Project S2 Motion Analysis Using Solidworks Motion: Chapter Outline

Project S2 Motion Analysis Using
SolidWorksÒ Motion
Chapter Outline
S2.1 Introduction to SolidWorks Motion 398
S2.1.1 Overall Process 398
S2.1.2 User Interface 399
S2.1.3 Defining Motion Entities 403
S2.1.4 Motion Simulation 404
S2.1.5 Viewing Results 404
S2.1.6 Examples 406
S2.2 Sliding Block 406
S2.2.1 SolidWorks Parts and Assembly 407
S2.2.2 Motion Model 408
S2.3 Using SolidWorks Motion for the Sliding Block 410
S2.3.1 Defining Gravity 411
S2.3.2 Defining Initial Position 411
S2.3.3 Defining and Running the Simulation 411
S2.3.4 Displaying the Simulation Results 414
S2.3.5 Results Verification 417
S2.4 Single-Piston Engine 418
S2.4.1 SolidWorks Parts and Assembly 419
S2.4.2 Motion Model 420
S2.5 Using SolidWorks Motion for the Single-Piston Engine 420
S2.5.1 Creating a Motion Study 420
S2.5.2 Displaying Simulation Results 423
S2.5.3 Results Verification 424
Exercises 429
Motion analysis was reviewed in Chapter 3, in which both theoretical and practical aspects of
the subject were discussed. There is no need to emphasize the importance of understanding
theory and using analytical methods to solve engineering problems. However, as discussed in
Chapter 3, analytical methods can only go so far. For many design applications, such as
mechanical system analysis, which involves multiple bodies, analytical methods can only
support a small number of rigid bodiesdthat is, one or two, at best. In many cases, engineers
must rely on tools such as motion analysis software to evaluate product performance in
mechanisms with high accuracy in support of design decision making. It is critical for design
Product Performance Evaluation using CAD/CAE. http://dx.doi.org/10.1016/B978-0-12-398460-9.15001-2

Copyright Ó 2013 Elsevier Inc. All rights reserved. 397
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engineers to learn and be able to use software tools for solving problems that are beyond hand
calculations relying on analytical methods.
In this project, we introduce SolidWorks Motion for kinematic and dynamic analysis of
mechanical systems. We include two simple examples: a sliding block and a single-piston
engine, which should provide a good overview of the motion analysis capabilities offered by
SolidWorks Motion. You may find the example files on the book’s companion website (http://
booksite.elsevier.com/9780123984609).
Overall, the objective of this project is to enable readers to use SolidWorks Motion for basic
applications. Those who are interested in learning more may want to go over the examples
provided by Motion or review other tutorials on the subject, such as Motion Simulation and
Mechanism Design with SolidWorks Motion (available at http://www.sdcpublications.com).
Note that the lessons in this project are developed using SolidWorks 2011 SP2.0. A different
version of SolidWorks may have slightly different menu options or dialog boxes. Since
SolidWorks is fairly intuitive to use, these differences should not be too difficult to figure out.
S2.1 Introduction to SolidWorks Motion

SolidWorks Motion (or Motion) is a computer software tool for analyzing the kinematic and
dynamic performance of mechanical systems, as well as for the support of mechanism design.
The main objective of this tutorial is to help new users to become familiar with it and to
provide a brief overview of the concept and detailed steps in using the software.
Motion is fully integrated and embedded in SolidWorks as an add-in module. The transition
from SolidWorks to Motion is seamless. All solid parts, materials, assembly mates, and so
forth defined in SolidWorks are automatically carried over into Motion. Also, assembly mates
created in solid models are directly utilized for defining motion analysis models. Motion can
be accessed through menus and windows in SolidWorks. The same parts and assemblies
created in SolidWorks are directly employed for motion models in Motion, whose menus and
dialog boxes are just like those in SolidWorks. For those who are familiar with SolidWorks,
Motion is relatively easy to learn.
S2.1.1 Overall Process
The use of SolidWorks Motion for mechanism design and analysis consists of three main
steps: model generation (or preprocessing), analysis (or simulation), and result visualization
(or postprocessing), as illustrated in Figure S2.1. Basic entities that constitute a motion model
include bodies, joints, initial conditions, and force or driver. A body can be stationary
(ground body) or movable. Joints, such as revolute joints and cylindrical joints, are defined
between bodies to constrain the relative movement between them. In Motion, joints are
Project S2 Motion Analysis Using SolidWorksÒ Motion 399
Figure S2.1: Overall Process for SolidWorks Motion.
implicitly defined by assembly mates (as in Motion 2011 and beyond). Users do not create
joints to constrain body motion directly. Instead, body motion is governed by assembly mates,
which must therefore be properly defined for the mechanism so that the motion model
captures essential characteristics and closely resembles the behavior of the physical
mechanism. In motion models, at least one degree of freedom must be free to allow the
mechanism to move. The free degrees of freedom are usually either driven by a servomotor
for kinematic analysis or by an external load (force and torque) for dynamic simulation.
The analysis capabilities in Motion employ a simulation engine, Adams/Solver, which solves
the equations of motion for the mechanism. Adams/Solver calculates the position, velocity,
and acceleration of individual moving bodies; as well as reaction forces acting on individual
moving parts at joints. Typical simulation problems, including static (equilibrium
configuration) and motion (kinematic and dynamic), are supported.
The analysis results can be visualized in various forms. You may animate motion of the
mechanism or generate graphs for more specific results, such as the reaction force of a joint in
the time domain. You may also query results at specific locations for a given time frame.
Furthermore, you may ask for a report on results that you specify, such as the acceleration of
a moving part in the time domain. You may also save the motion animation to an AVI for file
portability.
S2.1.2 User Interface
The Motion user interface is identical to that of SolidWorks, as shown in Figure S2.2.
SolidWorks users should find it is straightforward to maneuver in Motion. The main
interface is through MotionManager below the graphics area, as shown in Figure S2.2.
MotionManager creates and plays animations as well as conducts motion analysis. When an
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Figure S2.2: SolidWorks Motion user interfacedMotionManager.
existing assembly (or part) in SolidWorks is opened, the Motion Study tab (with the default
name Motion Study 1) appears at the bottom of the graphics area. Clicking it brings up the
MotionManager window.
As shown in Figure S2.2, the user interface window of MotionManager consists of the
MotionManager tree (or Motion browser), the Motion toolbar, filters, timeline area, and so
forth. Components are mapped from the SolidWorks assembly into the MotionManager tree
automatically, including root assembly, parts, subassemblies, and mates. Each part and
subassembly entity can be expanded to show its components. Motion entities, such as spring
and force, are added to the MotionManager tree once they are created. A result branch is
added to the tree once a motion analysis is completed and result graphs are created. As with
SolidWorks, right-clicking on a node in the MotionManager tree brings up command options
that you can choose to modify or adjust the entity.
The graphics area displays the motion model you are working on. The Motion toolbar shown
in Figure S2.3 (and in more detail in Table S2.1) provides the major functions required to
create and modify motion models, including creating and running analyses and visualizing
results. The toolbar includes type of study (animation, basic motion, or motion analysis),
calculation, animation controls, playback speed options, saving options, the Animation
Wizard, key point controls, and simulation elements.
Figure S2.3: Motion toolbar.
Table S2.1: Shortcut buttons in the Motion toolbar.
Symbol Name Function

