Solution Manual for Kinematics, Dynamics, And Design of Machinery 3rd Ed - Kenneth Waldron, Gary Kinzel

Access full Solution Manual only here http://www.book4me.xyz/solution-manual-kinematics-dynamics-and-design-of-machinery-waldron-kinzel/

Solutions to Chapter 2 Exercise Problems Introduction The solutions solutions in this this chapter have have been developed using SolidWorks. SolidWorks. Other parametric design design programs will follow the same procedures although the command structure will vary from program to program. The SolidWorks SolidWorks files for the individual individual figures are available in a separate separate folder. Typically, the the final figure gives the solution to the problem.

Problem 2.1 A slider crank mechanism is to move the slider slider 1” for 40° of rotation of the crank as shown in the figure. Using GCP methods, develop a graphical graphical solution to determine determine the necessary crank and coupler lengths. lengths. Explicitly identify the layer structure used, and make a separate separate layer for all possible input dimensions. dimensions. Also, explicitly list the driving and driven variables. variables. Show the use of your graphical graphical program to resolve the the problem when the slider slider distance is 1.5 in and the crank rotates through an angle of 60°

Figure P2-1.1 Original drawing for Problem 2.1.

Solution to Problem 2.1 If the fixed pivot and slider line lie on a horizontal line, the problem is defined by a total 6 variables, four of which are independent. We can represent these these as shown in Table P2-1.1. To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionConstruction, SolutionDimensions, FinalLinkage, and Dimensions. InputVariables contains only the input dimensions which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the dimensions for the two link lengths which were not specified. Dimensions contains miscellaneous dimensions such as those associated with pin

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bushings and ground pivots. At various times, we will want different classes of dimensions to be visible while the others are hidden.

-crank problem Table P2-1.1 Variables for slider -crank Variable

Type

Description

Initial Value

x1

Driving

Initial angle for input link

20°

x2

Driving

Displacement angle for input link

50°

x3

Driving

Initial position for slider

3"

x4

Driving

Displacement for slider

1"

x5

Driven

Length of input of input link

x6

Driven

Length of coupler of coupler

Set ProblemDrawing as the active layer and make make sure that the relation relation icons are visible. Draw a horizontal construction line of arbitrary length, length, and fix the the left end. Label the left left end of the line line as A*. From A* draw two lines at arbitrary arbitrary angles. Select the two lines and and click on Equal in the Add Relations window. Label the approximate locations of the input link as A1 and A2. Near the right end of the construction line, draw two small circles to represent represent the pins associated associated with the the slider. Label the two circles as B1 and B2 as shown in Fig P2-1.1. Set the color in InputVariables and SolutionConstruct to to red. Set the line color for the other layers to black. Make the InputVariables layer active, active, and and use Smart Smart Dimens Dimension ion ( ) to dimension dimension the the drawing drawing with with the input input information. The dimensioned dimensioned drawing is shown in Fig. P2-1.2. Set SolutionConstruction as the active layer and

Figure P2-1.2 Dimensions corresponding to the variables in Table P2-1.1.

draw two slider-crank linkages linkages to represent the two extreme positions of the solution solution linkage. Distinguish between between the two instances of the linkage by coloring the lines corresponding to the first position red. The lines for the second

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position can be black. Figure P2-1.3 shows shows two positions of the the approximate instances of the linkage. Because both of these sketches represent the two extreme positions of the same linkage, the following conditions/constraints must be satisfied: 1) 2) 3) 4) 5) 6)

The input links must be of equal length The coupler links must be of equal length The first position (red) of the input link must be collinear with line A*A1 The second position (black) of the input link must be collinear with line A*A2 The first position(red) of the end of the coupler must be the same as B1 The second position(black) of the coupler must be the same as B2

Figure P2-1.3 Initial linkages to start the solution procedure for problem 1.

These six conditions can be enforced by selecting the entities involved and selecting the proper relations under Add applied in any order. order. The results are are shown in Fig. Fig. P2-1.4. Relations. In general, the relations can be applied The unknown dimensions for the linkage are the driver link length length and the coupler length. Before measuring these using Smart Dimension ( ), make SolutionDimensions the active layer. layer. Dimensioning the lines normally would involve setting constraints. However, the drawing is already already fully constrained so the added dimensions dimensions would normally over constrain the drawing. When the dimensions are applied, a window window appears asking if the dimension is to be driving or driven. driven. Select driven driven which reports reports the dimension dimension but does not set it as a constraint. The measurements are shown in Fig. P2-1.5. The drawing in Fig. P2-1.5 is fully constrained. It is not possible to move the linkage instances from either the first or second position. To investigate the movement movement of the linkage from one position position to the other, we can redraw the final linkage in an intermediate intermediate position. We can also insert the fixed pivots, sliders, sliders, and pin bushings to make the linkage look more realistic. Before drawing the final linkage, set the active layer to FinalLinkage and hide the SolutionDimensions layer. To draw the final linkage, draw two lines starting from A* and ending at B as before. Then constrain the the two links of the linkage to be equal to the corresponding link lengths of the linkage instances instances in the extreme positions. Open the file (GroundPivot.SLDDRW ) containing the ground pivot and copy the ground pivot (with all of its dimensions and constraints) and paste an instance of it into the linkage linkage drawing. Select all of the dimensions for for the ground pivot, move them to the Dimensions layer, and hide that layer. layer. Merge the center of the ground pivot bushing bushing with the

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linkage point at A*. For the pin bushings, draw two circles circles Select the two circles circles and the bushing bushing of the ground pivot and select Equal under Add Relations. Next merge the center of the the circles with the points at the the two ends of the coupler. coupler. For the slider block, use the 3-point 3-point center rectangular for the rectangle type. Before moving the linkage, turn off automatic relations in SolidWorks by using the path Tools/Options/System allow the linkage to be moved without without snapping to the Options/Relations/Snaps/Automatiic Options/Relations/Snaps/Automatiic relations. This will allow nearest constraint. The final linkage design, with with the relation icons hidden, is is shown in Fig. P2-1.6. It is possible to move the linkage throughout (and beyond) the range of interest defined by the original problem statement.

Figure P2-1.4 Two linkages with inputs and couplers constrained to be equal.

Figure P2-1.5 Dimensions for crank and coupler for solution linkage.

Now that the solution solution drawing is developed, developed, we may change any of the values values by simply changing the dimensions dimensions in Fig. P2-1.6. The results for the alternate dimensions given in the problem statement statement are shown in Fig. P2-1.7.

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Figure P2-1.6 Final linkage.

Figure P2-1.7 Linkage dimensions for input changes.

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Problem 2.2 An inverted slider-crank mechanism is to move the slider 0.4” for 45° of rotation of the slide as shown in the figure. Using GCP methods, develop a graphical solution to determine the necessary crank ( B*B) and base ( A*B*) lengths. Explicitly identify identify the layer structure used, and make a separate layer for all possible input dimensions. dimensions. Also, explicitly list the driving and driven driven variables. Show the use of your graphical program to resolve the problem when the slider displacement is 0.8 in and the slide rotates through an angle of 55°


Solution to Problem 2.2 If the two fixed pivots lie on a horizontal line, the problem is defined by a total 6 variables, four of which are independent. We can represent these as shown shown in Table P2-2.1. Table P2-2.1 Variables for inverted slider -crank problem Variable

Type

Description

Initial Value

x1

Driving

Initial angle for slider line

30°

x2

Driving

Displacement angle for slider line

45°

x3

Driving

Initial position for slider

1.5"

x4

Driving

Displacement for slider

0.4"

x5

Driven

A*B*) Length of base of base link ( A*B*

x6

Driven

B*B) Length of output of output link ( B*B

To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionConstruction, SolutionDimensions, FinalLinkage, and Dimensions. InputVariables contains only the input dimensions which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the dimensions for the two link lengths which were not specified. Dimensions contains miscellaneous dimensions such as those associated with pin bushings and ground pivots. At various times, we will want different classes of dimensions to be visible while the others are hidden.

