اسم المؤلف
Harold Josephs, Ronald L. Huston
التاريخ
25 أغسطس 2021
المشاهدات
236
التقييم
(لا توجد تقييمات)

Dynamics of Mechanical Systems
Harold Josephs, Ronald L. Huston
Contents
Chapter 1 Introduction 1
1.1 Approach to the Subject 1
1.2 Subject Matter .1
1.3 Fundamental Concepts and Assumptions .2
1.4 Basic Terminology in Mechanical Systems 3
1.5 Vector Review .5
1.6 Reference Frames and Coordinate Systems .6
1.7 Systems of Units .9
1.8 Closure .11
References .11
Problems .12
Chapter 2 Review of Vector Algebra 15
2.1 Introduction .15
2.2 Equality of Vectors, Fixed and Free Vectors 15
2.4 Vector Components 19
2.5 Angle Between Two Vectors .23
2.6 Vector Multiplication: Scalar Product .23
2.7 Vector Multiplication: Vector Product 28
2.8 Vector Multiplication: Triple Products 33
2.9 Use of the Index Summation Convention .37
2.10 Review of Matrix Procedures .38
2.11 Reference Frames and Unit Vector Sets 41
2.12 Closure .44
References .44
Problems .45
Chapter 3 Kinematics of a Particle 57
3.1 Introduction .57
3.2 Vector Differentiation 57
3.3 Position, Velocity, and Acceleration 59
3.4 Relative Velocity and Relative Acceleration 61
3.5 Differentiation of Rotating Unit Vectors 63
3.6 Geometric Interpretation of Acceleration .66
3.7 Motion on a Circle .66
3.8 Motion in a Plane .68
3.9 Closure .71
References .71
Problems .71
Chapter 4 Kinematics of a Rigid Body .77
4.1 Introduction .77
4.2 Orientation of Rigid Bodies 774.3 Configuration Graphs 79
4.4 Simple Angular Velocity and Simple Angular Acceleration 83
4.5 General Angular Velocity 85
4.6 Differentiation in Different Reference Frames 87
4.7 Addition Theorem for Angular Velocity 90
4.8 Angular Acceleration .93
4.9 Relative Velocity and Relative Acceleration of Two Points
on a Rigid Body 97
4.10 Points Moving on a Rigid Body 103
4.11 Rolling Bodies .106
4.12 The Rolling Disk and Rolling Wheel 107
4.13 A Conical Thrust Bearing .110
4.14 Closure .113
References .113
Problems .114
Chapter 5 Planar Motion of Rigid Bodies — Methods of Analysis 125
5.1 Introduction .125
5.2 Coordinates, Constraints, Degrees of Freedom 125
5.3 Planar Motion of a Rigid Body 128
5.3.1 Translation .129
5.3.2 Rotation 130
5.3.3 General Plane Motion 130
5.4 Instant Center, Points of Zero Velocity .133
5.5 Illustrative Example: A Four-Bar Linkage .136
5.6 Chains of Bodies .142
5.7 Instant Center, Analytical Considerations .147
5.8 Instant Center of Zero Acceleration 150
Problems .156
Chapter 6 Forces and Force Systems 163
6.1 Introduction .163
6.2 Forces and Moments 163
6.3 Systems of Forces .165
6.4 Zero Force Systems 170
6.5 Couples 170
6.6 Wrenches 173
6.7 Physical Forces: Applied (Active) Forces .177
6.7.1 Gravitational Forces .177
6.7.2 Spring Forces .178
6.7.3 Contact Forces .180
6.7.4 Action–Reaction 181
6.8 First Moments .182
6.9 Physical Forces: Inertia (Passive) Forces 184
References .187
Problems .187
Chapter 7 Inertia, Second Moment Vectors, Moments and Products of Inertia,
7.1 Introduction .199
7.2 Second-Moment Vectors 1997.3 Moments and Products of Inertia .200
7.5 Transformation Rules 205
7.6 Parallel Axis Theorems 206
7.7 Principal Axes, Principal Moments of Inertia: Concepts 208