Calculate Calculates current simulation; if you alter the simulation
you must recalculate before replaying
Play from start Reset components and play simulation; use after
simulation has been calculated
Play Play simulation beginning at the current timebar location
Stop Stop animation
Playback mode: Normal Play from beginning to end once
Playback mode: Loop Continuous play from beginning to end then loop to
beginning and continue playing
Playback mode: Reciprocal Continuous play from beginning to end then reversedplay
from end to beginning
Save animation Save animation as AVI movie file
Animation Wizard Create rotate model, explode or collapse animation
Auto key Click to automatically place new key when you move or
change components; click again to toggle
Continued
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Table S2.1: Shortcut buttons in the Motion toolbardcont’d.
Symbol Name Function

Add/update key Click to add new key or update properties of existing key
Motor Create motor for motion analysis
Spring Add spring between two components
Damper Add damper between two components
Force Create force for motion analysis
Contact Create 3D contact between selected components
Gravity Add gravity to motion study
Results and graphs Calculate results and create graphs
Motion study properties Define motion study solution parameters
Collapse MotionManager Collapse MotionManager window
You can use Animation to animate simple operation of assemblies, such as Rotate, Zoom In/
Out, and Explode/Collapse. You may also add motors to animate simple kinematic motion of
the assembly. You can use Basic Motion for approximating the effects of motors, springs,
collisions, and gravity on assemblies. Basic Motion takes mass into account in calculating
motion. Its computation is relatively fast, so you can use this for creating presentation-worthy
animations using physics-based simulations. Both Animation and Basic Motion are available
in the basic version of SolidWorks. In addition, you can use Motion Analysis (available with
the SolidWorks Motion add-in from SolidWorks Premium) to accurately simulate and
analyze the motion of an assembly while incorporating the effects of forces such as springs,
dampers, and friction.
If you do not see the Motion Analysis option for study, you may have not activated the Motion
add-in module. It must be chosen from the pull-down menu Tools > Add-Ins. In the Add-Ins
window shown in Figure S2.4, click SolidWorks Motion in both boxes (Active Add-Ins and Start
Up), and then click OK. You may need to restart SolidWorks to activate the Motion module.
The area to the right of the MotionManager tree is the timeline area, which is the temporal
interface for animation. The timeline area displays the times and types of animation events in
the motion study. It is divided by vertical gridlines corresponding to the numerical markers
showing the time. The numerical markers start at 00:00:00. You may click and drag a key to
define the beginning or end time of the animation or motion simulation.
After a motion analysis is completed, you will see several horizontal bars appear in the timeline
area. They are Change bars for connecting key points. They indicate a change between key
points, which characterize the duration of animation, view orientation, and so forth.
Switching back and forth between Motion and SolidWorks is straightforward. Click the Model
tab (back to SolidWorks) and Motion Study tab (to Motion) at the bottom of the graphics area.
S2.1.3 Defining Motion Entities
As mentioned before, the basic entities of a valid Motion simulation model consist of ground
part (or ground body), moving parts (or moving bodies), joints (imposed implicitly by
assembly mates in SolidWorks assembly), initial conditions (usually position and velocity of
a moving body), and forces or drivers for dynamic and kinematic analyses, respectively.
A ground part, or a ground body, represents a fixed reference in space. The first component
brought into the assembly is usually stationary and so becomes a ground part. Parts (or
Figure S2.4: Add-Ins window.