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Set the color in InputVariables and SolutionConstruct to to red. Set the line color for the other layers to black. Set ProblemDrawing as the active active layer, make make sure that the the relation icons icons are visible. visible. Draw a horizontal horizontal construction line of arbitrary length, and fix fix the left end. end. Label the left left end of the line as A* and the right end as B*. From the A* end of the line, draw two lines lines at arbitrary angles. angles. Select the two lines lines and click on Equal in the locations of the input slide as A1 and A2. On each slide location, draw Add Relations window. Label the two end locations two small circles to represent represent the pins associated with with the slider. Label the two circles as B1 and B2 as shown in Fig P2-2.1. Draw an arc from the B1 location to the second position for the slide, and make it a construction construction line. Draw a similar arc from B2 to the first position of the slide, and make it a construction line. Make the InputVariables layer active, and use Smart Dimension ( ) to dimens dimension ion the drawin drawing g with with the the inpu inputt information. The dimensioned dimensioned drawing is shown in Fig. P2-2.2. Make SolutionConstruction the active layer and


draw two inverted slider-crank slider-crank linkages to represent the two extreme positions of the solution linkage. Note that all that is required is to draw the output link lines. However, when doing this, it is necessary necessary to ensure that the bottom of the lines are coincident with the horizontal horizontal base line through A*. Distinguish between between the two instances of the linkage by coloring the line corresponding to the first position position red. The line for the second position can be black. Figure P2-2.3 shows two positions positions of the approximate approximate instances of the linkage. Because both of these sketches of the solution linkage represent the two extreme positions of the same linkage, the following conditions/constraints must be satisfied: 1) 2)

The base links must be of equal length The output links must be of equal length

These two conditions are easily enforced. Because of the way the two instances of the linkage were constructed, the base links are automatically equal. Therefore, we need only enforce the second condition by selecting the two output link lines and setting them equal. The results are shown in Fig. P2-2.4. The unknown dimensions for for the linkage are the base length and and the output link length. Before measuring these usin using g Smar Smartt Dime Dimens nsio ion n ( ), mak makee SolutionDimensions the active layer. layer. Dimensioning the lines normally would would involve setting constraints. However, the drawing is already already fully constrained so the added dimensions dimensions would

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normally over constrain the drawing. When the dimensions are applied, a window window appears asking if the dimension is to be driving driving or driven. driven. Select Driven which reports the the dimension but does not set it as a constraint. The measurements are shown in Fig. P2-2.5.

Figure P2-2.3 Initial linkages to start the solution procedure for problem 2.2

The drawing in Fig. P2-2.5 is fully constrained. It is not possible to move the linkage instances from either the first or second position. To investigate the movement movement of the linkage from one position position to the other, we can redraw the final linkage in an intermediate position. We can also insert the fixed pivots, slider, and slider bushing to make the linkage look more realistic. Before drawing the final linkage, set the active layer to FinalLinkage and hide the SolutionDimensions layer. To draw the final linkage, linkage, draw two lines. lines. The first will will start from A* and will represent represent the slider. The second line is drawn from B* to the slider line, line, and the second line will represent represent the output link. A coincident relation will will be assigned when the line line is drawn to the slider line. Therefore, the only constraints constraints that need to be set are to make the the slider line equal to the original slider line positions and to make the output link lines equal.

Figure P2-2.4 Two linkages with base links and couplers constrained to be equal.

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Figure P2-2.5 Dimensions for crank and coupler for solution linkage.

To improve the appearance of the final linkage, open the file ( GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), and paste two instances of it into the linkage drawing. Select the dimensions dimensions of the the ground pivots, move them to to the Dimensions layer, and hide that layer. Merge the centers of the ground pivot bushings with the linkage points at A* and B*. For the slider bushing, draw a circle, use Smart Dimensions to set the diameter to be consistent with the drawing dimensions (approximately 0.1 in), and merge the center of the circle circle with the point at the moving moving end of the output link. For the slider block, use the 3-point center center rectangular for the rectangle rectangle type. Before moving the linkage, turn off automatic automatic relations relations in SolidWorks by using the path Tools/Options/System Tools/Options/System Options/Relations/Snaps/Automatii Options/Relations/Snaps/Automatiicc relations. This will allow the linkage to be moved without snapping to the nearest constraint. The final linkage design, with the relation icons hidden, is shown in Fig. Fig. P2-2.6. It is possible to move the linkage linkage throughout (and beyond) the range of interest defined by the original problem statement. Now that the solution solution drawing is developed, developed, we may change any of the values values by simply changing the dimensions dimensions in Fig. P2-2.6. The results for the alternate dimensions given in the problem statement statement are shown in Fig. P2-2.7.


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Problem 2.3 An elliptic trammel trammel is a mechanism where two sliders sliders are connected by a binary link. In the case considered in this problem, the slides are perpendicular to each other. As indicated in the drawing, one slider is to move 0.4 in when the other slider moves 0.5 in. Using GCP methods, methods, develop a graphical solution solution to determine the necessary necessary link length between A and B and the starting position for point A1. Explicitly identify identify the layer structure structure used, and make a separate layer for all all possible input dimensions. dimensions. Also, explicitly explicitly list the driving and and driven variables. Show the use of your graphical program to resolve the problem when the slider distance for the horizontal slider is 0.6 in and the slider distance for the vertical slider is 0.4 in.


Solution to Problem 2.3 For the configuration given, given, the problem is defined by a total 5 variables, variables, three of which are independent. independent. We can represent these as shown in Table P2-3.1. -crank problem Table P2-3.1 Variables for slider -crank Variable

Type

Description

Initial Value

x1

Driving

Initial position for output slider

1.2

x2

Driving

Displacement for output slider

0.4

x3

Driving

Displacement for input slider

0.5"

x4

Driven

Initial position of input of input slider

x5

Driven

Length of coupler of coupler

To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionConstruction, SolutionDimensions, FinalLinkage, and Dimensions. InputVariables contains only the input dimensions which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the dimensions for the initial position of the input slider and the coupler length. Dimensions contains miscellaneous dimensions such as those associated with slider lines. At various times, we will want different different classes of dimensions to be visible while the others are hidden. Set the color in InputVariables and SolutionConstruct to to red. Set the line color for the other other layers to black.

