كتاب Machines and Mechanisms Applied Kinematic Analysis - Fourth Edition

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Machines and Mechanisms Applied Kinematic Analysis
Fourth Edition
David H. Myszka
University of Dayton

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CONTENTS
1 Introduction to Mechanisms and
Kinematics 1
Objectives 1
1.1 Introduction 1
1.2 Machines and Mechanisms 1
1.3 Kinematics 2
1.4 Mechanism Terminology 2
1.5 Kinematic Diagrams 4
1.6 Kinematic Inversion 8
1.7 Mobility 8
1.7.1 Gruebler’s Equation 8
1.7.2 Actuators and Drivers 12
1.8 Commonly Used Links and Joints 14
1.8.1 Eccentric Crank 14
1.8.2 Pin-in-a-Slot Joint 14
1.8.3 Screw Joint 15
1.9 Special Cases of the Mobility Equation 16
1.9.1 Coincident Joints 16
1.9.2 Exceptions to the Gruebler’s
Equation 18
1.9.3 Idle Degrees of Freedom 18
1.10 The Four-Bar Mechanism 19
1.10.1 Grashof’s Criterion 19
1.10.2 Double Crank 20
1.10.3 Crank-Rocker 20
1.10.4 Double Rocker 20
1.10.5 Change Point Mechanism 20
1.10.6 Triple Rocker 20
1.11 Slider-Crank Mechanism 22
1.12 Special Purpose Mechanisms 22
1.12.1 Straight-Line Mechanisms 22
1.12.2 Parallelogram Mechanisms 22
1.12.3 Quick-Return Mechanisms 23
1.12.4 Scotch Yoke Mechanism 23
1.13 Techniques of Mechanism Analysis 23
1.13.1 Traditional Drafting Techniques 24
1.13.2 CAD Systems 24
1.13.3 Analytical Techniques 24
1.13.4 Computer Methods 24
Problems 25
Case Studies 29
2 Building Computer Models of
Mechanisms Using Working Model
Software 31
Objectives 31
2.1 Introduction 31
2.2 Computer Simulation of Mechanisms 31
2.3 Obtaining Working Model Software 32
2.4 Using Working Model to Model a Four-Bar
Mechanism 32
2.5 Using Working Model to Model a SliderCrank Mechanism 37
Problems 41
Case Studies 42
3 Vectors 43
Objectives 43
3.1 Introduction 43
3.2 Scalars and Vectors 43
3.3 Graphical Vector Analysis 43
3.4 Drafting Techniques Required in Graphical
Vector Analysis 44
3.5 CAD Knowledge Required in Graphical Vector
Analysis 44
3.6 Trigonometry Required in Analytical Vector
Analysis 44
3.6.1 Right Triangle 44
3.6.2 Oblique Triangle 46
3.7 Vector Manipulation 48
3.8 Graphical Vector Addition 48
3.9 Analytical Vector Addition : Triangle
Method 50
3.10 Components of a Vector 52
3.11 Analytical Vector Addition : Component
Method 53
3.12 Vector Subtraction 55
3.13 Graphical Vector Subtraction 55
3.14 Analytical Vector Subtraction : Triangle
Method 57
3.15 Analytical Vector Subtraction :
Component Method 59
3.16 Vector Equations 60
(- 7)
(- 7)
(- 7)
(- 7)
(+ 7)
(+ 7)
(+ 7)
ivContents v
3.17 Application of Vector Equations 62
3.18 Graphical Determination of Vector
Magnitudes 63
3.19 Analytical Determination of Vector
Magnitudes 66
Problems 67
Case Studies 71
4 Position and Displacement
Analysis 72
Objectives 72
4.1 Introduction 72
4.2 Position 72
4.2.1 Position of a Point 72
4.2.2 Angular Position of a Link 72
4.2.3 Position of a Mechanism 73
4.3 Displacement 73
4.3.1 Linear Displacement 73
4.3.2 Angular Displacement 73
4.4 Displacement Analysis 74
4.5 Displacement: Graphical Analysis 74
4.5.1 Displacement of a Single Driving
Link 74
4.5.2 Displacement of the Remaining Slave
Links 75
4.6 Position: Analytical Analysis 79
4.6.1 Closed-Form Position Analysis Equations
for an In-Line Slider-Crank 81
4.6.2 Closed-Form Position Analysis
Equations for an Offset SliderCrank 84
4.6.3 Closed-Form Position Equations for a
Four-Bar Linkage 87
4.6.4 Circuits of a Four-Bar Linkage 87
4.7 Limiting Positions: Graphical Analysis 87
4.8 Limiting Positions: Analytical Analysis 91
4.9 Transmission Angle 93
4.10 Complete Cycle: Graphical Position
Analysis 94
4.11 Complete Cycle: Analytical Position
Analysis 96
4.12 Displacement Diagrams 98
4.13 Coupler Curves 101
Problems 101
Case Studies 108
5 Mechanism Design 109
Objectives 109
5.1 Introduction 109
5.2 Time Ratio 109
5.3 Timing Charts 110
5.4 Design of Slider-Crank Mechanisms 113
5.4.1 In-Line Slider-Crank Mechanism 113
5.4.2 Offset Slider-Crank Mechanism 114
5.5 Design of Crank-Rocker Mechanisms 115
5.6 Design of Crank-Shaper Mechanisms 117
5.7 Mechanism to Move a Link Between Two
Positions 118
5.7.1 Two-Position Synthesis with a Pivoting
Link 118
5.7.2 Two-Position Synthesis of the Coupler
of a Four-Bar Mechanism 118
5.8 Mechanism to Move a Link Between Three
Positions 119
5.9 Circuit and Branch Defects 119
Problems 120
Case Studies 121
6 Velocity Analysis 123
Objectives 123
6.1 Introduction 123
6.2 Linear Velocity 123
6.2.1 Linear Velocity of Rectilinear
Points 123
6.2.2 Linear Velocity of a General
Point 124
6.2.3 Velocity Profile for Linear
Motion 124
6.3 Velocity of a Link 125
6.4 Relationship Between Linear and Angular
Velocities 126
6.5 Relative Velocity 128
6.6 Graphical Velocity Analysis: Relative Velocity
Method 130
6.6.1 Points on Links Limited to Pure
Rotation or Rectilinear
Translation 130
6.6.2 General Points on a Floating
Link 132
6.6.3 Coincident Points on Different
Links 135
6.7 Velocity Image 137
6.8 Analytical Velocity Analysis: Relative Velocity
Method 137
6.9 Algebraic Solutions for Common
Mechanisms 142
6.9.1 Slider-Crank Mechanism 142
6.9.2 Four-Bar Mechanism 142
6.10 Instantaneous Center of Rotation 142vi Contents
6.11 Locating Instant Centers 142
6.11.1 Primary Centers 143
6.11.2 Kennedy’s Theorem 144
6.11.3 Instant Center Diagram 144
6.12 Graphical Velocity Analysis: Instant Center