7.8 Principal Axes, Principal Moments of Inertia: Example .211
7.9 Principal Axes, Principal Moments of Inertia: Discussion 215
7.10 Maximum and Minimum Moments and Products of Inertia .223
7.11 Inertia Ellipsoid 228
7.12 Application: Inertia Torques .228
References .230
Problems .230
Chapter 8 Principles of Dynamics: Newton’s Laws and d’Alembert’s Principle .241
8.1 Introduction .241
8.2 Principles of Dynamics .242
8.3 d’Alembert’s Principle .243
8.4 The Simple Pendulum .245
8.5 A Smooth Particle Moving Inside a Vertical Rotating Tube .246
8.6 Inertia Forces on a Rigid Body 249
8.7 Projectile Motion 251
8.8 A Rotating Circular Disk 253
8.9 The Rod Pendulum 255
8.10 Double-Rod Pendulum .258
8.11 The Triple-Rod and N-Rod Pendulums .260
8.12 A Rotating Pinned Rod .263
8.13 The Rolling Circular Disk .267
8.14 Closure .270
References .270
Problems .271
Chapter 9 Principles of Impulse and Momentum 279
9.1 Introduction .279
9.2 Impulse 279
9.3 Linear Momentum .280
9.4 Angular Momentum 282
9.5 Principle of Linear Impulse and Momentum 285
9.6 Principle of Angular Impulse and Momentum 288
9.7 Conservation of Momentum Principles .294
9.8 Examples 295
9.9 Additional Examples: Conservation of Momentum 301
9.10 Impact: Coefficient of Restitution 303
9.11 Oblique Impact .306
9.12 Seizure of a Spinning, Diagonally Supported, Square Plate 309
9.13 Closure .310
Problems .311
Chapter 10 Introduction to Energy Methods 321
10.1 Introduction .321
10.2 Work .321
10.3 Work Done by a Couple .32610.4 Power .327
10.5 Kinetic Energy 327
10.6 Work–Energy Principles 329
10.7 Elementary Example: A Falling Object .332
10.8 Elementary Example: The Simple Pendulum .333
10.9 Elementary Example — A Mass–Spring System 336
10.10 Skidding Vehicle Speeds: Accident Reconstruction Analysis .338
10.11 A Wheel Rolling Over a Step .341
10.12 The Spinning Diagonally Supported Square Plate .342
10.13 Closure .344
References (Accident Reconstruction) 344
Problems .344
Chapter 11 Generalized Dynamics: Kinematics and Kinetics 353
11.1 Introduction .353
11.2 Coordinates, Constraints, and Degrees of Freedom 353
11.3 Holonomic and Nonholonomic Constraints .357
11.4 Vector Functions, Partial Velocity, and Partial Angular Velocity .359
11.5 Generalized Forces: Applied (Active) Forces 363
11.6 Generalized Forces: Gravity and Spring Forces .367
11.7 Example: Spring-Supported Particles in a Rotating Tube .369
11.8 Forces That Do Not Contribute to the Generalized Forces 375
11.9 Generalized Forces: Inertia (Passive) Forces .377
11.10 Examples 379
11.11 Potential Energy .389
11.12 Use of Kinetic Energy to Obtain Generalized Inertia Forces .394
11.13 Closure .401
References .401
Problems .402
Chapter 12 Generalized Dynamics: Kane’s Equations
and Lagrange’s Equations .415
12.1 Introduction .415
12.2 Kane’s Equations 415
12.3 Lagrange’s Equations 423
12.4 The Triple-Rod Pendulum 429
12.5 The N-Rod Pendulum .433
12.6 Closure .435
References .436
Problems .436
Chapter 13 Introduction to Vibrations .439
13.1 Introduction .439
13.2 Solutions of Second-Order Differential Equations .439
13.3 The Undamped Linear Oscillator 444
13.4 Forced Vibration of an Undamped Oscillator .446