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subassemblies) assembled to the stationary components without any possibility of movement

become part of the ground body. A symbol (f) is placed in front of the stationary components
in the browser (or model tree).
A moving part or body represents a single rigid component moving relative to other parts
(or bodies). It may consist of a single SolidWorks part or a subassembly composed of multiple
parts. When a subassembly is designated as a moving part, none of its composing parts are
allowed to move relative to one another within the subassembly.
An unconstrained rigid body in space has six degrees of freedom: three translational and three
rotational. When you add a joint (or an assembly mate) between two rigid bodies, you remove
degrees of freedom between them. Each independent movement permitted by a joint (or
assembly mate) is a free degree of freedom. The free degree of freedom that a joint allows can
be translational or rotational along the three perpendicular axes. It is extremely important to
understand the definition and characteristics of assembly mates to generate successful motion
models. In addition to standard mates such as concentric and coincident, SolidWorks provides
advanced and mechanical mates, such as gears. Advanced mates provide additional ways to
constrain or couple movements between bodies.
S2.1.4 Motion Simulation

The Adams/Solver employed by Motion is capable of solving typical engineering problems,
such as static (equilibrium configuration), kinematic, dynamic, and the like. Static analysis is
used to find the rest position (equilibrium condition), in which none of the bodies are moving,
of a mechanism. A simple example of static analysis is illustrated in Figure S2.5a, in which an
equilibrium position of the block is to be determined according to its own mass m, the two
spring constants k1 and k2, and the gravity g.
Kinematics is the study of motion without regard for the forces or torque. A mechanism
can be driven by a motion driver for a kinematic analysis, where the position, velocity,
and acceleration of its individual bodies can be analyzed at any given time. Figure S2.5b
shows a servomotor driving a mechanism at a constant angular velocity. Dynamic
analysis is employed for studying the mechanism motion in response to loads, as
illustrated in Figure S2.5c. This is the most complicated, common, and usually more
time-consuming, analysis.
S2.1.5 Viewing Results
In Motion, the results of the motion analysis can be realized using animations, graphs, reports,
and queries. Animations show the configuration of the mechanism in consecutive time
frames. They provide a global view of the mechanism’s behaviordfor example, the motion of
Figure S2.5: Motion analysis capabilities in SolidWorks Motion: (a) static analysis, (b) kinematic
analysis, and (c) dynamic analysis.
the single-piston engine as shown in Figure S2.6 (a screen capture of the motion animation).
You may also export the animation to AVI for various purposes.
In addition, you may choose an assembly mate or a part to generate result graphsdfor
example, position versus time of the mass center of the piston in the engine example, shown in
Figure S2.7. These graphs give you a quantitative understanding of the characteristics of the
mechanism.
You may also query the results by moving the mouse pointer closer to the curve in a graph and
leaving it there for a short period. The results data appear next to the pointer. And you may ask
Figure S2.6: Motion animation.

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Figure S2.7: Body position versus time.
SolidWorks Motion for a report that includes a complete set of results in the form of textual
data or a Microsoft Excel spreadsheet.
In addition to the capabilities just discussed, Motion allows you to check the interference
between bodies during motion. Furthermore, the reaction forces calculated can be used to
support structural analysis using, for example, SolidWorks Simulation.
S2.1.6 Examples
The two simple examples included in this tutorial project illustrate step-by-step details of
modeling, analysis, and result visualization in Motion. We start with a very simple sliding
block in Section S2.2. The second example illustrates the steps for carrying out kinematic
analysis for a single-piston engine, in which the propeller is driven by a rotary motor at
a constant angular speed (Sections S2.4 and S2.5). Both examples are summarized in
Table S2.2.
S2.2 Sliding Block

The physical model of the sliding block is very simple. The block is made of cast alloy steel
with a size of 1 in. 1 in. 1 in. As shown in Figure S2.8, the block travels a total of 9 in. on
the slope surface due to gravity. The units system employed for this example is IPS (in.-lbf-
sec), in which the gravitational acceleration is 386 in./sec2. The slider is released from a rest
position at the top of the slope (that is, the initial velocity is 0). We assume no friction
between the block and the ground.
Table S2.2: Project examples.
Problem
Example FEA Model Type Things to Learn
Sliding block Particle Basic operation in MotionManager

dynamics Create motion model from SolidWorks
assembly, define and run motion analysis,
visualize simulation results
Verify simulation results using analytical
equations of motion
Single-piston Kinematic Kinematic analysis of four-bar linkage