Method 149
6.13 Analytical Velocity Analysis: Instant Center
Method 152
6.14 Velocity Curves 155
6.14.1 Graphical Differentiation 157
6.14.2 Numerical Differentiation 159
Problems 161
Case Studies 168
7 Acceleration Analysis 170
Objectives 170
7.1 Introduction 170
7.2 Linear Acceleration 170
7.2.1 Linear Acceleration of Rectilinear
Points 170
7.2.2 Constant Rectilinear Acceleration 171
7.2.3 Acceleration and the Velocity
Profile 171
7.2.4 Linear Acceleration of a General
Point 173
7.3 Acceleration of a Link 173
7.3.1 Angular Acceleration 173
7.3.2 Constant Angular Acceleration 173
7.4 Normal and Tangential Acceleration 174
7.4.1 Tangential Acceleration 174
7.4.2 Normal Acceleration 175
7.4.3 Total Acceleration 175
7.5 Relative Motion 177
7.5.1 Relative Acceleration 177
7.5.2 Components of Relative
Acceleration 179
7.6 Relative Acceleration Analysis: Graphical
Method 181
7.7 Relative Acceleration Analysis: Analytical
Method 188
7.8 Algebraic Solutions for Common
Mechanisms 190
7.8.1 Slider-Crank Mechanism 190
7.8.2 Four-Bar Mechanism 191
7.9 Acceleration of a General Point on a Floating
Link 191
7.10 Acceleration Image 196
7.11 Coriolis Acceleration 197
7.12 Equivalent Linkages 201
7.13 Acceleration Curves 202
7.13.1 Graphical Differentiation 202
7.13.2 Numerical Differentiation 204
Problems 206
Case Studies 213
8 Computer-Aided Mechanism
Analysis 215
Objectives 215
8.1 Introduction 215
8.2 Spreadsheets 215
8.3 User-Written Computer Programs 221
8.3.1 Offset Slider-Crank Mechanism 221
8.3.2 Four-Bar Mechanism 221
Problems 222
Case Study 222
9 Cams: Design and Kinematic
Analysis 223
Objectives 223
9.1 Introduction 223
9.2 Types of Cams 223
9.3 Types of Followers 224
9.3.1 Follower Motion 224
9.3.2 Follower Position 224
9.3.3 Follower Shape 225
9.4 Prescribed Follower Motion 225
9.5 Follower Motion Schemes 227
9.5.1 Constant Velocity 228
9.5.2 Constant Acceleration 228
9.5.3 Harmonic Motion 228
9.5.4 Cycloidal Motion 230
9.5.5 Combined Motion Schemes 236
9.6 Graphical Disk Cam Profile Design 237
9.6.1 In-Line Knife-Edge Follower 237
9.6.2 In-Line Roller Follower 238
9.6.3 Offset Roller Follower 239
9.6.4 Translating Flat-Faced
Follower 240
9.6.5 Pivoted Roller Follower 241
9.7 Pressure Angle 242
9.8 Design Limitations 243
9.9 Analytical Disk Cam Profile
Design 243
9.9.1 Knife-Edge Follower 244
9.9.2 In-Line Roller Follower 246
9.9.3 Offset Roller Follower 249
9.9.4 Translating Flat-Faced
Follower 249
9.9.5 Pivoted Roller Follower 250Contents vii
9.10 Cylindrical Cams 251
9.10.1 Graphical Cylindrical Cam Profile
Design 251
9.10.2 Analytical Cylindrical Cam Profile
Design 251
9.11 The Geneva Mechanism 252
Problems 254
Case Studies 258
10 Gears: Kinematic Analysis and
Selection 260
Objectives 260
10.1 Introduction 260
10.2 Types of Gears 261
10.3 Spur Gear Terminology 262
10.4 Involute Tooth Profiles 264
10.5 Standard Gears 266
10.6 Relationships of Gears in Mesh 268
10.6.1 Center Distance 268
10.6.2 Contact Ratio 269
10.6.3 Interference 270
10.6.4 Undercutting 271
10.6.5 Backlash 272
10.6.6 Operating Pressure Angle 273
10.7 Spur Gear Kinematics 273
10.8 Spur Gear Selection 275
10.8.1 Diametral Pitch 276
10.8.2 Pressure Angle 276
10.8.3 Number of Teeth 276
10.9 Rack and Pinion Kinematics 281
10.10 Helical Gear Kinematics 282
10.11 Bevel Gear Kinematics 285
10.12 Worm Gear Kinematics 286
10.13 Gear Trains 288
10.14 Idler Gears 290
10.15 Planetary Gear Trains 290
10.15.1 Planetary Gear Analysis by
Superposition 291
10.15.2 Planetary Gear Analysis by
Equation 293
Problems 295
Case Studies 299
11 Belt and Chain Drives 302
Objectives 302
11.1 Introduction 302
11.2 Belts 302
11.3 Belt Drive Geometry 304
11.4 Belt Drive Kinematics 305
11.5 Chains 308
11.5.1 Types of Chains 308
11.5.2 Chain Pitch 309
11.5.3 Multistrand Chains 309
11.5.4 Sprockets 310
11.6 Chain Drive Geometry 310
11.7 Chain Drive Kinematics 311
Problems 313
Case Studies 315
12 Screw Mechanisms 316
Objectives 316
12.1 Introduction 316
12.2 Thread Features 316
12.3 Thread Forms 316
12.3.1 Unified Threads 317
12.3.2 Metric Threads 317
12.3.3 Square Threads 317
12.3.4 ACME Threads 317
12.4 Ball Screws 317
12.5 Lead 317
12.6 Screw Kinematics 318
12.7 Screw Forces and Torques 322
12.8 Differential Screws 324
12.9 Auger Screws 325
Problems 325
Case Studies 328
13 Static Force Analysis 330
Objectives 330
13.1 Introduction 330
13.2 Forces 330
13.3 Moments and Torques 330
13.4 Laws of Motion 333
13.5 Free-Body Diagrams 333
13.5.1 Drawing a Free-Body Diagram 333
13.5.2 Characterizing Contact Forces 333
13.6 Static Equilibrium 335
13.7 Analysis of a Two-Force Member 335
13.8 Sliding Friction Force 341
Problems 343
Case Study 345
14 Dynamic Force Analysis 346
Objectives 346
14.1 Introduction 346viii Contents
14.2 Mass and Weight 346
14.3 Center of Gravity 347
14.4 Mass Moment of Inertia 348
14.4.1 Mass Moment of Inertia of Basic
Shapes 348
14.4.2 Radius of Gyration 350
14.4.3 Parallel Axis Theorem 350
14.4.4 Composite Bodies 351
14.4.5 Mass Moment of Inertia—
Experimental Determination 352
14.5 Inertial Force 352
14.6 Inertial Torque 357
Problems 363
Case Study 366
Answers to Selected Even-Numbered
Problems 367
References 370
Index 371
370
REFERENCES
1. Barton, Lyndon, Mechanism Analysis: Simplified Graphical
and Analytical Techniques, 2nd ed., Marcel Dekker Inc.,
New York, 1993.