13.5 Damped Linear Oscillator 447
13.6 Forced Vibration of a Damped Linear Oscillator .449
13.7 Systems with Several Degrees of Freedom 450
13.8 Analysis and Discussion of Three-Particle Movement:
Modes of Vibration 45513.9 Nonlinear Vibrations .458
13.10 The Method of Krylov and Bogoliuboff .463
13.11 Closure .466
References .466
Problems .467
Chapter 14 Stability .479
14.1 Introduction .479
14.2 Infinitesimal Stability .479
14.3 A Particle Moving in a Vertical Rotating Tube .482
14.4 A Freely Rotating Body .485
14.5 The Rolling/Pivoting Circular Disk .488
14.6 Pivoting Disk with a Concentrated Mass on the Rim .493
14.6.1 Rim Mass in the Uppermost Position 498
14.6.2 Rim Mass in the Lowermost Position 502
14.7 Discussion: Routh–Hurwitz Criteria .505
14.8 Closure .509
References .509
Problems .510
Chapter 15 Balancing .513
15.1 Introduction .513
15.2 Static Balancing .513
15.3 Dynamic Balancing: A Rotating Shaft 514
15.4 Dynamic Balancing: The General Case 516
15.5 Application: Balancing of Reciprocating Machines 520
15.6 Lanchester Balancing Mechanism .525
15.7 Balancing of Multicylinder Engines 526
15.8 Four-Stroke Cycle Engines .528
15.9 Balancing of Four-Cylinder Engines .529
15.10 Eight-Cylinder Engines: The Straight-Eight and the V-8 532
15.11 Closure .534
References .534
Problems .534
Chapter 16 Mechanical Components: Cams .539
16.1 Introduction .539
16.2 A Survey of Cam Pair Types 540
16.3 Nomenclature and Terminology for Typical Rotating Radial Cams
with Translating Followers .541
16.4 Graphical Constructions: The Follower Rise Function 543
16.5 Graphical Constructions: Cam Profiles 544
16.6 Graphical Construction: Effects of Cam–Follower Design .545
16.7 Comments on Graphical Construction of Cam Profiles 549
16.8 Analytical Construction of Cam Profiles .550
16.9 Dwell and Linear Rise of the Follower 551
16.10 Use of Singularity Functions 553
16.11 Parabolic Rise Function .557
16.12 Sinusoidal Rise Function .560
16.13 Cycloidal Rise Function 563
16.14 Summary: Listing of Follower Rise Functions 56616.15 Closure .568
References .568
Problems .569
Chapter 17 Mechanical Components: Gears .573
17.1 Introduction .573
17.2 Preliminary and Fundamental Concepts: Rolling Wheels 573
17.3 Preliminary and Fundamental Concepts: Conjugate Action 575
17.4 Preliminary and Fundamental Concepts: Involute Curve Geometry .578
17.5 Spur Gear Nomenclature 581
17.6 Kinematics of Meshing Involute Spur Gear Teeth .584
17.7 Kinetics of Meshing Involute Spur Gear Teeth .588
17.8 Sliding and Rubbing between Contacting Involute Spur Gear Teeth 589
17.9 Involute Rack 591
17.10 Gear Drives and Gear Trains .592
17.11 Helical, Bevel, Spiral Bevel, and Worm Gears 595
17.12 Helical Gears .595
17.13 Bevel Gears 596
17.14 Hypoid and Worm Gears .597
17.15 Closure .599
17.16 Glossary of Gearing Terms .599
References .601
Problems .602
Chapter 18 Introduction to Multibody Dynamics 605
18.1 Introduction .605
18.2 Connection Configuration: Lower Body Arrays .605
18.3 A Pair of Typical Adjoining Bodies: Transformation Matrices .609
18.4 Transformation Matrix Derivatives .612
18.5 Euler Parameters 613
18.7 Transformation Matrices, Angular Velocity Components,