engine analysis mechanism
Review assembly mates that are defined between
parts and subassemblies for such a four-bar
linkage
Create rotary motor that drives mechanism,
carry out motion simulation, visualize simulation
results
Verify simulation results using analytical
equations of motion
Figure S2.8: Sliding block: (a) schematic view and (b) motion model in CAD (SolidWorks).
S2.2.1 SolidWorks Parts and Assembly
For this lesson, the parts and assembly have been created in SolidWorks. There are
four model files created: block.SLDPRT, ground.SLDPRT, Lesson2.SLDASM, and
Lesson2withresults.SLDASM. We start with Lesson2.SLDASM, in which the block is
assembled to the ground and no motion entities have been added. The assembly file
Lesson2withresults.SLDASM contains the complete simulation model with simulation results.
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Figure S2.9: Assembly mates defined in Lesson2.SLDASM: (a) coincident1, (b) coincident3, and (c)
LimitDistance1.
In the assembly models, there are three assembly mates, as shown in Figure S2.9:
Coincident1(ground<1>,block<1>)
Coincident3(ground<1>,block<1>)
LimitDistance1(ground<1>,block<1>)
The LimitDistance mate allows the block to move along the slope surface for a limited 9 in.
distance. You may drag the block in the graphics area; you should be able to move it on the
slope surface but not beyond it because the limitDistance mate does not allow this. Choose
Edit > Undo Move Component from the pull-down menu to restore the block to its previous
position.
We now take a look at the assembly mate LimitDistance1. From the SolidWorks browser,
click LimitDistance1, and choose Edit Feature , as shown in Figure S2.10. The mate is
brought back for reviewing or editing, as shown in Figure S2.11.
Note that the distance between the two faces, Face<2>@block-1 and Face<1>@ground-1
(Figure S2.9c) is 4 in. The upper and lower limits of the distance are 9 in. and 0 in.,
respectively. The length of the slope surface is 10 in.; therefore, the upper limit is set to 9 in.
so that the block stops when its front lower edge reaches the end of the slope surface (since the
block width is 1 in.). Note that LimitDistance1 is an advanced mate in SolidWorks.
S2.2.2 Motion Model
The block and ground parts (or bodies) are assumed rigid. As mentioned earlier, a limit
distance mate is defined to prevent the block from sliding out of the slope surface. The block
reaches the end of the slope surface in about 0.3 sec, as shown in Figure S2.12, which is the
Figure S2.10: Edit LimitDistance1 mate.
Figure S2.11: Mate Selection dialog box.
Y-position of the mass center of the block. The graph shows that it bounces back when it
reaches the end; this action is due the limitDistance mate and is artificial. The Y-position of
the mass center of the block is about 0.18 in., and travels down to about 4.31 in. at 0.306 sec.
You may export the graph to an Excel file to check these numbers in SolidWorks Motion. The
total vertical travel distance is 4.49 in.
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Figure S2.12: Sliding block in SolidWorks Motion: (a) reaching the end of the slope surface;
(b) graph of the Y-position of the mass center of the block.
S2.3 Using SolidWorks Motion for the Sliding Block

Start SolidWorks and open assembly file Lesson2.SLDASM. Before creating any entities, it is
always a good idea to check the unit system. From the pull-down menu select Tools > Options
and choose the Document Properties tab in the Document Properties-Units dialog box
(Figure S2.13); click Units. IPS should have been selected. Close the dialog box. Note that in
Figure S2.13: Document Properties-Units dialog box.

this units system, the gravity is 386 in./sec2 in the negative Y-direction of the global coordinate
system.
Click the Motion Study tab (Motion Study 1) at the bottom of the graphics area to bring up the
MotionManager window.
S2.3.1 Defining Gravity

Click the Gravity button in the Motion toolbar to bring up the Gravity dialog box. Choose
Y and keep the g-value (386.09 in./s2), as shown in Figure S2.14. In the graphics area, an
arrow appears at the right lower corner , pointing downward to indicate the direction of the
gravity.
Click the checkmark on top of the dialog box to accept the gravity. A gravity node
(Gravity) should appear in the MotionManager tree.
S2.3.2 Defining Initial Position
Bring the block to the upper end of the slope surface as its initial position. The block is
released from this position to simulate sliding without friction. We edit the mate
LimitDistance1 and enter 0 for the distance dimension.
From the SolidWorks browser, expand the Mates branch, click LimitDistance1
(ground<1>,ball<1>), and choose Edit Feature . You should see the definition of the
assembly mate in the dialog box (Figure S2.15). Enter 0.00 in. for the distance, and click the
checkmark on top to accept the change. In the graphics area, the block should move to the top
position on the slope face, as shown in Figure S2.15.
S2.3.3 Defining and Running the Simulation
Choose Motion Analysis from the motion study selection (directly above the MotionManager
tree, as shown in Figure S2.16). Click the Motion Study Properties button from the Motion
Figure S2.14: Gravity dialog box.

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Y
X Enter 0 for distance to
move the block to thr top
Z position
Figure S2.15: Define the initial position for the sliding block.
Figure S2.16: Motion analysis.
toolbar. In the Motion Study Properties dialog box (Figure S2.17), enter 500 for Frames per
second, and click the checkmark at the top of the box.
Zoom in to the timeline area until you can see tenth-sec marks. Drag the end time key to the
0.4-sec mark (see Figure S2.18) in the timeline area to define the simulation duration. Click
the Calculate button on the Motion toolbar to start the motion analysis. A 0.4-sec
simulation is carried out.
Figure S2.17: Motion study properties dialog box.
Drag this key to

Zoom in
0.4 second mark
Figure S2.18: Timeline area.
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After a few seconds, you should see the block start moving down along the slope surface.
Since the total simulation duration is only 0.4 sec, you may want to adjust the playback speed
to 10% to slow down the animation by choosing 0.1x from the scroll-down menu next to the
animation slider.
Next, we graph the Y-position of the block in two ways: Y-position of the mass center of
the block and then Y-distance between the front face of the block and the top end face of
the slope. Both displacement graphs should reveal a parabolic curve, as is common in
physics.
S2.3.4 Displaying the Simulation Results
From the MotionManager, right click block<1>, and choose Create Motion Plot, as shown
in Figure S2.19. In the Results dialog box (Figure S2.20), choose Displacement/Velocity/
Acceleration, select Linear Displacement, Y Component, and then click the checkmark to
accept the graph. You should see a graph like that in Figure S2.12b. Next we define another
graph, distance, to show the same information.
Click the Results and Plots button from the Motion toolbar. In the Results dialog box
(refer to Figure S2.21), choose Displacement/Velocity/Acceleration, select Linear
Displacement, and then Y Component. Pick the two vertices, as seen in Figure S2.21. Click
the checkmark to accept the graph. A graph like that of Figure S2.22 should appear. From
the graph, the block moves along the slope surface from 0 (the distance between two
Figure S2.19: Create Motion Plot.