2. Baumeister, Theodore III, Avallone, Eugene, and Sadegh,
Ali, Mark’s Standard Handbook for Mechanical Engineers,
11th ed., McGraw-Hill Book Company, New York, 2006.
3. Chironis, Nicholas and Sclater, Neil, Mechanisms and
Mechanical Drives Sourcebook, 4th ed., McGraw-Hill Book
Company, New York, 2007.
4. Erdman, Aurthur, Sandor, George, and Kota, Sridhar,
Mechanism Design, Vol 1: Analysis and Synthesis, 4th ed.,
Prentice Hall, Upper Saddle River, NJ, 2001.
5. Kepler, Harold, Basic Graphical Kinematics, 2nd ed.,
McGraw-Hill Book Company, New York, 1973.
6. Jensen, Preben, Cam Design and Manufacture, 2nd ed.,
Marcel Dekker, New York, 1987.
7. Jensen, Preben, Classical Modern Mechanisms for Engineers
and Inventors, Marcel Dekker, Inc., New York, 1991.
8. Jones, Franklin, Holbrook, Horton, and Newell, John,
Ingenious Mechanisms for Designers and Inventors, Vols. I–IV,
Industrial Press Inc, New York, 1930.
9. Mabie, Hamilton and Reinholtz, Charles, Mechanisms and
Dynamics of Machinery, 4th ed., John Wiley and Sons Inc.,
New York, 1987.
10. Martin, George, Kinematics and Dynamics of Machines,
2nd ed., Waveland Press Inc., Long Groove, IL, 2002.
11. Norton, Robert, Design of Machinery, 4th ed., McGraw-Hill
Book Company, New York, 2008.
12. Uicker, John, Pennock, Gordon, and Shigley, Joseph, Theory
of Machines and Mechanisms, 4th ed., Oxford University
Press, New York, 2010.
13. Townsend, Dennis and Dudley, Darle, Dudley’s Gear Handbook, 2nd ed., McGraw-Hill Book Company, New York,
1991.
14. Waldron, Kenneth and Kinzel, Gary, Kinematics, Dynamics,
and Design of Machinery, 2nd ed., John Wiley and Sons Inc.,
Hoboken, NJ, 2004.
15. Wilson, Charles and Sadler, Peter, Kinematics and Dynamics
of Machinery, 3rd ed., Pearson Education, Upper Saddle
River, NJ, 2003.
16. Working Model Demonstration Guide, Knowledge Revolution
Inc., San Mateo, CA, 1995.A
Absolute motion, 128
Acceleration. See also Coriolis acceleration,
Normal acceleration, Relative
acceleration, Tangential acceleration,
Total acceleration
analysis of, 175
general summary problems, 206
kinematic analysis, 2
paths of, 179–180, 180i
point of interest, 4
vector, 43
velocity profile, 178–179, 179t, 206–207, 207i
Working Model, 208i–209i, 213
Acceleration curves
description of, 202
graphical differentiation, 202–203, 203i
numerical differentiation, 204–205, 205
summary problems, 206i–209i, 212–213
Acceleration images, description of, 196–197
ACME thread types, 314, 315i, 317t
Actuators
definition of, 4
role of, 12–13
types of, 12–13
Addendum, gear terminology, 260, 260i, 263i
Air/hydraulic motors, actuator type, 12
Algebraic solution, common mechanism,
142, 190–191
American Gear Manufacturer’s Association
(AGMA)
diametrical pitch, 261
gear quality, 273, 273t
gear standardization, 264–266, 264t
American National Standards Institute (ANSI),
gear standardization, 265
Analytical method
cam follower displacement diagrams
summary problems, 253–254
cycle position analysis, 96–98, 97i, 98i
cylindrical cam profile design, 250, 255
disk cam profile design, 242–249, 243i–245i,
247i, 249i
disk cam profile design summary problems,
254i–255i, 255
displacement analysis, 79, 79i, 80–81
displacement analysis summary problems,
101i–105i, 106
instant center location summary problems,
162i–164i, 164–165
instant center method, 123, 152, 153i
instant center method summary problems,
162i–164i, 165
limiting positions analysis, 91–93, 92i
limiting positions summary problems,
101i–105i, 105–106
mechanism analysis technique, 24
motion curves summary problems, 254
relative acceleration analysis, 188i,
188–190, 190t
relative acceleration summary problems,
208i–209i, 210
relative velocity method, 137–141, 138i,
140i, 140i
relative velocity method summary problems,
162i–164i, 164–165
vector component addition, 53–55, 54i, 54t
vector component subtraction, 55–60,
56i–57i, 59t
vector magnitude determinations, 66–71,
67i–70i, 66t
vector triangle addition, 50–51, 51i, 53–54,
59–60, 59i, 759, 69, 69i
vector triangle subtraction, 57i, 55–57
velocity curves summary problems,
162i–164i, 165
Angle method, 50–51
Angle of contact
belt drive, 303–304, 303t
chain drive, 308–309
Angular acceleration, 173, 174i
Angular displacement, 73, 73i
Angular inertia of a body, 355
Angular position vector, 72–73
Angular velocity
and linear velocity, 126–127, 127i
links, 125–126, 126i
and relative velocity, 128–129
Annular gears, 259
“Archimedes Screw,” See Auger screws
Assembly circuit
branch defect, 120
circuit defect, 119
Auger screws, 323, 323i
Automatic Dynamic Analysis of Mechanical
Systems (ADAMS), 24, 31
Avoirdupois pound, 328
B
Backlash
gear mesh relationship, 270–271
gear terminology, 260
Ball screws, 315, 317i, 321
Base circle
cam profile design, 237, 237i
gear terminology, 260i, 262i–263i
Base diameter, 260
Bellcrank, 3i, 4
Belt drive geometry, 302–303, 302i, 311
Belt drive kinematics, 303–306, 303i, 305i, 311
Belt drives
description of, 300–301
selection summary problems, 310
types of, 300–301
Belt length, 302, 303t
Belt speed, 303–304
Belts, 300–302, 301i–302i, 301t
Bevel gear kinematics, 283–284, 283i
Bevel gears, 259–260, 259i, 283
Bull gear, 266
INDEX
Note: The letter ‘i’ and ‘t’ followed by locators refers to illustrations and tables cited in the text
371
C
Cam follower displacement diagrams
analytical summary problems, 253–254
description of, 224–225, 238i
graphical summary problems, 252–253