and Euler Parameters 623
18.8 Degrees of Freedom, Coordinates, and Generalized Speeds 628
18.9 Transformations between Absolute and Relative Coordinates 632
18.10 Angular Velocity .635
18.11 Angular Acceleration .640
18.12 Joint and Mass Center Positions 643
18.13 Mass Center Velocities .645
18.14 Mass Center Accelerations 647
18.15 Kinetics: Applied (Active) Forces 647
18.16 Kinetics: Inertia (Passive) Forces .648
18.17 Multibody Dynamics .650
18.18 Closure .651
References .651
Problems .652
Chapter 19 Introduction to Robot Dynamics 661
19.1 Introduction .661
19.2 Geometry, Configuration, and Degrees of Freedom 661
19.3 Transformation Matrices and Configuration Graphs .66319.4 Angular Velocity of Robot Links .665
19.5 Partial Angular Velocities .667
19.6 Transformation Matrix Derivatives .668
19.7 Angular Acceleration of the Robot Links 668
19.8 Joint and Mass Center Position .669
19.9 Mass Center Velocities .671
19.10 Mass Center Partial Velocities 673
19.11 Mass Center Accelerations 673
19.12 End Effector Kinematics 674
19.13 Kinetics: Applied (Active) Forces 677
19.14 Kinetics: Passive (Inertia) Forces .680
19.15 Dynamics: Equations of Motion 681
19.16 Redundant Robots 682
19.17 Constraint Equations and Constraint Forces .684
19.18 Governing Equation Reduction and Solution: Use of Orthogonal
Complement Arrays 687
19.19 Discussion, Concluding Remarks, and Closure 689
References .691
Problems .691
Chapter 20 Application with Biosystems, Human Body Dynamics .701
20.1 Introduction .701
20.2 Human Body Modeling 702
20.3 A Whole-Body Model: Preliminary Considerations 703
20.4 Kinematics: Coordinates .706
20.5 Kinematics: Velocities and Acceleration .709
20.6 Kinetics: Active Forces 715
20.7 Kinetics: Muscle and Joint Forces .716
20.8 Kinetics: Inertia Forces 719
20.9 Dynamics: Equations of Motion 721
20.10 Constrained Motion .722
20.11 Solutions of the Governing Equations .724
20.12 Discussion: Application and Future Development 727
References .730
Problems .731
Appendix I Centroid and Mass Center Location for Commonly Shaped Bodies
with Uniform Mass Distribution .735
Appendix II Inertia Properties (Moments and Products of Inertia)
for Commonly Shaped Bodies with Uniform Mass Distribution 743
Index .75
Index
A
Absolute orientation angles, 142
Acatastatic system, 690
Acceleration, 5, 59, 66
Accident reconstruction, 338
Action–reaction, 181, 241
Active forces, 2, 177, 244, 379, 647, 677, 715
Addition theorem for angular velocity, 90
Amplitude, 440
Angle, 9
Angle between two vectors, 23, 28
Angle of action, 584, 599
Angle of approach, 584, 599
Angle of contact, 584, 599
Angular acceleration, 83, 93, 640
Angular impulse, 280
Angular momentum, 282
Angular speed, 83
Angular velocity, 9, 83, 85, 635, 667
Anticyclic indices, 30
Antisymmetric matrix, 39
Applied forces, 177, 677
Articulation angles, 662, 688
Associative law, 18, 40
Axial pitch, 599
B
Backlash, 582, 599
Balancing, 513
Ball-and-socket joint, 4
Base circle, 578, 599
Basic rack, 591
Bevel gears, 596, 599
Biceps, 716, 717
Biosystem, 701
Boltzmann-Hamel equations, 242, 243
Branching body, 608
Buridan, John, 241
C
Cam-pair, 539