Figure S2.20: Results dialog box for Create Motion Plot.
coincided faces) to about -4 in. in about 0.3 sec. The block then “bounces” back because of
the LimitDistance mate defined for the block. The graph does not seem to be correct since
we know that the block will travel 4.5 in. in the Y-direction. This is because the distance the
block travels is 9 in. and the slope is 30 deg. Therefore, the Y-distance the block travels
should be 9 sin 30 deg. ¼ 4.5 in.
To examine the results in more detail, you may export the graph data, for example, by right-
clicking the graph and choosing Export CSV. Open the spreadsheet and examine the data. As
shown in the spreadsheet exported (Figure S2.23), the time for the block to reach the lowest
position is 0.306 sec, in which the Y-distance is about 4.5 in. This is accurate.
Figure S2.21: Results dialog boxdchoosing vertices.

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Figure S2.22: Y-distance graph.
Figure S2.23: Spreadsheet.

We will carry out calculations to verify these results in the following section. Save your model
by choosing File > Save from the pull-down menu.
S2.3.5 Results Verification
In this section, we verify the analysis results obtained from Motion. We assume that the block
is of a concentrated mass so that particle dynamics theory applies. In addition, we assume that
there is no air friction and no friction between the sliding faces.
It is well known that the equations of motion can be derived from Newton’s second law for the
block. By sketching a free-body diagram as shown in Figure S2.24, we have the following
force equilibrium equation:
F ¼ ma ¼ mg sin 30 ¼ 0:5mg (S2.1a)
Hence, the acceleration of the block is a ¼ 0.5g. The velocity and position of the block can
then be obtained by integrating Eq. S2.1a over time:
v ¼ at ¼ 0:5gt (S2.1b)
1
s ¼ at2 ¼ 0:25gt2 (S2.1c)
2
The Y-position of the block can be obtained as
1 1
Py ¼ at2 sin 30 ¼ gt2 (S2.2)
2 8
These equations can be implemented using, for example, Microsoft Excel for numerical
solutions. The Y-position of the block from 0 to 3.05 sec is shown in Figure S2.25. This
Figure S2.24: Free-body diagram.

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Figure S2.25: Y-position of the block obtained from spreadsheet calculations.
compares very well with that of SolidWorks Motion result (check spreadsheet results). At
t ¼ 3.05 sec, the Y-position of the block is 4.49 in., which again matches well with the
SolidWorks Motion result.
S2.4 Single-Piston Engine

In this lesson, we learn how to create a simulation model for the single-piston engine shown in
Figure S2.26a, including how to select assembly mates to connect parts for an adequate
motion model. We drive the mechanism by rotating the crankshaft with a constant angular
velocity, basically conducting a kinematic analysis. We start this lesson with a brief overview
of the engine assembly, which was created in SolidWorks. At the end of this lesson, we will
verify the kinematic simulation results using theory and computational methods commonly
found in a mechanism design textbook.
Kinematically, the single-piston engine is essentially a four-bar linkage, as shown in Figure
S2.26b. For an internal combustion engine, the linkage is driven by a firing load that pushes
the piston, converting the reciprocal motion into rotational motion at the crank. However, in
this lesson, since our goal is to conduct a kinematic analysis, we will apply a rotary motor at
the crank. The rotational motion is then converted into a reciprocal motion at the piston.
Figure S2.26: Single-piston engine: (a) CAD model and (b) schematic view of the kinematic model.
For a four-bar linkage, the length of the crank must be less than that of the rod for the
mechanism to operate. This is commonly referred to as Grashof’s law. In this example, the
lengths of the crank and rod are 0.58 and 2.25 in., respectively, which satisfies the requirement
of Grashof’s law.
The unit system chosen for this example is IPS (in.-lbf-sec). All parts are assumed of aluminum,
2014 alloy. No friction is present between any pair of the components (parts or subassemblies).
S2.4.1 SolidWorks Parts and Assembly
The engine example consists of four major components: case (case_asm), propeller
(propeller_asm), connecting rod (connectingrod_asm), and piston, as shown in Figure S2.27a.
For this lesson, the parts and assemblies have been created in SolidWorks. There are 23 model
files, including 5 assemblies. Among the 5 assemblies, 3 are subassemblies mentioned
previously as part of the major components of the engine. The remaining two assembly files
are Lesson3.SLDASM, and Lesson3withresults.SLDASM. Note that the assembly file
Lesson3withresults.SLDASM contains the complete simulation model with simulation results.
You may open this file and review motion simulation results before going over this lesson.
We start with Lesson3.SLDASM, in which the engine is properly assembled with one free
degree of freedom. When the propeller, which is the crank in the standard four-bar linkage, is
driven by the rotary motor, it rotates and drives the connecting rod. The connecting rod pushes
the piston up and down within the piston sleeve.
The engine assembly consists of three subassemblies (case, propeller, and connecting rod)
and one part (piston). The case is fixed (ground body). The propeller is assembled to the case
using concentric and coincident mates, as shown in Figure S2.27b. It is free to rotate along
the X-direction. The connecting rod is assembled to the propeller (at the crankshaft) using
concentric and coincident mates. It is free to rotate relative to the propeller (at the crankshaft)
along the X-direction. Finally, the piston is assembled to the connecting rod (at the piston pin)
Figure S2.27: Single-piston engine: (a) exploded view and (b) constraints defined between bodies
(or subassemblies).
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using a concentric mate. It is also assembled to the engine case using another concentric mate.
This mate restricts the piston movement along the Y-direction, which in turn restricts the top
end of the connecting rod to moving vertically.
S2.4.2 Motion Model