Cam followers, 223
motion scheme nomenclature, 227–228
prescribed motion, 225–226
types of, 224–225, 224i
Cam followers motion scheme
constant acceleration, 228, 228t, 229t, 230i
constant velocity, 228, 228t
cycloidal motion, 230–236, 233i, 234i,
235i, 236i
harmonic motion, 228–230, 228t, 230i
Cam joint
definition of, 3, 3i
kinematic diagram symbol, 5t–6t
Cams
description of, 223, 224i, 226–227, 226i,
types of, 223–224, 224i
Case studies
acceleration analysis, 213–214, 213i–214i
belt/chain drives, 312–313, 312i–313i
cam design/analysis, 255–257, 256i–257i
displacement/position analysis, 108, 108i
dynamic force analysis, 364, 364i
gears, 297–299, 298i–299i
kinematic motion/classification, 29–30, 30i
machine analysis, 42, 42i
machine design, 121–122, 121i–122i
screw mechanisms, 326–327, 326i–327i
spread sheets, 222, 222i
static force analysis, 343, 343i
vectors, 71, 71i
velocity, 168–169, 168i–169i
Center distance
belt drive, 302–303
chain drive, 308–309, 308i
gear mesh relationship, 266i, 267
Center of gravity, 345–346, 345i, 346t
Chain drive
description of, 300, 306–309
selection summary problems, 312
Chain drive geometry, 308i, 308–309, 312
Chain drive kinematics, 309–310, 309
Chain length, 308–309, 308i
Chain pitch, 307, 307t
Chain speed, 309
Chains, types of, 306i, 306–307
Change point, 19t, 20, 21
Circular pitch, 260, 260i
Clearance, 260
Clockwise, 125
Closed-form position analysis
four-bar linkage, 87
in-line slider-crank, 81–83, 81i–82i
offset slider-crank, 84–86, 84i–85i
Coarse pitch, 261t, 264t
Cog belt, 301, 301iCoincident joint, 16–18
Combined motion schemes
comparisons, 237t
computer software for, 236
description, 236
goals of, 236
jerk, 236
modified sinusoidal acceleration, 237
modified trapezoidal acceleration, 236
polynomial displacement, 236
trapezoidal acceleration, 236
Common mechanisms, algebraic solutions,
142, 190–191
Common units, 173, 329, 346, 348
Commutative law of addition, 49
Complex link, 3i, 4
Component method
analytical addition, 53–55, 754i, 54t
analytical subtraction, 59–60, 59i, 59t
Components, 4, 12
Composite bodies, 349–350, 349i
Computer methods/programs
dynamic analysis programs, 31
mechanism analysis technique, 24–25
user–written programs, 221–222, 221i
value of, 31
Computer-aided design (CAD) systems
mechanism analysis technique, 24–25
vector analysis, 44
Configuration, 74–75
Connecting arm, 19
Constant acceleration, 228, 229i–230i, 229t
Constant angular acceleration, 173–174, 174i
Constant rectilinear acceleration, 171
Constant velocity, 228, 228t
Contact forces, 331–332, 331i, 339–340
Contact line, 262
Contact ratio, 267–268
Coriolis acceleration
description of, 197–201
summary problems, 210–212, 210i–211i
Cosine, 44, 47
Counterclockwise, 126
Coupler, 19
Coupler curve, 101, 101i
Crank
definition of, 3–4, 3i
eccentric, 14, 14i
slider-crank mechanism, 22
Crank-rockers
circuits of, 87, 87i
four-bar mechanism, 19–20, 19t, 20i, 22
machine design, 115–117, 117i
summary problems, 120
Crank-shapers
analytical methods, 118
graphical procedure, 117–118
machine design, 117–118, 117i
summary problems, 120
Cross drives, 303, 303i
Crossed helical gears, 280
Cycle analysis
analytical position, 96, 97i, 99, 100i
description of, 94
displacement diagram, 101–106, 101i–105i
graphical position, 94–96, 94i–96i
Cycloidal motion, follower motion scheme,
230–236, 231t–232t, 231i–236i
Cylinders, actuator type, 4
Cylindrical cams
analytical profile design, 250
description of, 224, 224i, 362
graphical profile design, 249–250, 250ii
D
D’Alembert’s principle, 351
Dedendum, 260i, 260
Degree of freedom
beer crusher computation, 10i, 10–11
description of, 8
equation for, 74
four-bar mechanism calculation, 19, 19i
lift table computation, 15–16, 15i–16i
mechanism types, 8, 8i
outrigger computation, 13–14, 13i–14i
shear press computation, 11–12, 11i–12i
toggle clamp computation, 9i, 9–10
Degree of freedom mechanical press, 17–18,
17i–18i
Diametral pitch
gear terminology, 261
spur gear selection, 273–279, 273t, 276i, 278i
Differential screw, description of, 322–323,
322i–323i, 326
Disk cam profile design
analytical method, 242–249
design limitations, 241–242, 242i
flat-faced follower, 239–240, 239i
graphical features, 237i, 237
in-line knife-edge follower, 238i, 237–238
in-line roller follower, 238i, 238
offset roller follower, 239, 239i
pivoted roller follower, 240–241, 240i
Disk cams, 223–224, 224i
Displacement
analytical method, 79–81, 80i
analytical summary problems, 101i–105i, 106
description of, 74
general summary problems, 101, 101i–105i
and linear velocity, 123
graphical driver analysis, 74i, 74–75
graphical problems, 76–78, 76i, 78i–79i, 80
graphical slave links analysis, 75–76, 75i, 76i
graphical summary problems, 101–106,
101i–105i
kinematic analysis, 2
point of interest, 4
types of, 73
vector, 43
Working Model problems, 101i–103i, 105i,
107–108
Displacement diagrams. See also Cam follower
displacement diagrams
cycle position analysis, 98–99, 99i–100i
summary problems, 101i–103i, 105i, 107
velocity curves, 155, 156i, 157–158, 158i
Double crank, 20, 19t, 20i
Double enveloping worm gear set, 284, 285i
Double rocker, 20, 19t, 20i
Drafting
as technique, 24
vector analysis, 43–44
Driver, 98
Driver link
mechanism analysis, 73
position analysis, 74i, 74–75
Driver point, 73
372 Index
Drivers, 12–13, 15
Drum cam, 224, 224i
Dynamic Analysis of Dynamic Systems (DADS),
dynamic analysis program, 31