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Access full Solution Manual only here http://www.book4me.xyz/solution-manual-kinematics-dynamics-and-design-of-machinery-waldron-kinzel/ Set ProblemDrawing as the active layer and make make sure that the relation relation icons are visible. Draw a horizontal construction line of arbitrary arbitrary length. Next draw a vertical construction construction line that intersects intersects the horizontal line. line. Draw four circles, and and set their diameters diameters equal. Make the Dimensions layer active, and use Smart Dimension to constrain the diameter of the circles to be 0.1”. Make the ProblemDrawing layer active again. again. Place the centers centers of two of the the circles on the horizontal axis using the Coincident relation. Similarly, place place the centers of the remaining two circles circles on the vertical axis using the Coincident relation. Label the approximate approximate locations of the input link as A1 and A2 and the approximate locations of the output slider as B1 and B2 according to the drawing in Fig. 2-3.1. Make the InputVariables layer active, and use Smart Dimension to dimension the drawing with the input information. The dimensioned dimensioned drawing is shown in Fig. P2-3.2. Set SolutionConstruction as the active layer and


hide the input dimensions shown shown in Fig. P2-3.2. Next, draw lines from A1 to B1 and from A2 to B2 to represent the coupler of the linkage. Distinguish between between the two instances of the linkage by coloring coloring the lines corresponding to the first position red. The lines for for the second position position can be black. black. Figure P2-3.3 P2-3.3 shows two positions of the the approximate instances of the linkage. linkage. Because both of these sketches of the solution solution linkage represent the two extreme positions of the same linkage, the coupler coupler links must be of equal length. This condition can be enforced by selecting the two coupler lines and selecting Equal under Add Relations. The results are shown in Fig. P2-3.4. The unknown dimensions for the linkage are the starting position of the input slider and the coupler lengt length. h. Before measuring these using Smart Dimension, make SolutionDimensions the active layer. layer. Dimensioning the lines lines normally would involve involve setting constraints. However, the drawing drawing is already fully constrained constrained so the added dimensions would normally normally over constrain the drawing. Therefore, make the dimensions dimensions driven which reports the the dimension but does not set it as a constraint. The measurements are shown in Fig. P2-3.5. The drawing in Fig. P2-3.5 is fully constrained. It is not possible to move the linkage instances from either the first or second position. To investigate the movement movement of the linkage from one position to the other, we can can redraw the final linkage in an intermediate intermediate position. We can also insert the sliders sliders and slider lines to make the linkage linkage look more realistic.

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Figure P2-3.3 Initial linkages to start the solution procedure for problem 3.

Figure P2-3.4 Two linkages with couplers constrained to be equal.

Before drawing the final linkage, set the active layer to FinalLinkage and hide the SolutionDimensions layer. To draw the final linkage, draw a line starting on the vertical line from between A1 and A2 to the horizontal line between B1 and B2. Then constrain the line to be equal to the coupler line. line. The top point of the coupler line is is the point A and the bottom point is B. To draw the sliders, click on the 3-Point Center Rectangle drawing tool and draw a vertical rectangle starting at the slider point at A. Select a vertical vertical side of the rectangle rectangle and click on the the Vertical relation. Draw a second rectangle rectangle at B for the horizontal rectangle. rectangle. Select the horizontal horizontal side of the rectangle rectangle and click on the Horizontal relation. Next select a long side of each of the two rectangles and use the Equal relation. Similarly constrain the short sides to be equal.

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Prior to including the slider lines, draw a horizontal construction line below the bottom slider and in the approximate location of the slider line. Select the bottom line of the slider and the horizontal horizontal construction line and make them collinear. Fix the left left end of the construction line. Similarly, draw a vertical vertical construction line to the left left of the vertical slider in the approximate approximate location of the slider line. Select both the vertical construction construction line and the left most vertical line of the vertical slider and make the lines collinear.

Figure P2-3.5 Dimensions for starting slider position and coupler for solution linkage.

Open the file ( Long_Inclined_Slider Long_Inclined_SliderLine.SLDDRW Line.SLDDRW ) containing the inclined slider line and copy it (with all of its dimensions and constraints) constraints) and paste two instances of it into the linkage drawing. drawing. Select all of the slider-line slider-line dimensions, move them to the Dimensions layer, and hide hide that layer. To make one instance instance of the slider slider line horizontal, draw a horizontal construction line near the instance of the slider line and fix the construction line. Using Smart Dimension, set the angle between the the construction line line and the horizontal slider slider line to zero. Delete the construction line. Next locate the construction construction line below the horizontal slider slider and select the left end of it and the left end of the horizontal slider line, and click Merge. The slider line will appear below the bottom slider. For the vertical slider line, construct a second horizontal construction line near the second instance of the inclined slider line. Fix the construction line. Using Smart Dimension, set the angle between the inclined slider line and the horizontal line to be -90°. Locate the previously drawn drawn vertical construction construction line next to the vertical slider and and select the bottom bottom point of the line. Hold the Ctrl key down, select the bottom end of the horizontal slider line, and click Merge. The slider line will appear beside the vertical slider. Before moving the linkage, turn off automatic relations in SolidWorks by using the path Tools/Options/System allow the linkage to be moved without without snapping to the Options/Relations/Snaps/Automatiic Options/Relations/Snaps/Automatiic relations. This will allow nearest constraint. The final linkage design, with with the relation icons hidden, is is shown in Fig. P2-3.6. It is possible to move the linkage throughout (and beyond) the range of interest defined by the original problem statement. Now that the solution drawing is developed, we may change any of the values by simply changing the input dimensions in Fig. P2-3.5. The results for the alternate dimensions given in the problem statement are shown in Fig. P2-3.7.

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Problem 2.4 Using GCP methods, develop a graphical program that will let you animate the Scotch-Yoke mechanism with the crank ( A*A structure used and the driving and driven variables. A*A) as the input. Explicitly identify the layer structure


Solution to Problem 2.4 The problem statement does not give any specific dimensions so we need to identify the main variables required to use GCP to develop a general graphical program program for the Scotch Yoke. If the slider at A moves on a vertical slide and the other slider moves on a horizontal slide, from a kinematics standpoint, the only critical dimension is the length of the coupler. The output dimensions dimensions are the vertical distance between between A and A* and the horizontal dimensions between A and A*. These are represented represented in Table P2-4.1.

Scotch Yoke problem problem Table P2-4.1 Variables for Scotch Variable

Type

Description

x1

Driving

Coupler Coupler length

x2

Driven

Vertical distance between A and A*

x3

Driven

Horizontal distance between A and A*

Initial Value

Blank_Worksheet.SLDWRK ) in SolidWorks. Set up To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK the following layers: ProblemDrawing, InputVariables, SolutionDimensions, and Dimensions. InputVariables contains only the input dimension for the coupler length which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the dimensions for the two distances which were not specified. Dimensions contains miscellaneous dimensions such as those associated with pin bushings, slider lines, and ground pivots. At various times, we will will want different classes of dimensions dimensions to be visible while the others are hidden.

Set the color in InputVariables to red. Set the line color for the other other layers to black. The steps in producing the drawing which becomes the graphical program are given in the following:

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1. Make ProblemDrawing the active layer and make sure that the relation icons are visible. 2. Draw an inclined line for the crank. crank. Fix the beginning beginning of the line. Label the fixed fixed end A* and the other end A. 3. Draw a vertical line for the vertical vertical slider. Select the point on the inclined line at A and the vertical slider line. Click the Coincident relation. 4. Draw a second vertical line to the right of the slider slider line. Select the bottom points of this line and the vertical slider line and click on the Horizontal relation. 5. Use the 3 Point Arc drawing tool and connect the two vertical lines at the bottom with a semicircular arc. 6. Draw a horizontal line from the top point of the second vertical line. 7. Use the Fillet drawing tool and create a fillet between the two lines. 8. At the right end of the horizontal line, use the 3 Point Center Rectangle tool and draw a horizontal rectangle. Select the top of the rectangle and click click on the Horizontal relation to force the rectangle to remain horizontal after other changes are made. 9. Use the Trim Entities tool to trim the part of the horizontal line inside the rectangle. 10. Use the 3 Point Center Rectangle tool again to draw a vertical rectangle at A. 11. Make InputVariables the active layer. 12. Use Smart Dimension to dimension all of the features constructed constructed above. These dimensions are shown shown in red in Fig. 2-4.2. 13. Make SolutionDimensions the active layer. 14. Use Smart Dimensions to measure the horizontal and vertical distances between A and A*. When the second of these is dimensioned, the program will asked if we want the dimension to be a Driven dimension. Select the Driven option. The program made the first of the the dimensions a driving dimension. dimension. To make it a driven driven dimension, click on the dimension. Then click on the Other tab and select Driven under Options. This will keep the the dimension from being a constraint. It should now be possible possible to move the linkage to show its motion. The driven dimensions are shown in black in Fig. 2-4.2. To improve the appearance of the linkage, we can add a fixed pivot at A*, a bushing at A, and a slider line for the horizontal slider. First make ProblemDrawing the active layer. layer. Next open the file (GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), and paste an instance of it into the linkage drawing. drawing. Move the dimensions for for the ground pivot to the Dimensions layer, and hide the Dimensions layer. Merge the center of the ground pivot pivot bushing with with the linkage point point at A*. For the slider bushing, draw a circle. circle. Select the circle and and the circle for the ground pivot pivot and use the Equal relation. Then merge the center of the circle with the point at the moving end of the output link. Open the file ( LongSliderLine.SLDDRW ) containing the horizontal slider line and copy it (with all of its dimensions and constraints) and paste an instance instance of it into the linkage drawing. drawing. Move the dimensions of the slider slider line to the Dimensions layer. Next draw a construction line below the horizontal slider in the approximate location of the slider line. Select the construction construction line and the bottom of the slider and click on the Collinear relation. relation. Then fix the left end of the construction line. Next select both the left end of the construction construction line and the and the left end of the horizontal