We add a rotary motor to drive the propeller for a kinematic analysis. The position and
velocity of the piston obtained from motion analysis are shown in Figure S2.28a and S2.28b,
respectively. Note that from the position graph, the piston moves between about 1.0 and 2.1
in. vertically. The total travel distance is about 1.1 in., which can be easily verified by the
radius of the crankshaft, which is 0.58 in. The piston travel distance is 2 times the radius of the
crankshaft, which is 1.16 in.
S2.5 Using SolidWorks Motion for the Single-Piston Engine

Start SolidWorks and open assembly file Lesson3.SLDASM. First take a look at the exploded
view by selecting the root assembly (Lesson3), and press the right mouse button. In the menu
appearing (Figure S2.29) choose Explode. You should see the assembly in an exploded view
similar to that of Figure S2.27. Right click the root assembly and choose Collapse to collapse it.
Click the Motion Study tab (with the default name Motion Study 1) at the bottom of the
graphics area to bring up the MotionManager window.
S2.5.1 Creating a Motion Study
We create the kinematic analysis model by adding a rotary motor to the propeller; we use the
Motion Analysis option to simulate the motion.
Figure S2.28: Result graphs obtained from SolidWorks Motion: (a) Y-position of the piston and (b)
Y-velocity of the piston.
Figure S2.29: Display Explode view.
Choose Motion Analysis from the motion study selection (directly above the MotionManager
tree, as shown Figure S2.30). Click the Motor button from the Motion toolbar to bring up
the Motor window (Figure S2.31). Choose Rotary Motor (default). Move the mouse pointer to
the graphics area, and pick a circular arc that defines the rotational direction of the rotary
motordfor example, the circle on the drive washer of the propeller, as shown in Figure S2.32.
A circular arrow appears indicating the rotational direction of the rotary motor.
A counter-clockwise direction is desired. You may change the direction by clicking the
Direction button directly under Component/Direction. Choose Constant speed and enter
60 rpm. Click the checkmark at the top of the dialog box to accept the motor definition.
You should see a RotaryMotor1 added to the MotionManager tree.
Click the Motion Study Properties button from the Motion toolbar to see the Motion Study
Properties dialog box. Change Frames per second to 100, and then click the checkmark to
accept the change. Calculate and animate the motion.
Figure S2.30: Motion Analysis.

422 Project S2
Figure S2.31: Rotary Motor.
Click the Calculate button on the Motion toolbar to carry out a motion analysis. A default 5-
sec simulation is carried out. The propeller should make 5 turns (recall we entered 60 rpm for
the motor earlier), and a 5-sec simulation timeline should be created in the timeline area.
You may want to hide the case_asm to see how the connecting rod and piston move. Right-
click case_asm in the MotionManager tree and select Hide (Figure S2.33). The case is hidden
in the graphics area. Play the animation again. You should now see the motion of the
connecting rod and piston (Figure S2.34).
Figure S2.32: Choosing an arc for the rotary motor.

Figure S2.33: Hide engine case.
Figure S2.34: Animation without engine case.
You may want to reduce the overall simulation period to just 1 sec and increase the number
of time frames to create a smoother animation. The steps are similar to those described in
Section S2.2.
Calculate and play the animation. Now the propeller should rotate only one cycle. You may
want to change the playback mode to loop and play the animation continuously.
S2.5.2 Displaying Simulation Results
Click the Results and Plots button from the Motion toolbar. In the Results dialog box (refer
to Figure S2.35), choose Displacement/Velocity/Acceleration, select Center of Mass Position,
424 Project S2
Figure S2.35: Results dialog box: Center of Mass Position.

and then Y Component. Select the piston (any surface), and click the checkmark to accept
the graph.
A graph like that in Figure S2.28a should appear. It indicates that the piston moves between
about 1.0 and 2.1 in. vertically. As mentioned earlier, the total travel distance of the piston is
about 1.1 in., which is twice the radius of the crankshaft, 0.58 in.
Next, we create a graph for the Y-velocity of the mass center of the piston. Right click
piston_<1> in the motion entity tree, and choose Create Motion Plot, as shown in Figure
S2.36. In the Results dialog box (Figure S2.37), Face<1>@piston_1 is listed. Choose
Displacement/Velocity/Acceleration, select Linear Velocity, and then Y Component. Click the
checkmark to accept the graph. A graph like that in Figure S2.28b should appear. The
graph indicates that the Y-velocity of the piston is between about 4.0 and 4.0 in./sec vertically.
We will carry out calculations to verify these results in the next section. Save your model by
choosing File > Save from the pull-down menu.
S2.5.3 Results Verification
In this section, we verify the motion analysis results using standard kinematic analysis theory.
Note that in kinematic analysis, the position, velocity, and acceleration of given bodies,
points, or axes of joints in the mechanism are analyzed.
In kinematic analysis, forces and torques are not involved. All bodies (or links) are assumed
massless. Hence, mass properties defined for bodies do not influence the analysis results.
Figure S2.36: Create Motion Plot.
Figure S2.37: Results dialog box for Create Motion Plot.