Dynamic equilibrium, 328
Dynamic force analysis
design questions, 2
purpose of, 344
static force analysis, 343, 343i
and static equilibrium, 328
strategy for, 31
Dynamic force analysis programs, 24
E
Eccentric crank, 14, 14i
Efficiency, 321
Elastic parts, 2
Electric motors, 12
Engines, actuator type, 4, 12
Enveloping worm gear teeth, 284, 285i
Epicyclic train, 288–293, 289i
Equilibrium, 333–338, 334i–337i
Equivalent linkage, 201
F
Face width, 260i, 260
Fine pitch, 315, 316t
Flat belt, 300, 301i
Flat-faced follower
analytical profile design, 248
description of, 224i, 225
profile design, 239–240, 239i
Floating link
relative acceleration analysis, 191i,
191–192, 193i–194i, 195–196
relative acceleration summary problems,
210, 210i
relative velocity method, 132–135, 133i–134i
Follower, 19. See also Cam followers
Follower motion, 224, 224i
Follower position, 224–225, 224i
Follower shape, 224i, 225
Foot-pound, 328–329
Force
definition of, 328
screw mechanisms, 320i–321i, 320–322
summary problems, 341, 341i
vector, 43
Force analysis. See also Dynamic force analysis,
Static force analysis
and acceleration, 170
machine design, 1
Formula, spreadsheets, 215–218, 217i–218i
Four-bar linkage, 87
Four-bar mechanisms
algebraic solutions, 142, 190–191
categories of, 19t, 19–20
circuits of, 87, 87i
coupler two–point synthesis, 119i, 118–119
description of, 19, 19i
Grashof’s theorem, 19
motion classification, 20–21, 21i, 29, 29i
nomenclature, 19
three-point synthesis, 119, 119i
transmission angle, 93–94, 94i
user-written programs, 221i, 221–222
Working Model tutorial, 32–37, 33i–34i, 36iFrame
definition of, 2
four-bar mechanism, 19
kinematic diagram, 8
Free-body diagrams, 331–333, 331i–333i
Friction
coefficients of, 339, 339t
force analysis, 1
screw mechanisms, 320
Friction force, 339
Full joints, 3, 3i
G
Gear joint, 3, 3i, 5t–6t
Gear kinematics
gear function, 271–273, 271i–272i, 293
Gear mesh relationship
backlash, 270–271
center distance, 266–267, 266i
contact ratio, 267–268
interference, 268–269, 268t
operating pressure angle, 271
undercutting, 269–270, 270i
Gear rack, 259, 259i, 262, 279
Gear selection, 294
Gear standardization, 264–266, 264t
Gear trains
description of, 286–288, 286i
design summary problems, 296
summary problems, 295i–296i, 295–296
Gear-driven mechanisms, summary
problems, 296, 296i
Gears
description of, 258–259, 258i–259i
terminology, 260i, 260–262, 261t, 262i
types of, 259–260, 259i, 284
General triangles, 46–48, 47i, 48i
Geneva mechanism, 250–252, 250i, 252i, 255
Graphical analysis
cam follower displacement diagrams
summary problems, 252–253
cycle position, 94–96, 94i–96i
cylindrical cam profile design, 250, 250i
disk cam profile design, 237–242, 237i–242i
disk cam profile design summary problems,
254i–255i, 254–255
displacement, 74–79, 74i–79i
displacement diagrams summary
problems,102i–105i, 107
displacement summary problems, 101–106,
101i–105i
driver link displacement, 74i
instant center location summary problems,
162i–164i, 165
instant center method, 123, 149–152,
150i, 152i
instant center method summary problems,
162i–164i, 166
limiting positions, 88i, 87–88
mechanism analysis, 23–24
relative acceleration analysis, 181–187,
182i–183i, 185i–186i
relative acceleration summary problems,
208–209, 208i–209i
relative velocity method, 130–137,
130i–131i, 133i–136i
relative velocity method summary
problems, 162–164, 162i–164i
slave links displacement, 75–76, 75i–76i
vector addition, 48–50, 49i–50i
vector magnitudes, 63–65, 63i–65i,
70–71, 70i–71i
vector subtraction, 55–57, 55i–57i
Graphical differentiation
acceleration curves, 202–203, 203i
velocity curves, 157i, 157
velocity curves summary problems,
162i–164i, 167
Graphical disk cam profile design
features of, 237i, 237
flat-faced follower, 239–240, 239i
in-line knife-edge follower, 238i, 237–238
in-line roller follower, 238i, 238
offset roller follower, 239, 239i
pivoted roller follower, 240–241, 240i
Grashof’s theorem, 19
Gruebler’s equation
description of, 8
exceptions to, 18
special cases, 16–18, 16i–18i
Gyration radius, 348
H
Half joint, 3, 3i
Harmonic motion, 228–230, 228t–229t,
229i–230i
Helical gear kinematics, 280–282, 281i,
281t–282t
Helical gears, 259, 259i, 294–295
Helix angle, 280, 281i
Herringbone gears, 259, 259i
Higher order joint, 3, 3i
Hinge joint, 3, 3i
Home position, 237, 237i
Hydraulic cylinders, 13i, 12–13
Hydraulic motors, 12
I
Idler gears, 288i, 288
Idler pulley, 301
In-line follower, 225, 224i
In-line knife-edge follower, 238i, 237–238
In-line roller follower
analytical profile design, 245–247, 245i, 247i
graphical profile design, 238i, 238
In-line slider-crank
closed-form analysis, 81–83, 81i–82i
machine design, 113–114, 114i
Inch-pound, 329
Included angle
screw efficiency, 321
thread feature, 314, 314i
Inertia, 170, 328
Inertia-force method of dynamic
equilibrium, 351
Inertial forces
description of, 350–355, 351i–352i, 354i
summary problems, 362, 362i
Inertial torques
description of, 355–361, 355i–357i, 359i
summary problems, 362–363, 362i–363i
Input link, 19
Instant center, 142, 142i
Instant center diagram, 144–145, 145i
Instant center method
Index 373
analytical velocity method, 123,
152–154, 153i
analytical velocity method summary
problems, 162i–164i, 166–167
graphical velocity method, 123, 149–152,
150i, 152i
graphical velocity method summary
problems, 162i–164i, 166
Instant centers
