411097818 Solution Manual for Kinematics Dynamics And Design of Machinery 3rd Ed Kenneth Waldron Gary Kinzel PDF

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Solutions to Chapter 2 Exercise Problems 

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

Problem 2.1 A slider crank mechanism is to move the slider 1” for 40° of rotation of the crank as shown in the figure. Using GCP methods, develop a graphical solution to determine the necessary crank and coupler lengths. Explicitly identify the layer structure used, and make a separate layer for all possible input dimensions. Also, explicitly list the driving and driven variables. Show the use of your graphical program to resolve the problem when the 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 as shown in Table P2-1.1. To begin the solution procedure, open the blank drawing sheet (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.

Table P2-1.1 Variables for slider -crank problem 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link

x6

Driven

Lengthofcoupler

Set ProblemDrawing as the active layer and make sure that the relation icons are visible. Draw a horizontal construction line of arbitrary length, and fix the left end. Label the left end of the line as A*. From A* draw two lines at arbitrary angles. Select the two lines 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 the pins associated with 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 red. Set the line color for the other layers to black. Make the InputVariables layer active, and use Smart Dimension ( ) to dimension the drawing with the input information. The 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 to represent the two extreme positions of the solution linkage. Distinguish 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 two positions of 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 Relations. In general, the relations can be applied in any order. The results are shown in Fig. P2-1.4. The unknown dimensions for the linkage are the driver link length and the coupler length. Before measuring these using Smart Dimension ( ), make SolutionDimensions the active layer. Dimensioning the lines normally would involve setting constraints. However, the drawing is already fully constrained so the added dimensions would normally over constrain the drawing. When the dimensions are applied, a window appears asking if the dimension is to be driving or driven. Select driven which reports the 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 of the linkage from one position to the other, we can redraw the final linkage in an intermediate position. We can also insert the fixed pivots, 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 two links of the linkage to be equal to the corresponding link lengths of the linkage 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 drawing. Select all of the dimensions for the ground pivot, move them to the Dimensions layer, and hide that layer. Merge the center of the ground pivot bushing with the

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linkage point at A*. For the pin bushings, draw two circles Select the two circles and the bushing of the ground pivot and select Equal under Add Relations. Next merge the center of the circles with the points at the two ends of the coupler. For the slider block, use the 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 Options/Relations/Snaps/Automatiic 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. 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 drawing is developed, we may change any of the values by simply changing the dimensions in Fig. P2-1.6. The results for the alternate dimensions given in the problem 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 the layer structure used, and make a separate layer for all possible input dimensions. Also, explicitly list the driving and 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°

Figure P2-2.1 Original drawing for Problem 2.2.

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 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

Lengthofbaselink(A*B*)

x6

Driven

Lengthofoutputlink(B*B)

To begin the solution procedure, open the blank drawing sheet (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 red. Set the line color for the other layers to black. Set ProblemDrawing as the active layer, make sure that the relation icons are visible. Draw a horizontal construction line of arbitrary length, and fix the left end. Label the left end of the line as A* and the right end as B*. From the A* end of the line, draw two lines at arbitrary angles. Select the two lines and click on Equal in the Add Relations window. Label the two end locations of the input slide as A1 and A2. On each slide location, draw two small circles to represent the pins associated 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 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 dimension the drawing with the input information. The dimensioned drawing is shown in Fig. P2-2.2. Make SolutionConstruction the active layer and

Figure P2-2.2 Dimensions corresponding to the variables in Table P2-2.1.

draw two inverted 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 to ensure that the bottom of the lines are coincident with the horizontal base line through A*. Distinguish between the two instances of the linkage by coloring the line corresponding to the first position red. The line for the second position can be black. Figure P2-2.3 shows two positions of the 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) The base links must be of equal length 2) 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 the linkage are the base length and the output link length. Before measuring these using Smart Dimension ( ), make SolutionDimensions the active layer. Dimensioning the lines normally would involve setting constraints. However, the drawing is already fully constrained so the added dimensions would

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normally over constrain the drawing. When the dimensions are applied, a window appears asking if the dimension is to be driving or driven. Select Driven which reports 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 of the linkage from one 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, draw two lines. The first will start from A* and will represent the slider. The second line is drawn from B* to the slider line, and the second line will represent the output link. A coincident relation will be assigned when the line is drawn to the slider line. Therefore, the only constraints that need to be set are to make 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 of the ground pivots, move them 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 with the point at the moving end of the output link. For the slider block, use the 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 Options/Relations/Snaps/Automatiic 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. P2-2.6. 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 dimensions in Fig. P2-2.6. The results for the alternate dimensions given in the problem statement are shown in Fig. P2-2.7.

Figure P2-2.6 Final linkage.

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Figure P2-2.7 Linkage dimensions for input changes.

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Problem 2.3 An elliptic trammel is a mechanism where two 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, develop a graphical solution to determine the necessary link length between A and B and the starting position for point A1. Explicitly identify the layer structure used, and make a separate layer for all possible input dimensions. Also, explicitly list the driving 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.

Figure P2-3.1 Original drawing for Problem 2.3.

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

Type

Description

Initial Value

x1

Driving

Initialpositionforoutputslider

x2

Driving

Displacementforoutputslider

0.4

x3

Driving

Displacementforinputslider

0.5"

x4

Driven

Initialpositionofinputslider

x5

Driven

Lengthofcoupler

1.2

To begin the solution procedure, open the blank drawing sheet (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 classes of dimensions to be visible while the others are hidden. Set the color in InputVariables and SolutionConstruct to red. Set the line color for the 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 sure that the relation icons are visible. Draw a horizontal construction line of arbitrary length. Next draw a vertical construction line that intersects the horizontal line. Draw four circles, and set their 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. Place the centers of two of the circles on the horizontal axis using the Coincident relation. Similarly, place the centers of the remaining two circles on the vertical axis using the Coincident relation. Label the 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 drawing is shown in Fig. P2-3.2. Set SolutionConstruction as the active layer and

Figure P2-3.2 Dimensions corresponding to the variables in Table P2-3.1.

hide the input dimensions 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 the two instances of the linkage by coloring the lines corresponding to the first position red. The lines for the second position can be black. Figure P2-3.3 shows two positions of the approximate instances of the linkage. Because both of these sketches of the solution linkage represent the two extreme positions of the same linkage, the coupler links must be of equal length. This condition can be enforced by selecting the two coupler lines and selecting Equa...