426 Project S2
The motion characteristics of the single-piston engine can be modeled as a slider-crank

mechanism, which is a planar kinematic analysis problem of a four-bar linkage. A vector plot
that represents the positions of joints of the planar mechanism is shown in Figure S2.38. The
vector plot serves as the first step in computing position, velocity, and accelerations.
The position equations of the system can be described by the following vector
summation:
Z1 þ Z2 ¼ Z3 (S2.3a)
where
Z1 ¼ Z1 cos qA þ iZ1 sin qA ¼ Z1 eiq A
Z2 ¼ Z2 cos qB þ iZ2 sin qB ¼ Z2 eiq B
Z3 ¼ Z3 since qC is always 0
The real and imaginary parts of Eq. S2.3a, corresponding to the X- and Y-components of the
vectors, can be written as
Z1 cos qA þ Z2 cos qB ¼ Z3 (S2.3b)
Z1 sin qA þ Z2 sin qB ¼ 0 (S2.3c)
In Eqs. S2.3b and S2.3c, Z1, Z2, and qA are given. We are solving for Z3 and qB. Equations
S2.3b and S2.3c are nonlinear in terms of qB. Solving them directly for Z3 and qB is not
straightforward. Instead, we will calculate Z3 first, using trigonometric relations for the
triangle ABC shown in Figure S2.38:
Z22 ¼ Z12 þ Z32 2Z1 Z3 cos qA
Hence,
Z32 2Z1 cos qA Z3 þ Z12 Z22 ¼ 0
Figure S2.38: Vector plot of the slider-crank mechanism.

Solving Z3 from the above quadratic equation, we have

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ffi
2
2Z1 cos qA ð2Z1 cos qA Þ 4 Z1 Z2 2
Z3 ¼ (S2.4)
2
where two solutions of Z3 represent the two possible configurations of the mechanism shown
in Figure S2.39. Note that point C can be either at C or C0 for a given Z1 and qA.
From Eq. S2.3c, qB can be solved by

1 Z1 sin qA
qB ¼ sin (S2.5)
Z2
Similarly, qB has two possible solutions, corresponding to vector Z3.

Taking derivatives of Eqs. S2.3b and S2.3c with respect to time, we have
: : :
Z1 sin qA qA Z2 sin qB qB ¼ Z 3 (S2.6a)
: :
Z1 cos qA qA þ Z2 cos qB qB ¼ 0 (S2.6b)
: dqA
where qA ¼ ¼ uA is the angular velocity of the rotation driver, which is a constant.
dt
B
θB
Z1
θA Z3 C
A
Configuration 1: θB < 180o
(a)
θB
B
Z1
C' θA
Z3 A
Configuration 2: θB > 180o
(b)
Figure S2.39: Two possible configurations of the mechanism.
428 Project S2
: :
Note that Eqs. S2.6a and S2.6b are linear functions of Z 3 and qB . Rewrite the equations in
matrix form:
: " : #
Z2 sin qB 1 qB Z1 sin qA q: A
: ¼ (S2.7)
Z2 cos qB 0 Z 3 Z1 cos qA qA
Equation S2.7 can be solved by

" : # " #1 " : #
qB Z2 sin qB 1 Z1 sin qA qA
: ¼ :
Z3 Z2 cos qB 0 Z1 cos qA qA
" #" : #
1 0 1 Z1 sin qA qA
¼ :
Z2 cos qB Z2 cos qB Z2 sin qB Z1 cos qA qA
" : #
1 Z1: cos qA qA
¼ :
Z2 cos qB Z1 Z2 cos qB sin qA qA Z1 Z2 sin qB cos qA qA
2 : 3
Z1 cos qA qA
6 7
6 Z2 cos qB
7
6
¼6 : : 7 (S2.8)
7
4 Z1 cos qB sin qA qA sin qB cos qA qA 5