locating, 142–149, 143i–149i, 146t, 148t
summary problems, 162i–164i, 165–166
Instantaneous center of rotation, 142
Interference, 268–269, 268t
Internal angle
triangle addition problem, 51
triangle subtraction problem, 57–58, 58i
Internal gears, 259, 259i
International Organization for
Standardization (ISO)
force unit, 328
metric threads, 315
moment unit, 329
Inverted tooth/silent chain, 306i, 307
Involute tooth profile, 262–264, 262i, 263i
J
Joint, definition of, 3, 3i
Joints
coincident, 16i, 16–17
commonly used, 14–15
K
Kennedy’s theorem, instant centers,
144–146, 147
Kinematic analysis, 1i, 2, 3
Kinematic diagram
four-bar mechanism, 19, 19i
manual water pump, 22
symbol system, 4, 5t–6t
Kinematic diagram problems
beer crusher, 10i, 10–11
lift table, 15i–16i, 15–16
mechanical press, 17i–18i, 17–18
nose wheel assemble, 20–21, 21i
outrigger, 13–14, 13i–14i
shear presses, 6–7, 6i–7i, 11–12, 11i–12i
sketching diagrams, 25–28, 25i–28i
toggle clamp, 9i, 9–10
vice grip, 7, 7i
Kinematic inversion, 8
Kinematics, 2
Knife-edge follower
analytical profile design, 242–244, 243i–244i
description of, 224i, 225
L
Law of cosines, oblique triangles, 46
Law of sines, oblique triangles, 46
Lead, 315–316
Lead angle
screw threads, 316
thread feature, 314, 314i
worm gears, 284, 285i
Limiting positions
analytical analysis, 91–93, 92i
definition of, 87, 88iLimiting positions (Continued)
graphical analysis, 88i, 87–88
graphical analysis problems, 88–91, 88i–90i
summary problems, 101i–105i, 106–107
Line of center, 149, 150i
Line of contact, 262, 262i
Line of proportion, 149, 150i
Linear acceleration, 170–173
Linear cam, 224, 224i
Linear displacement, 73
Linear motion, 125i, 124–125
Linear velocity
and angular velocity, 126–127, 127i
definition of, 123
general point, 124, 124i
rectilinear points, 124i, 123–124
Link, angular position, 72
Linkage acceleration. See also Timing charts
Linkage, definition of, 2
Linkage velocity analysis. See also Timing charts
Links
acceleration analysis, 170, 173–174, 210, 210i
angular velocity, 125–126, 126i
commonly used, 14
definition of, 2
four-bar mechanism tutorial, 32–33, 33i
relative velocity method, 130i, 130–135,
131i, 133i–134i
resizing, 33
slider-crank mechanism tutorial, 37–38, 38i
types of, 3
Locked mechanism, 8, 8i
Long and short addendum system, 269
Lowering a load (screw drive), 321
Lubrication, chain drive kinematics, 309
M
Machine design
crank-shaper, 117–118, 117i
crank-rocker, 115, 116i, 117, 120
slider-crank ratio, 113–115, 114i–115i, 120
three point synthesis, 119, 119i, 121
time ratio problems, 109–110, 120
two position links, 118–121, 118i–119i
Machines, 1
Magnitude, 73, 73i
Magnitude direction
triangle addition, 52
triangle subtraction, 57, 58i
Major diameter, 314, 314i
Manual force, 13
Mass, 344, 361–362, 361i–362i
Mass moment of inertia
basic shapes, 346, 347i, 347t, 348
composite bodies, 349i, 349–350
description of, 346, 346i
experiential determination, 350, 350i
parallel axis theorem, 348i, 348–349
radius of gyration, 348
summary problems, 361–362, 361i–362i
Mechanism
basic components of, 2–4, 3i
definition of, 1–2
degrees of freedom computation, 74
motion analysis, 73
phases of, 80
vectors, 43
Mechanism analysis, 2, 23
Metric thread, 314–315, 315i, 317t
Minor diameter, 314, 314i
Miter gears, 260, 259i, 283
Mobility (M)
equation, 8
equation exceptions, 18
special cases, 16–18, 16i–18i
Mobility (M) calculation
can crusher, 11
four-bar mechanism, 19
graphical displacement analysis, 76
lift table, 16
manual water pump, 22
mechanical press, 17–18
outrigger, 14
shear press, 12
sketching diagrams, 25i–29i, 29
toggle clamp, 9–12, 14
Module, 261, 261t
Moment
description, 328–331, 329i–330i
summary problems, 341, 341i
Moment of inertia
basic shapes, 346–348, 347i, 347t
composite bodies, 349i, 349–350
description of, 346, 346i
experiential determination,
350, 350i
parallel axis theorem, 348i, 348–349
radius of gyration, 348
summary problems, 361–362, 361i
Motion
laws of, 331, 350
mechanism analysis, 1, 1i, 73
Motor
actuator types, 4
four-bar mechanism tutorial, 35–36
slider-crank mechanism tutorial, 41
Multiple threads, 315–316, 317i
Multiple-strand roller chain, 306, 306i
Multi-strand chains, 307, 307t
Multi-V-belt, 300, 301i
N
Newton, force magnitude unit, 328
Newton, Sir Isaac, 170, 331
Normal acceleration
acceleration analysis, 174–177,
175i–176i
description of, 173, 173i
summary problems, 206–207, 207i
Normal circular pitch, 281, 281i
Normal diametral pitch, 281
Normal force, 339
Normal module, 281
Normal pressure angle, 281
Normal section, 281, 281i
Numerical differentiation
acceleration curves, 204–205, 205i
velocity analysis, 159–160, 160i
O
Oblique triangle, 46–48, 46i–48i
Offset follower, 225, 224i
Offset roller follower
analytical profile design, 248
graphical profile design, 239, 239i
Offset sidebar roller chain, 306i, 307
374 Index
Offset slider-crank, 221i, 221
closed-form analysis, 84–87, 84i–85i
machine design, 114–115, 115i
Off-set slider crank Mechanism, 221i, 221
Open, 32
Open-loop linkages, 8, 8i
Operating pressure angle, 271
Output link, 19
P
Parallel axis theorem, 248i, 348–349
Parallelogram mechanisms, 22, 23i
Phase, 94
Pin, 3, 3i
Pin joint
kinematic diagram symbol, 5t
four-bar mechanism tutorial, 33–35, 34i
slider-crank mechanism tutorial, 38–41, 40i
Pin-in-a-slot joint, commonly used, 14, 15i
Pinion, 266, 266i. See also Gear rack
Piston, 3, 3i
Pitch