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slider line. Click the Merge relation. The slider line will appear below the horizontal slider. The final linkage design, with the relation icons hidden, is shown in Fig. P2-4.3. Before moving the linkage, turn off automatic relations in SolidWorks by using the path Tools/Options/System allow the linkage to be moved without without snapping to the Options/Relations/Snaps/Automatii Options/Relations/Snaps/Automatiicc relations. This will allow nearest constraint. constraint. The SolidWorks SolidWorks drawing of the linkage is a graphical program. The user can change any of the the red dimensions in Fig. 2-4.3, and the program will recreate the linkage with the geometry adjusted in a way consistent with the the dimension change. The user can also animate animate the linkage by clicking clicking on the point at A and dragging it around the fixed pivot at A*.

Figure P2-4.2 Basic GCP graphical program for Problem 2.4.

Figure P2-4.3 Linkage with ground pivot and slider line included (relations are hidden).

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Problem 2.5 Using GCP methods, develop a graphical program that will let you animate the elliptical cam mechanism with the cam rotation as the the input. Explicitly identify identify the layer structure structure used and the the driving and driven variables. Change the base length to 2” and the minor diameter to 1” and show the results.


Solution to Problem 2.5 The cam rotates 360º, and the flat-faced follower oscillates. oscillates. The distance between the fixed pivots is to be 1.5”. The follower need be only long enough to contact the cam at all times; therefore, somewhat arbitrarily, select the distance to be 3”. If the fixed pivots lie lie on a horizontal line and the rotation axis is through through the center of the ellipse, ellipse, the problem is defined by a total 6 variables, five of which which are independent. We can represent these as shown in Table 2-4.1. for cam mechanism mechanism Table 2-5.1 Variables for Variable

Type

Description

Initial Value

x1

Driving

Major diameter of cam of cam

1 5/8"

x2

Driving

Minor diameter of cam of cam

4/4"

x3

Driving

Center distance

3"

x4

Driving

Length of follower of follower

1"

x5

Driving

Cam rotation angle

0-2

x6

Driven

Angle between follower and frame

To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionDimensions, SolutionDimensions, SolutionDimensions, SolutionDimensions, and Dimensions.

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The logic for selecting selecting these layers is similar similar to that used in Example Example 2.1. Use red for the line color color in the SolutionDimensions layer. Use black for the the other layers. The steps for constructing the mechanism are as follows: 1.

Set ProblemDrawing as the active layer and make sure that the relation icons are visible.

2.

Draw a horizontal construction construction line to represent the base of the mechanism, and fix the left end. Label the ends of the line as A* and B*.

3.

Draw an ellipse with its center at A*.

4.

Draw an arbitrary line from B* to represent the follower. follower. Label the other end of the line as B.

5.

Select both the ellipse and the follower line, and click on the Tangent relation under Add Relations. The drawing is shown in Fig. 2-5.2

6.

Make the InputVariables layer active

7.

Select Select Smart Dimen Dimension sion ( ) and dimension dimension the the base length, length, the follower follower length, length, and and the major major and minor minor diameter of the ellipse according to the drawing in Fig. 2-5.1.

8.

Make the SolutionDimensions layer active

9.

A*B*) and the follower. Select Select Smart Smart Dimens Dimension ion ( ) and measur measuree the angle angle betwee between n the base base line line ( A*B* follower. Make this dimension a driven dimension. dimension. To do this, click on the Other tab in the Dimension window and select Fig. 2-5.3. Driven under Options. The results are shown in Fig.

It is now possible to animate the cam mechanism by clicking on one of the points at the ends of either the major or minor diameter and dragging it around the fixed pivot at A*. To improve the appearance of the drawing, open the Solidworks file GroundPivot.SLDDWR, and copy the ground pivot with all of its constraints and dimensions. Set the active layer to ProblemDrawing and paste two instances of the ground pivot into the cam-follower cam-follower drawing. Move the dimensions of the ground pivots to the Dimensions layer and hide it. Merge the centers of the bushings with with points A* and B*. The results are are shown in Fig. Fig. 2-5.4 The cam mechanism can now be be used as a graphical program by changing changing any of the independent variables. variables. The results for the set of changes specified in the problem statement is given in Fig. 2-5.5.

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Figure 2-5.2 Cam mechanism prior to applying dimension constraints

Figure 2-5.3 Basic GCP graphical program for Problem 2.5

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Figure 2-5.4 GCP graphical program for Problem 2.5 with fixed pivots added and constraint icons hidden

Figure 2-5.5 GCP graphical program for changed cam dimensions given in problem statement

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Problem 2.6 The inversion of the slider crank in the figure is used extensively extensively for walking toys. Using GCP methods, develop develop a graphical program that will let you animate the mechanism with the crank ( A*A) as the input so that you can observe the path of the “foot”. Explicitly identify the layer structure structure used, and make a separate layer for all possible input dimensions. Also, explicitly explicitly list the driving and driven variables. variables.


Solution to Problem 2.6 The problem statement does not give any specific dimensions so we need to identify the main variables required to use GCP to develop a general graphical program for the inverted slider-crank slider-crank mechanism. If the slider at B* moves through the oscillating slider, from a kinematics standpoint, the only critical dimensions are the length of the crank ( AA* ). The main output dimensions dimensions are AA*), the horizontal and vertical location of B*, and the length of the slide ( AC ). the x and y coordinates of C and and the orientation of the slide ( AC ). ). These are represented represented in Table P2-6.1. Scotch Yoke problem problem Table P2-6.1 Variables for Scotch Variable

Type

Description

x1

Driving


x2

Driving

Horizontal location of B*

x3

Driving

Vertical location of B* B*

x4

Driving

Length of slide ( AC )

x5

Driven

C Horizontal location of C

x6

Driven

Vertical location of C

x7

Driven

Angle of slide ( AC )