cos qB
:
: Z1 cos qA qA
qB ¼ (S2.9)
Z2 cos qB
and
: : :
Z 3 ¼ Z1 tan qB cos qA qA sin qA qA (S2.10)
In this example, Z1 ¼ 0.58, Z2 ¼ 2.25, and the initial conditions are qA(0) ¼ q and qB(0) ¼ 0.
The solutions can be implemented using a spreadsheet. The Excel spreadsheet file,
lesson3.xls, can be found on the book’s companion website (http://booksite.elsevier.com/
9780123984609). As shown in Figure S2.40, Columns A through I represent time, Z1, Z2, q_ A ,
qA, Z3, qB, Z_ 3 , and q_ B , respectively. Note that in this calculation, Z3 (0) > 0 is assumed; hence,
qB(0) < 0 (clockwise), as illustrated in Figure S2.39. This is consistent with the initial
configuration we created in the Motion model.
Figure S2.40: Excel spreadsheet
Figures S2.41a and S2.41b show the graphs of data in Columns F and Hdthat is, piston
position and velocity, respectively. Comparing these figures with Figures S2.28a and S2.28b,
the simulation analysis results are verified. Note that in Figure S2.41a, the piston position
varies between 1.7 and 2.8 in.; that is, the distance the piston travels is about 1.1 in., which is
the same as that observed in Figure S2.28a.
Note that the accelerations of a given joint in the mechanism can be formulated by taking one
more derivative of Eqs. S2.6a and S2.6b with respect to time. The resulting two coupled
equations can be solved using the Excel spreadsheet.
Exercises
S2.1 Use the model files provided in Section S2.2 to create the spring-mass system shown in
Figure S2.42. The spring constant and the unstretched length (or free length) are k ¼ 20
430 Project S2
Figure S2.41: Result graphs obtained from spreadsheet calculations: (a) Y-position of the piston
(Column F of spreadsheet) and (b) Y-velocity of the piston (Column H of spreadsheet).
lbf /in. and U ¼ 3 in., respectively. The initial position of the block is 4 in. from the top of
the slope surface (use the LimitDistance1 assembly mate). You are simulating a free-
vibration problem, where the block is stretched 1 in. downward along the 30 deg. slope.
No friction is assumed between the block and the slope surface. We assume a gravity of
g ¼ 386 in./sec2 in the negative Y-direction.
(a) Carry out a motion analysis for the system, and graph the position, velocity, and accel-
eration of the block in the Y-direction.
(b) Derive equations of motion for the system, and implement the solutions of the equations
using a spreadsheet. Graph the results and compare them with those of (a). Are you getting
accurate motion simulation results from SolidWorks Motion?
(c) Calculate the natural frequency of the system and compare your calculation with that of
Motion. How do you determine the natural frequency of the system from results obtained
from Motion?
S.2.2 Open the single-piston engine assembly from Section S2.3. Use the Animation Wizard
to create the following animations. Note that Animation Wizard is very easy to use. To
Figure S2.42: Spring-mass system.

Figure S2.43: Animation Wizard: (a) select Rotate model, (b) define rotation axis, and
(c) define animation time period.
access it, simply click the Animation Wizard button on the Motion toolbar. In the
Animation Wizard window (Figure S2.43), click Rotate model (default) and Next. Then
follow the steps to choose rotation axis and animation time interval, as shown in Figure
S2.43b and c, respectively, to create a rotation animation.
(a) Explode for 5 sec; start time: 0 sec.
(b) Rotate along the Y-axis for 5 sec; start time: 6 sec.
(c) Rotate along the X-axis for 5 sec; start time: 12 sec.
(d) Collapse for 5 sec; start time: 18 sec.

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Project S2 Motion Analysis Using

Product Performance Evaluation using CAD/CAE. http://dx.doi.org/10.1016/B978-0-12-398460-9.15001-2

S2.1 Introduction to SolidWorks Motion

S2.1.1 Overall Process

Figure S2.1: Overall Process for SolidWorks Motion.

S2.1.2 User Interface

Figure S2.2: SolidWorks Motion user interfacedMotionManager.

Figure S2.3: Motion toolbar.

Table S2.1: Shortcut buttons in the Motion toolbar.

Symbol Name Function

Play Play simulation beginning at the current timebar location

Stop Stop animation

Playback mode: Normal Play from beginning to end once

Save animation Save animation as AVI movie file

Animation Wizard Create rotate model, explode or collapse animation

Table S2.1: Shortcut buttons in the Motion toolbardcont’d.

Symbol Name Function

Motor Create motor for motion analysis

Spring Add spring between two components

Damper Add damper between two components

Force Create force for motion analysis

Contact Create 3D contact between selected components

Gravity Add gravity to motion study

Results and graphs Calculate results and create graphs

Motion study properties Define motion study solution parameters

Collapse MotionManager Collapse MotionManager window

S2.1.3 Defining Motion Entities

Figure S2.4: Add-Ins window.

subassemblies) assembled to the stationary components without any possibility of movement

S2.1.4 Motion Simulation

S2.1.5 Viewing Results

Figure S2.6: Motion animation.

Figure S2.7: Body position versus time.

S2.2 Sliding Block

Table S2.2: Project examples.

Sliding block Particle Basic operation in MotionManager

Single-piston Kinematic Kinematic analysis of four-bar linkage

S2.2.1 SolidWorks Parts and Assembly

S2.2.2 Motion Model

Figure S2.10: Edit LimitDistance1 mate.

Figure S2.11: Mate Selection dialog box.

S2.3 Using SolidWorks Motion for the Sliding Block

Figure S2.13: Document Properties-Units dialog box.

S2.3.1 Defining Gravity

S2.3.2 Defining Initial Position

S2.3.3 Defining and Running the Simulation

Figure S2.14: Gravity dialog box.

Figure S2.16: Motion analysis.

Figure S2.17: Motion study properties dialog box.

Drag this key to

S2.3.4 Displaying the Simulation Results

Figure S2.19: Create Motion Plot.

Figure S2.20: Results dialog box for Create Motion Plot.

Figure S2.21: Results dialog boxdchoosing vertices.

Figure S2.22: Y-distance graph.

Figure S2.23: Spreadsheet.

S2.3.5 Results Verification

F ¼ ma ¼ mg sin 30 ¼ 0:5mg (S2.1a)

Figure S2.24: Free-body diagram.