thread features, 315, 315i
worm gears, 284, 285i
Pitch circle, 260, 260i, 262, 262i
Pitch curve, 237, 237i
Pitch diameter
belt drive, 301i–302i, 302–303
chain drive, 308, 308i
gear terminology, 260, 260i
thread feature, 314, 314i
Pitch line
gear terminology, 262, 262i
spur gear kinematics, 271, 271i
Pitch point, 260
Pivot link, 118i, 118
Pivoted followers, 224, 224i
Pivoted roller follower
analytical profile design, 249i, 248–249
profile design, 240–241, 240i
Planar mechanism, 2
Planet gear, 288, 289i
Planetary gear analysis
equation, 291–292
summary problems, 292–293
superposition, 289
summary problems, 289–291
Planetary gear trains
description of, 288–293, 289i, 290t–291t, 291i
summary problems, 297, 297i
Plate cams, 224, 224i
Pneumatic cylinders, 13i, 12–13
Point (P), 73i, 72–73
Point of interest, 4
Point of interest path, 37, 37i
Point position measurement, 36–37
Points
linear acceleration, 173
linear velocity, 124, 124i
relative acceleration analysis, 274, 191–196,
191i–194i
relative acceleration summary problems,
210, 210i
Points/floating link, 132–135, 133i–134i
Points/multiple, relative velocity method,
135–137, 135i–136i
Points/one link, relative velocity method,
130–132, 130i–131iPoints of interest
four-bar mechanism tutorial, 33, 34i
slider-crank mechanism tutorial, 55i
Position, 2, 72
Position analysis
analytical displacement, 80i, 80–81
graphical displacement, 74–76, 74i–76i
graphical displacement problems,
76–79, 76i–79i
in-line slider-crank, 81, 81i
limiting positions, 91–93, 92i
offset slider crank, 84, 84i
purpose of, 72i, 72
Position vector, 73i, 72
Pound, 328
Pressure angle
description of, 241, 241i
gear terminology, 262, 262i
spur gear selection, 274–279, 276i, 278i
Primary centers
locating problems, 145–149, 145i–149i, 146t,
148t
rules of, 203i, 143–144, 143i–144i
Primary joints, 3, 3i
Prime circle, 237, 237i
Prismatic joint, 3, 3i
Pulleys, 301i, 301, 301t
Pythagorean theorem, 45
Q
Quick-return mechanisms, 23, 23i
R
Rack, 259, 259i, 279
Rack and pinion kinematics, 279–280, 280i, 294
Radian, description of, 125–126
Rectilinear points
linear acceleration, 170–171
linear velocity, 123–124, 124i,
Rectilinear translation, 130–132, 130i–131i
Relative acceleration
components, 179–181, 180i, 197–201,
197i–200i
description of, 177–179, 178i, 179t
summary problems, 207i, 207–208
Relative acceleration analysis
analytical method, 188i, 188–190, 190t
analytical summary problems, 208i–209i,
209–210
graphical method, 181–187, 182i–183i,
185i–186i
graphical summary problems, 208–209,
208i–209i
Relative displacement, 317
Relative motion
definition of, 177
description of, 128, 177
Relative velocity, 128–129, 128i, 129i
Relative velocity method
analytical method, 137–141, 138i, 140i
analytical method summary problems,
162i–164i, 164–165
graphical analysis, 130–137, 130i–131i,
133i–136i
graphical analysis summary problems,
162–164, 162i–164i
velocity analysis, 123, 137–141, 138i, 140i
velocity image, 137, 137i
Resultant
definition of, 49
graphical addition problems, 49, 49i, 50
graphical subtraction problem, 56–57, 57i
Resultant components, 53–55, 54i
Resultant force, summary problems, 341, 341i
Resultant magnitude
triangle addition problem, 51
triangle subtraction problem, 58, 58i
Reversible gearset, 285
Revolute joint, 3, 3i
Richardson method (numerical differentiation)
acceleration curves, 204
velocity curves, 159
Right triangle, 44–46, 44i–46i
Ring gear, 288, 289i
Rocker, 3i, 4
Rocker arm link, 4
Roller chain, 306, 306i
Roller follower, 224i, 225
Rotation
instantaneous center of, 142, 142i
kinematic analysis, 2
relative velocity method, 130–132, 130i–131i
S
Scalar quantities, 43
Scotch Yoke mechanism, 23, 23i
Screw actuators, 13
Screw forces/torques, 320–322, 320i–321i, 326
Screw joints, 15, 15i
Screw kinematics, 316–320, 318i–320i
Screw mechanisms, 314
Screw thread, 315, 314i–315i, 323–324
Screw-driven acceleration, 326, 324i–325i
Screw-driven displacement, 324–325, 324i–325i
Screw-driven velocity, 325–326, 324i–325i
Self-locking, 316
Serpentine drives, 303, 303i
Servomotors, 12
Shaft angle, 283, 283i
Sheaves, 301i, 301, 301t
Simple link, 3, 3i, 5t
Simulation
four-bar mechanism, 32–37, 33i–37i
slider-crank mechanism tutorial, 37–41,
38i–40i
Sine, 44, 46
Sketching, practice problems, 25–28, 25i–28i
Slave links, 75–76, 75i–76i
Slider-crank
transmission angle, 93–94, 94i
Slider joint, symbol, 6t
Slider-crank mechanisms
algebraic solutions, 142, 190–191
description of, 22
limiting positions, 88i
machine design, 113–115, 114i–115i
summary problems, 120
Working Model tutorial, 37–41, 38i–40i
Sliding friction force, 339t, 339i–340i, 339–341
Sliding joint, 3, 3i
Sliding link, 38, 38i–39i
Slot joints, 38, 39i
Slug, derivation of, 344
Software. See Computers methods/programs
Solenoids, actuator type, 4
Speed, 2
Index 375
Spherical-faced follower, description of,
224i, 225
Spreadsheets
acceleration curves, 205i
cycle position analysis, 97, 98i
cycloidal motion, 235i
displacement curve, 155, 156i
displacement diagram, 100i
general description, 215–220, 215i–220i
in-line roller follower design, 247i
knife-edge follower design, 244i
mechanism analysis technique, 24
summary problems, 222
velocity analysis, 160i
Sprocket, 307, 307i, 308t
Spur gear geometry, summary problems, 293
Spur gear kinematics
gear function, 271–273, 271i–272i
summary problems, 293
Spur gear selection
diametral pitch, 273–279, 273t, 276i, 278i