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Initial Value

0-2

To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionDimensions, and Dimensions. InputVariables contains only the input dimension for the coupler length which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the dimensions for the two distances and angle which were not specified. Dimensions contains miscellaneous dimensions such as those associated with pin bushings and ground pivots. At various times, we we will want different classes classes of dimensions to be visible while the the others are hidden. Set the color in InputVariables to red. Set the line color for the other other layers to black. The steps in producing the drawing which becomes the graphical program are given in the following: 1. Make ProblemDrawing the active layer and make sure that the relation icons are visible. 2. Draw an inclined line for the crank. crank. Fix the beginning beginning of the line. Label the fixed end A* and the other end as A. 3. Draw a second line for the slide starting from A and inclined downward. Label the bottom bottom end of the second line as C . 4. Draw a small circle below and to the right of A*. Fix the center of the circle circle and label the point as B*. 5. Select the center of the circle and the slide line and click on Coincident in the Add Relations window. 6. Select the 3 Point Center Rectangle tool, and starting from C, draw a rectangle rectangle to represent the foot. The orientation of the rectangle is not important as long as it is not horizontal or vertical. 7. Select the top of the rectangle and the line AC . Click on the Perpendicular relation in the Add Relations window to force the rectangle to remain perpendicular to the slide. 8. Make InputVariables the active layer. 9. Select and delete the Fix cons constr trai aint nt ( ) form form poin pointt B*. 10. Use Smart Dimension to dimension all of the features constructed constructed above. The dimensions are somewhat somewhat arbitrary and were chosen to make the drawing conform approximately to what would be required for a walking toy 11. Make SolutionDimensions the active layer. 12. Use Smart Dimensions to measure the horizontal and vertical distances between A* and C and and the angle between A*A and AC . When the second and third of these is dimensioned, dimensioned, the program will asked if we want the dimension to be a driving or driven dimension. dimension. Select the Driven option. option. The program program made the first of the dimensions a driving dimension. To make it a driven dimension, click on the dimension. Then click on the Other tab and select Driven under Options. This will keep keep the dimension from being a constraint. It should now be possible to move the linkage to show show its motion. The driven dimensions dimensions are shown in black in Fig. 2-6.2. To improve the appearance of the linkage, we can add fixed pivots at A* and B* and a bushing at A. First make ProblemDrawing the active active layer. Next open the file (GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), and paste an instance of it into the linkage drawing.

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Move the dimensions for the ground pivot to the Dimensions layer. Merge the center of the ground pivot bushing with the linkage point at A*. For the second ground pivot, open the file ( InclinedGroundPivot ) which contains the inclined version of the ground pivot, copy the inclined ground pivot (with all of its dimensions and constraints), constraints), and paste an instance of it into the linkage drawing. To simplify the drawing area, area, move the dimensions to the Dimensions layer. Draw a horizontal horizontal construction line and and use Smart Dimension Dimension to set the inclination inclination angle to -90°. -90°. Delete the construction construction line. Finally select the bushing circle of the inclined circle and the small circle at B* and select Coradial from the Add Relations window. Finally, draw a circle somewhere somewhere in the drawing area. Select the center of the circle and the point at A. and select Merge from the Add Relations window. Select the circle at A and the center circle from one of the fixed pivots and click on Equal in the Add Relations window. The final GCP GCP graphical program, with with constraints hidden, hidden, is shown in Fig. 2-6.3. By using the mouse pointer to to drag the point at A, it is possible to animate the linkage and observe the motion of the foot at C. Also, any of the dimensions dimensions can be changed to study other geometries. geometries.


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Figure P2-6.3 Basic GCP graphical program with ground pivots included and constraint icons hidden

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Problem 2.7 The mechanism shown is used to change rotary motion into oscillating motion. Using GCP methods, develop develop a graphical program that will let you animate the mechanism with the crank ( A*A) as the input. Explicitly identify identify the layer structure used, and make a separate layer for all possible possible input dimensions. Also, explicitly list list the driving and driven variables.


Solution to Problem 2.7 The problem statement does not give any specific dimensions so we need to identify the main variables required to use GCP to develop a general graphical program for the pin-in-a-slot pin-in-a-slot mechanism. mechanism. If A* and B* lie on a horizontal line, from a kinematics standpoint, the only critical dimensions are the length of the crank ( AA*), the horizontal location of B*, the diameter of the pin at A, the length B* to the beginning of the slide, and the distance from B* to end of slide. The pin diameter and the lengths to the beginning and end of the slide are somewhat somewhat arbitrary, but we need to select values to be able to produce a drawing. The main output dimensions dimensions are the distance B*A and the angle from the horizontal to the line B*A. These are represented represented in Table Table P2-7.1. for Problem 2.7 Table P2-7.1 Variables for Variable

Type

Description

x1

Driving


x2

Driving


x3

Driving

Diameter of pin at A

x4

Driving

Length from B* to end of slide

x5

Driving

Length from B* to start of slide

x6

Driven

Distance from B* to A

x7

Driven

Angle between the horizontal and B*A

Initial Value

0-2

To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionDimensions, and Dimensions. InputVariables contains only the input dimension for the coupler length which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the dimension for the distance and angle which were not specified. Dimensions contains miscellaneous dimensions such as those associated with pin bushings and ground pivots. At various times, we we will want different classes classes of dimensions to be visible while the the others are hidden.

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Set the color in InputVariables to red. Set the line color for the other layers to black. The steps in producing the drawing which becomes the graphical program are given in the following: 1. Make ProblemDrawing the active layer, and make sure that the relation icons are visible. 2. Draw a horizontal construction line and label the left end as A* and the right end as B*..Fix the point at the A* end. 3. Draw a line for the slide starting from B* and inclined upward and to the left. 4. Draw a second inclined line for the crank starting from A*. Make the line shorter than the the distance A*B*, and label the free end A. 5. Select the point at A and the line starting from B* and click on Coincident in the Add Relations window. 6. Draw a small circle at A. 7. Draw two inclined lines, one below A and one above A. Select the the two lines lines and the inclined line line from B* through A and click on Parallel in the Add Relations window. 8. Select the circle and one of the two lines and click on Tangent in the Add Relations window. 9. Repeat Step 8 for the second line. 10. Draw a construction line perpendicular to the parallel line that is closest to B* in the direction of the other parallel line. 11. Select the end of the other parallel line and the construction line and click on Concident in the Add construction line. This will make make both ends equidistant equidistant from B*. Relations window. Delete the construction 12. Follow the procedure given in Steps 10 and 11 to make the upper ends of the parallel lines equidistant from B*. 13. Use the 3 Point Arc drawing tool and draw a semicircle between the two parallel lines at both the top and bottom. The top semicircle is added both for appearance and to provide a center point that can be used as a reference point for measuring the length of the slide. 14. Use the Trim Entities tool to remove all of the lines interior to the slide except for those associated with the circle drawn in Step 6. 15. Make InputVariables the active layer. 16. Use Smart Dimension to dimension all of the features constructed constructed above. The dimensions are somewhat somewhat arbitrary and were chosen to make the drawing conform approximately to what would be required for a walking toy 17. Make SolutionDimensions the active layer. 18. Use Smart Dimensions to measure the distance from B* to A and the angle between A*B* and B*A. When the second of these is dimensioned, the program will asked if we want the dimension to be a driving or driven dimension. Select the Driven option. The program made made the first of the the dimensions a driving driving dimension. To make it a driven driven dimension, click on the the dimension. Then click on the Other tab and

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Access full Solution Manual only here http://www.book4me.xyz/solution-manual-kinematics-dynamics-and-design-of-machinery-waldron-kinzel/ select Driven under Options. This will keep the dimensions dimensions from being being a constraint. constraint. It should now be possible to move move the linkage to show show its motion. motion. The driven dimensions dimensions are shown in in black in Fig. Fig. 2-7.2. To improve the appearance of the linkage, we can add fixed pivots at A* and B*. First make ProblemDrawing the active layer. Next open the file (GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), constraints), and paste two instance instance of it into the linkage drawing. Move the dimensions for the ground pivot to the Dimensions layer. Merge the centers of the ground pivots bushing with the linkage linkage points at A* and B*. The final graphical program, with constraints constraints hidden, is shown shown in Fig. 2-7.3. By using the mouse to to drag the point at A, it is possible to to animate the linkage and observe observe the motion of the the slide. Also, any of the dimensions can be changed to study other geometries.


