7.
(7)
Knowing that
, the other z values can be determined using Equation 7:
. si n . +cos . . si n + . . c os +cos . . si n + . . c os =.cos. +. sin ..
To obtain the Jacobian matrix related to the linear velocity it is necessary to realize the vector multiplication as described in Equation 8. 7 December/2014
Wayne State University MIT 5700 Industrial Robots Modeling and Simulation
=− ×6 −
(8)
After this it is possible to determine the complete Jacobian matrix applying the equation 8 in the equation 3.
=[ × 6 ×6 ×6 ×6 ×6 ×6 ]
(9)
*The complete Jacobian matrix is in the appendix.
5. Workspace LT® Simulation and Validation
The evaluation of the robot has been done using the FANUC LR Mate 200iC Model on the software Workspace LT® to create five points and then validating these points numerically with Maple® Software as described in the following pictures.
Figure 4 – First point determined in Workspace LT® and its validation.
Figure 5 – Second point determined in Workspace LT® and its validation.
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Wayne State University MIT 5700 Industrial Robots Modeling and Simulation
Figure 6 – Third point determined in Workspace LT® and its validation.
Figure 7 – Fourth point determined in Workspace LT® and its validation.
Figure 8 – Fifth point determined in Workspace LT® and its validation.
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6. Conclusions
This work provides information related to the forward kinematics for a FANUC LR Mate 200iC and the Jacobian Matrix using the vector multiplication method. Also provides the evaluation of the model validated by Workspace LT® software. Determining those conditions is an important step in the improvement of the robot model and the creation of integrated robotic systems for a wide range of applications.
7. Other References
[1] ABDERRAHMANE, M. S.; DJURIC, A. M.; CHEN, W.; YEH, C. P. Study and Validation of Singularities for a Fanuc LR Mate 200iC Robot. March, 2014. [2] DJURIC, A. M. FILIPOVIC, M. CHEN, W. Visualization of the Three Critical Spaces Related to the 6-DOF Machinery. Fourth Serbian Congresso n Theoretical and Applied Mechanics. Serbia. 2013. [3] RED, Edward. Robotics Overview . Accessed in 12/08/2014 in: http://eaal.groups.et.byu.net/html/RoboticsReview/body_robotics_review.html [4] SERDAR, K. and BINGUL, Z. Robot Kinematics: Forward and Inverse Kinematics, Industrial Robotics: Theory, Modeling and Control. ISBN: 386611-285-8. 2006.
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8. Appendix – Jacobian Matrix
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