pressure angle, 274–279, 276i, 278i
set center distance summary problems, 294
teeth number, 274–279, 276i, 278i
Spur gears
gear type, 259, 259i
terminology, 260i, 260–262, 261t
Square thread, 314–315, 315i
Static equilibrium
conditions of, 333
definition of, 328
Static machine forces, summary problems,
341–343, 341i–343i
Straight-line mechanisms, 22
Peaucellier-Lipkin linkage, 22i
Watt linkage, 22i
Stroke, 88i, 88
Stub teeth, 269
Sun gear, 288, 289i
Superposition method, 289
Swing arm followers, 224, 224i
Synthesis, 109
T
Tangent, right triangle, 44
Tangential acceleration
acceleration analysis, 174–175
description of, 173, 173i, 175–177, 176i
summary problems, 206–207, 207i
Tangential velocity, 126
Teeth. See also Involute tooth profile
chain drive, 308, 308i
gear terminology, 260–262
spur gear selection, 273–279, 274t–275t,
276i, 278i
worm gears, 284, 285i
Thread features, 314, 314i
Thread forms, 314–315, 315i, 316t–317t
Thread number, 315–316, 317i
Three-point synthesis, machine design, 119,
119i, 121
Throw angle, 115
Time ratio, 109–110, 120
Timing belt, 301, 301i
Timing charts
problems, 112–113
uses of, 110–111, 111i
Tip-to-tail method, 48Torque
definition of, 328, 329i
screw mechanisms, 320–322, 320i–321i
Total acceleration, 175–177, 176i
Trace, 101
Trace point, 237, 237i
Translating followers, 224, 224i
Transmission angle
definition, 93
mechanical advantage, 93
Transverse section, 281, 281i
Triangles
summary problems, 67–69, 67i–68i
trigonometric relationships, 44, 44i
types of, 44, 46
vector addition, 50–51, 51i
vector subtraction, 57–60, 58i–60i, 59t
Trigonometry, 44
Triple rocker, 19t, 20, 20i
Truss, 8, 8i
Two-armed synchro loader, 4, 5t
Two-force member, 333–338, 334i–337i
Two-point synthesis
coupler of four-bar mechanism, 119i, 118–119
design class, 118
pivot link, 118–119, 118i–119i
single pivot summary problems, 120–121
two pivots summary problems, 121
U
Undercutting, 269–270, 270i
Unified thread, 314–315, 315i, 316t
United States Customary System
force unit, 328
mass/weight, 344
moment unit, 328–329
threads per inch, 314
V
V-belt, belt type, 300–302, 301i–302i
Vector analysis
analytical magnitude determination, 66–67,
66i,
66t, 71, 71i
component addition, 53–55, 54i, 54t
component subtraction, 59–60, 59i–60i, 59t
graphical addition, 48–50, 49i–50i
graphical magnitude determination, 63–65,
63i–65i
graphical subtraction, 55–57, 55i–57i
triangle addition, 50–51, 51i, 53–55,
54i, 54t, 69i, 69
triangle subtraction, 58i, 57–58
Vector components, 52i, 52
Vector diagram
graphical addition problems, 49–50,
49i–50i
graphical subtraction problems, 55–56, 56i
magnitude determination, 65, 63i–65i
triangle addition problem, 51
triangle subtraction problem, 58–59, 58i
Vector equations, 60, 60i
analytical magnitude determination,
66–67, 71
application of, 62
formation of, 60–62, 61i–62i
graphical magnitude determination,
63–65, 70–71
subtraction, 59
Vector magnitude
analytical determination, 66–67, 66i, 66t,
71, 71i
graphical determination, 63–65, 63i–65i,
70–71, 70i–71i
Vector problems
analytical addition, 51–55, 51i–52i,
54i, 54t, 69i, 69
analytical magnitude determination, 66–67,
66i, 66t, 70–71, 70i–71i
analytical subtraction, 57–60, 58i–60i, 59t,
69i, 70
equations, 61–62, 70, 70i
graphical addition, 49–50, 49i–50i, 69i, 69
graphical magnitude determination, 63–65,
63i–64i, 70i–71i, 70–71
graphical subtraction, 55–57, 55i–57i, 69i, 69
triangle addition, 51i, 51, 53
triangle subtraction, 59–60, 59i–60i, 59t
Vectors
addition methods, 43, 48–55, 48i–52i, 54i, 54t
mechanism characteristics, 43
oblique/general triangles, 46–48
right triangle, 44–46, 44i
subtraction methods, 55–60, 55i–60i, 59t
triangle types, 44–48, 44i–48i, 47i–48i
Velocity
kinematic analysis, 2
point of interest, 4
summary general problems, 161, 161i
summary relative problems, 162, 162i
vector property, 43
Working Model, 162i–164i, 168
Velocity analysis
algebraic solutions, 142
analytical methods, 137–141, 138i, 140i
description of, 123
graphical methods, 130–137,
130i–131i, 133i–136i
376 Index
graphical methods summary problems,
162–164, 162i–164i
instant center analytical method,
123, 152, 153i
instant center graphical analysis, 123,
149–152, 150i, 152i
Velocity curves
analytical summary problems, 162i–164i,
167–168
description of, 155–157, 156i
graphical differentiation, 157–158, 157i–158i
graphical summary problems, 162i–164i, 167
numerical differentiation, 159–161, 160i
Velocity image, 137, 137i
Velocity profile
acceleration, 171–172, 172i
linear motion, 125i, 124–125
Velocity ratio
belt drive kinematics, 303
chain drive kinematics, 309
spur gear kinematics, 271–273, 271i–272i
Volume, 323
Volumetric acceleration, 323
Volumetric flow, 323
W
Weight, 344
Whole depth, 260
Windshield wiper system, design concept, 1, 1i
Wipe pattern, components, 1
Working Model software
acceleration, 208i–209i, 213
computer simulation software, 31
displacement problems, 101i–105i,
107–108
four-bar mechanism tutorial, 32–37,
33i–37i
practice problems, 41–42, 41i–42i
purchase information, 32
slider-crank mechanism, 37–41, 38i–40i
velocity problems, 162i–164i, 168
Worm, 284
Worm gear kinematics, 284–286, 285i
Worm gears, 259i, 260, 295
Worm pitch diameter, 284, 285i
Worm wheel, 284
X
X–axis
angle addition, 53
angle subtraction, 59t
component determination, 66, 66t
rotational equation, 15

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