Figure P2-7.3 Basic GCP graphical program with ground pivots included and constraint icons hidden.

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Problem 2.8 The mechanism shown is one inversion of the Watt mechanism. Using GCP methods, develop a graphical program that will let you animate the mechanism with the crank ( A*A) as the input. input. Explicitly identify identify the layer layer structure structure used, and make a separate layer layer for all possible input input dimensions. Also, explicitly explicitly list the driving and driven driven variables.


Solution to Problem 2.8 The problem statement does not give any specific dimensions so we need to identify the main variables required to use GCP to develop a general graphical program for the Watt Watt mechanism. If A*, B*, and C* are all on a horizontal line, there are 10 independent variables and two dependent variables. These are represented in Table P2-8.1. Scotch Yoke problem problem Table P2-8.1 Variables for Scotch Variable

Type

Description

x1

Driving


x2

Driving


x3

Driving

Horizontal location of C*

x4

Driving

Length of A*A A*A

x5

Driving

Length of B*B B*B

x6

Driving

Length of C*C

x7

Driving

AB Length of AB

x8

Driving

B*D Length of B*D

x9

Driving

Length of BD BD

x10

Driving

Length of CD

x11

Driven

Angle between the horizontal and B*B

x12

Driven

Angle between the horizontal and C*C

Initial Value

0-2

To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionDimensions, and Dimensions. InputVariables contains only the input dimension for the lengths which will be used as input variables for the graphical program we

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will develop. SolutionDimensions contains only the dimensions for the two angles which were not specified. Dimensions contains miscellaneous miscellaneous dimensions such as those associated associated with pin bushings and ground pivots. At various times, we will want different classes of dimensions to be v isible while the others are hidden. Set the color in InputVariables to red. Set the line color for the other layers to black. The steps in producing the drawing which becomes the graphical program are given in the following: 1. Make ProblemDrawing the active layer and make sure that the relation icons are visible. 2. Draw a horizontal construction line and label the left end as A* and the right end as B*..Fix the point at the A* end. 3. Draw a second horizontal construction line from B* and label the right end C* 4. Draw the lines A*A, AB, B*B, B*D, BD , DC, and C*C . 5. Make InputVariables the active layer. 6. Use Smart Dimension to dimension all of the the lines constructed above. above. The dimensions are somewhat somewhat arbitrary and any reasonable numbers can be used here. The basic idea is to develop a graphical graphical program where the dimensions can be changed later. 7. Make SolutionDimensions the active layer. 8. Use Smart Dimensions to measure the angle between the horizontal and B*B and C*C . When the second and of these is dimensioned, the program will asked if we want the dimension to be a driving or driven dimension. Select the Driven option. The program made the first first of the angles angles a driving dimension. To make it a driven dimension, click click on the dimension. Then click on the Other tab and select Driven under dimension from being a constraint. It should now be possible to move the Options. This will keep the dimension linkage to show its motion. The driven dimensions are shown in black in Fig. 2-8.2. To improve the appearance of the linkage, we can add fixed pivots at A*, B*, and C*, add bushings at A, B, C , and solid fill to the triangle. triangle. First make make ProblemDrawing the active layer. layer. Next open the file D, and add a solid (GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), and paste three instances of it into the linkage drawing. drawing. Move the dimensions for the ground pivots to the Dimensions layer and hide it. Merge the centers of the ground ground pivots bushing with the linkage linkage points at A*, B*, and C*. To add the bushings, draw four circles and merge the centers of the circles to A, B, C , and D. Next select the four circles and the bushing at one of the ground pivots and select Equal in in the Add Relations window. To fill the triangle, first click click on the line line color icon icon ( ) and select a color (for example gray). gray). Next click click on the interior of the Annotations tab of the CommandManager window and click on Area Hatch/Fill. Select the interior triangle as the fill area and select Solid under Properties. Click on the green check mark to exit the window. window. The final graphical program, with constraints hidden, is shown in Fig. 2-8.3. Any of the dimensions can be changed changed to study other geometries. geometries. By using the mouse to drag the point at A, it is possible to animate the linkage and observe the motion of the links. However, before moving the linkage, turn off automatic relations in SolidWorks by using the path Tools/Options/System Tools/Options/System Options/Relations/Snaps/Automatic Options/Relations/Snaps/Automatic linkage to be moved without snapping to the nearest nearest constraint. If the linkage will not relations. This will allow the linkage

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move, check for unwant unwanted ed constra constraints ints such as as perpendi perpendicula cularity rity ( ) or colli collineari nearity ty ( ) and delete delete the icon for for any unwanted relation.


Figure P2-8.3 Basic GCP graphical program with ground pivots included and relation icons hidden

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Problem 2.9 The mechanism shown is a second inversion inversion of the Watt mechanism. mechanism. Using GCP methods, develop develop a graphical program that will let you animate the mechanism with the crank ( A*A) as the input. Explicitly identify the layer structure used, and make a separate layer for all possible input dimensions. Also, explicitly list the driving and driven variables.


Solution to Problem 2.9 The problem statement does not give any specific dimensions so we need to identify the main variables required to use GCP to develop a general graphical program for this inversion of the Watt mechanism. mechanism. If A* and B* are on a horizontal line, there are 11 independent variables and one dependent variable. These are represented in Table P29.1. Scotch Yoke problem problem Table P2-9.1 Variables for Scotch Variable

Type

Description

x1

Driving


x2

Driving


x3

Driving

Length of A*A A*A

x4

Driving

B*B Length of B*B

x5

Driving

AC Length of AC

x6

Driving

Length of BC BC

x7

Driving

Length of BD BD

x8

Driving

B*D Length of B*D

x9

Driving

AB Length of AB

x10

Driving

Length of CE

x11

Driving

Length of DE DE

x12

Driven


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Initial Value

0-2

To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionDimensions, and Dimensions. InputVariables contains only the input dimension for the lengths which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the dimensions for the two angles which were not specified. Dimensions contains miscellaneous miscellaneous dimensions such as those associated associated with pin bushings and ground pivots. At various times, we will want different classes of dimensions to be visible while the others are hidden. Set the color in InputVariables to red. Set the line line color for the other layers layers to black. The steps in producing the drawing which becomes the graphical program are given in the following: 1. Make ProblemDrawing the active layer, make sure that the relation icons are visible. 2. Draw a horizontal construction line and label the left end as A* and the right end as B*..Fix the point at the A* end. 3. Draw the lines A*A, B*B, AC , BC , BD, B*D, AB, CE, and DE. DE. . 4. Make InputVariables the active layer. 5. Use Smart Dimension to dimension all of the the lines constructed above. above. The dimensions are somewhat somewhat arbitrary and any reasonable numbers numbers can be used here. The basic idea is to develop a graphical program program where the dimensions can be changed later. 6. Make SolutionDimensions the active layer. 7. Use Smart Dimensions to measure the angle between the horizontal and B*B. To make make this a driven driven dimension, click on the dimension then on the Other tab and finally select Driven under Options. This will keep the dimension from being being a constraint. It should now be possible to move the linkage to show its motion. The driven dimension dimension is shown in black in Fig. 2-9.2. To improve the appearance of the linkage, we can add fixed pivots at A*and B*, add bushings at A, B, C, D , and E, and add a solid fill to to the triangles. First make ProblemDrawing the active layer. Next open open the file (GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), and paste two instances of it into the linkage drawing. Move the dimensions for the ground pivots to the Dimensions layer and hide the Dimensions layer. Merge the centers centers of the ground pivots bushing bushing with the linkage points at A* and B*. To add the bushings, draw five circles and merge the centers of the circles with A, B, C , D, and E. Next select the five circles and the bushing bushing at one of the ground ground pivots. Select Equal in in the Add Relations window. To fill the triangles, first click click on the line color icon ( ) and select select a color color (for example example gray). Next click on the interior of one of the Annotations tab of the CommandManager window and click on Area Hatch/Fill. Select the interior triangles as the fill area and select Solid under Properties. Click on the green check mark to exit the window. Repeat the process for the other triangle. The final graphical program, with with constraints hidden, is shown in Fig. 29.3. Any of the dimensions can be changed changed to study other geometries. geometries. By using the mouse to drag the point at A, it is possible to animate the linkage and observe the motion of all links. However, before moving the linkage, turn off automatic relations in SolidWorks by using the path Tools/Options/System Tools/Options/System Options/Relations/Snaps/Automatic Options/Relations/Snaps/Automatic linkage to be moved without snapping to the nearest nearest constraint. If the linkage will not relations. This will allow the linkage

- 88 -

move, check for unwant unwanted ed constra constraints ints such as as perpendi perpendicula cularity rity ( ) or colli collineari nearity ty ( ) and delete delete the icon for for any unwanted relation.



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Problem 2.10 The mechanism shown is an inversion inversion of the Stephenson me mechanism. chanism. Using GCP methods, methods, develop a graphical program that will let you animate the mechanism with the crank ( A*A) as the the input. input. Explicitly identify the layer layer structure used, and make make a separate layer for all all possible input dimensions. dimensions. Also, explicitly explicitly list the driving and driven variables.


Solution to Problem 2.10 The problem statement does not give any specific dimensions so we need to identify the main variables required to use GCP to develop a general graphical graphical program for the Stephenson Stephenson mechanism. If A* and B* are on a horizontal line, there are 11 independent variables and one dependent variable. These are represented in Table P2-10.1. problem Table P2-10.1 Variables for Scotch Yoke problem Variable

Type

Description

x1

Driving


x2

Driving


x3

Driving

A*A Length of A*A

x4

Driving

Length of B*B B*B

x5

Driving

Length of AC AC

x6

Driving

BC Length of BC

x7

Driving

BE Length of BE

x8

Driving

Length of B*E B*E

x9

Driving

Length of A*C A*C

x10

Driving

Length of AD AD

x11

Driving

DE Length of DE

x12

Driven


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Initial Value

0-2

Access full Solution Manual only here http://www.book4me.xyz/solution-manual-kinematics-dynamics-and-design-of-machinery-waldron-kinzel/ To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionDimensions, and Dimensions. InputVariables contains only the input dimension for the lengths which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the angle between the horizontal and B*B. Dimensions contains miscellaneous dimensions dimensions such as those associated with pin bushings bushings and ground pivots. At various times, we will will want different classes of dimensions to be visible while the others are hidden. Set the color in InputVariables to red. Set the line color for the other layers to black. The steps in producing the drawing which becomes the graphical program are given in the following: 1. Make ProblemDrawing the active layer, make sure that the relation icons are visible. 2. Draw a horizontal construction line and label the left end as A* and the right end as B*..Fix the point at the A* end. 3. Draw the lines A*A, B*B, AC , BC , BE, B*E, A*C , AD, and DE. DE. . 4. Make InputVariables the active layer. 5. Use Smart Dimension to dimension all of the the lines constructed above. above. The dimensions are somewhat somewhat arbitrary and any reasonable numbers numbers can be used here. The basic idea is to develop a graphical program program where the dimensions can be changed later. 6. Make SolutionDimensions the active layer. 7. Use Smart Dimensions to measure the angle between the horizontal and B*B. To make make this a driven driven dimension, click on the dimension then on the Other tab and finally select Driven under Options. This will keep the dimension from being being a constraint. It should now be possible to move the linkage to show its motion. The driven dimension dimension is shown in black in Fig. 2-10.2. 2-10.2. To improve the appearance of the linkage, we can add fixed pivots at A*and B*, add bushings at A, B, C , D, and E, and add a solid fill to to the triangles. First make ProblemDrawing the active layer. Next open open the file (GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), and paste two instances of it into the linkage drawing. Move the dimensions for the ground pivots to the Dimensions layer. Merge the centers of the ground pivots bushing with the linkage linkage points at A* and B*. To add the bushings, draw five circles and merge the centers of the circles the points at A, B, C, D, and E. Next select the five circles and the bushing bushing at one of the ground pivots. Select Equal in in the Add Relations window. To fill fill the triangle triangles, s, first first click click on the line line color color icon ( ) and select select a color color (for exampl examplee gray). gray). Next click click on on the interior of one of the Annotations tab of the CommandManager window and click on Area Hatch/Fill. Select the interior triangles as the fill area and select Solid under Properties. Click on the green check mark to exit the window. Repeat the process for the other triangle. The final graphical program, with with the relations icons hidden, is shown in Fig. 2-10.3. Any of the dimensions can be changed changed to study other geometries. geometries. By using the mouse to drag the point at A, it is possible to animate the the linkage and observe the motion motion of all of the links. links. However, before moving moving the linkage, turn off automatic relations in SolidWorks by using the path Tools/Options/System allow the linkage to be moved moved without snapping to to the Options/Relations/Snaps/Automatic Options/Relations/Snaps/Automatic relations. This will allow

- 91 -

nearest constraint. If the linkage will not move, move, check for unwanted unwanted relations relations such as perpendicularity ( ) or collineari collinearity ty ( ) and delete delete the the icon icon for any any unwanted unwanted relat relation. ion.



- 92 -

Problem 2.11 The mechanism shown is is a second inversion of the Stephenson Stephenson mechanism. mechanism. Using GCP methods, methods, develop a graphical program that will let you animate the mechanism with the crank ( A*A) as the input. Explicitly identify identify the layer structure used, and make a separate layer for all possible possible input dimensions. Also, explicitly list list the driving and driven variables.


Solution to Problem 2.11 The problem statement does not give any specific dimensions so we need to identify the main variables required to use GCP to develop a general graphical graphical program for the Stephenson Stephenson mechanism. If A* and B* are on a horizontal line, there are 11 independent variables an one dependent variable. These are represented in Table P2-11.1. problem Table P2-11.1 Variables for Scotch Yoke problem Variable

Type

Description

x1

Driving


x2

Driving


x3

Driving

A*A Length of A*A

x4

Driving

B*B Length of B*B

x5

Driving

Length of AC AC

x6

Driving

Length of BC BC

x7

Driving

BE Length of BE

x8

Driving

Length of B*E B*E

x9

Driving

Length of AD AD

x10

Driving

Length of CD

x11

Driving

DE Length of DE

x12

Driven


Initial Value

0-2

Blank_Worksheet.SLDWRK ) in SolidWorks. Set up To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK the following layers: ProblemDrawing, InputVariables, SolutionDimensions, and Dimensions. InputVariables

- 93 -

contains only the input dimension for the lengths which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the angle between the horizontal and B*B. Dimensions contains miscellaneous dimensions dimensions such as those associated with pin bushings bushings and ground pivots. At various times, we will will want different classes of dimensions to be visible while the others are hidden. Set the color in InputVariables to red. Set the line line color for the other layers layers to black. The steps in producing the drawing which becomes the graphical program are given in the following: 1. Make ProblemDrawing the active layer, make sure that the relation icons are visible. 2. Draw a horizontal construction line and label the left end as A* and the right end as B*..Fix the point at the A* end. 3. Draw the lines A*A, B*B, AC , BC , BE, B*E, AD, CD, and DE. DE. . 4. Make InputVariables the active layer. 5. Use Smart Dimension to dimension all of the the lines constructed above. above. The dimensions are somewhat somewhat arbitrary and any reasonable numbers can be used here. The basic idea is to develop a graphical graphical program where the dimensions can be changed later. 6. Make SolutionDimensions the active layer. 7. Use Smart Dimensions to measure the angle between the horizontal and B*B. To make make this a driven driven dimension, click on the dimension then on the Other tab and finally select Driven under Options. This will keep the dimension from being being a constraint. It should now be possible to move the linkage to show its motion. The driven dimension dimension is shown in black in Fig. 2-11.2. 2-11.2. To improve the appearance of the linkage, we can add fixed pivots at A*and B*, add bushings at A, B, C , D, and E, and add a solid fill to to the triangles. First make ProblemDrawing the active layer. Next open open the file (GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), and paste two instances of it into the linkage drawing. Move the dimensions for the ground pivots to the Dimensions layer and hide the Dimensions layer. Merge the centers centers of the ground pivot bushings with the linkage points at A* and B*. To add the bushings, draw five circles and merge the centers of the circles with A, B, C , D, and E. Next select the five circles and the bushing at one of the the ground pivots. Select Equal in the Add Relations window. example gray). Next click on the To fill the triangles, first click on the line color icon ( ) and select a color (for example Annotations tab of the CommandManager window and click on Area Hatch/Fill. Select the interior of one of the triangles as the fill area and select Solid under Properties. Click on the green check mark to exit the window. Repeat the process for the other triangle. triangle. The final graphical program, program, with the relation icons hidden, hidden, is shown in Fig. 2-11.3. Any of the dimensions can be changed changed to study other geometries. geometries. By using the mouse to drag the point at A, it is possible to animate the linkage and observe the motion of all links. However, before moving the linkage, turn off automatic relations in SolidWorks by using the path Tools/Options/System Tools/Options/System Options/Relations/Snaps/Automatic Options/Relations/Snaps/Automatic linkage to be moved without snapping to the nearest nearest constraint. If the linkage will not relations. This will allow the linkage move, check for unwant unwanted ed relati relations ons such such as perpe perpendicu ndiculari larity ty ( ) or colli collineari nearity ty ( ) and delete delete the icon icon for for any unwanted relation.

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Problem 2.12 The mechanism shown is a third inversion inversion of the Stephenson mechanism. Using GCP methods, develop develop a graphical program that will let you animate the mechanism with the crank ( A*A) as the input. Explicitly identify the layer structure used, and make a separate layer for all possible input dimensions. Also, explicitly list the driving and driven variables.


Solution to Problem 2.12 The problem statement does not give any specific dimensions so we need to identify the main variables required to use GCP to develop a general general graphical program for the Stephenson Stephenson mechanism. mechanism. If A*, B*, and C* are all on a horizontal line, there are 10 independent variables and two dependent variables. These are represented in Table P212.1. problem Table P2-12.1 Variables for Scotch Yoke problem Variable

Type

Description

x1

Driving


x2

Driving


x3

Driving

Horizontal location of C*

x4

Driving

A*A Length of A*A

x5

Driving

B*B Length of B*B

x6

Driving

Length of C*C

x7

Driving

Length of AD AD

x8

Driving

Length of BD BD

x9

Driving

Length of BC BC

x10

Driving

Length of CD

x11

Driven


x12

Driven

Angle between the horizontal and C*C

Initial Value

0-2

To begin the solution procedure, open the blank drawing sheet ( Blank_Worksheet.SLDWRK Blank_Worksheet.SLDWRK ) in SolidWorks. Set up the following layers: ProblemDrawing, InputVariables, SolutionDimensions, and Dimensions. InputVariables contains only the input dimension for the lengths which will be used as input variables for the graphical program we will develop. SolutionDimensions contains only the dimensions for the two angles which were not specified.

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Dimensions contains miscellaneous miscellaneous dimensions such as those associated associated with pin bushings and ground pivots. At various times, we will want different classes of dimensions to be v isible while the others are hidden.

Set the color in InputVariables to red. Set the line line color for the other layers layers to black. The steps in producing the drawing which becomes the graphical program are given in the following: 1. Make ProblemDrawing the active layer and make sure that the relation icons are visible. 2. Draw a horizontal construction line and label the left end as A* and the right end as B*. Fix the point at the A* end. 3. Draw a second horizontal construction line from B* and label the right end C* 4. Draw the lines A*A, B*B, C*C , AD, BD, BC , and CD. 5. Make InputVariables the active layer. 6. Use Smart Dimension to dimension all of the the lines constructed above. above. The dimensions are somewhat somewhat arbitrary and any reasonable numbers numbers can be used here. The basic idea is to develop a graphical program program where the dimensions can be changed later. 7. Make SolutionDimensions the active layer. 8. Use Smart Dimensions to measure the angle between then horizontal and B*B and C*C . When the second and of these is dimensioned, the program will asked if we want the dimension to be a driving or driven dimension. Select the Driven option. The program made the first first of the the angles a driving dimension. To make it a driven driven dimension, click on the the dimension. Then click on the Other tab and select Driven under Options. This will will keep the dimension from being a constraint. constraint. It should now now be possible to move move the linkage to show show its motion. motion. The driven dimensions dimensions are shown in in black in Fig. Fig. 2-12.2. To improve the appearance of the linkage, we can add fixed pivots at A*, B*, and C*, add bushings at A, B, C , and D, and add a solid solid fill to the triangle. triangle. First make make ProblemDrawing the active layer. layer. Next open the file (GroundPivot.SLDDRW ) containing the ground pivot, copy the ground pivot (with all of its dimensions and constraints), and paste three instances of it into the linkage drawing. drawing. Move the dimensions for the ground pivots to the Dimensions layer and hide the Dimensions layer. Merge the centers centers of the ground pivot bushings with the linkage points at A*, B*, and C*. To add the pin b ushings, draw four circles and merge the centers of the circles with A, B, D, and C . Next select the four circles and the bushing at one of of the ground pivots. Select Equal in the Add Relations window. To fill the triangle, first click click on the line line color icon icon ( ) and select a color (for example gray). gray). Next click click on the interior of the Annotations tab of the CommandManager window and click on Area Hatch/Fill. Select the interior triangle as the fill area and select Solid under Properties. Click on the green check mark to exit the window. window. The final graphical program, with constraints hidden, is shown in Fig. 2-12.3. Any of the dimensions can be changed changed to study other geometries. geometries. By using the mouse to drag the point at A, it is possible to animate the the linkage and observe the of all links. links. However, before moving moving the linkage, turn off automatic automatic relations in SolidWorks by using the path Tools/Options/System Tools/Options/System Options/Relations/Snaps/Automat Options/Relations/Snaps/Automatic ic relations. This will allow the linkage to be moved without without snapping to the nearest constraint. If the linkage will not move, check for unwant unwanted ed constr constraints aints such as as perpendi perpendicular cularity ity ( ) or colli collinear nearity ity ( ) and delete delete the icon for for any unwanted relation.

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Solution Manual for Kinematics, Dynamics, And Design of Machinery 3rd Ed - Kenneth Waldron, Gary Kinzel

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