Cam profiles, 544
Cams, 5, 15, 539
Cam systems, 3
Cartesian coordinate system, 6, 8
Center of percussion, 298
Centroid, 735
Chord vector, 60
Circular frequency, 440
Circular pitch, 582, 599
Clearance, 583, 599
Closed loops, 606
Coefficient of restitution, 303
Column matrix, 39
Commutative law, 16, 23
Complete elliptic integral, 462
Components of vectors, 16, 19
Compression stroke, 529
Configuration graphs, 79, 614, 664
Conformable matrix, 39
Conjugate action, 575, 600
Connection configuration, 605
Conservation of momentum, 294, 301
Constrained motion, 722
Constraint equations, 125, 126, 684
Constraint forces, 684
Constraint matrix, 683
Constraints, 3, 125, 353
Contact forces, 180
Contact ratio, 585, 600
Coordinates, 6, 125, 353, 628
Couples, 170
Cross product, 29
Cyclic indices, 30
Cycloidal rise function, 563
Cylindrical coordinate system, 7
D d’
Alembert’s principle, 185, 242, 243, 262, 279, 290
Damped linear oscillator equation, 442
Dedendum, 581, 600
Degrees of freedom, 3, 125, 353, 628, 661
Derivative of transformation matrices, 612, 668754 Dynamics of Mechanical Systems
Determinant, 40
Dextral rotation, 43
Dextral vectors, 30
Diagonal matrix, 39
Diametral pitch, 583
Dirac’s delta function, 554
Directed line segment, 5
Direct impact, 306
Direction cosines, 21
Direction of a vector, 5
Distributive law, 17, 25, 32, 40
Dot product, 23
Double-rod pendulum, 258, 381, 396, 418, 426
Driver, 3, 539
Driver gear, 574
Dwell, 542
Dynamic balancing, 514
Dynamics, 1
Dynamic unbalance, 516
E
Earth rotation effect, 89
Eigen unit vector, 209
Eigenvalue of inertia, 209
Elastic collision, 304
Elements of a matrix, 39
Elliptic integral 460
End effector, 661, 674, 692, 698
Ending body, 607-608
Energy, 9, 10
Equality of vectors, 15
Equivalent force systems, 170
Euler angles, 82
Euler parameters, 613, 707-709
Euler torque, 230
Exhaust stroke, 529
Extremity body, 607
F
Finite segment model, 142
Firing order of internal combustion engines, 530
First integral, 459
First moments, 182
Fixed stars, 244
Fixed vector, 15
Follower, 3, 539
Follower gear, 574
Force, 2, 5, 9, 163
Forced vibration, 446, 449
Forcing function, 442
Four-stroke engines, balancing of, 528
Free-body diagram, 245-246
Free index, 38
Free vector, 15
Frequency, 440
G
Gear drive, 592
Gear glossary, 599-601
Gears, 539, 573
Gear systems, 3
Gear train, 592
Generalized active force, 363
Generalized applied force, 363
Generalized coordinates, 242, 353
Generalized forces, 360
Generalized inertia forces, 360, 377
Generalized passive force, 377
Generalized speeds, 628
General plane motion, 129, 130
Gibbs equations, 243
Gibbs function, 243
Gravity forces, 177
Gripper, 661
Gross-motion model, 702
H
Hamilton’s principle, 242
Helical gears, 595
Helix joint, 4
Holonomic constraint, 357
Human body dynamics, 702
Human body model, 704
Hypoid gears, 597
I
Identity matrix, 39
Imbalance, 513
Impact, 303
Impulse, 279
Impulse-momentum, 242
Incomplete elliptic integral, 462
Inertia, 1, 2, 199, 241
Inertia coefficients, 651
Inertia ellipsoid, 228
Inertia forces, 177, 184, 243, 244, 248, 648, 680, 719
Inertial reference frame, 2, 185, 244
Inertia properties (common shapes), 743
Inertia torque, 228, 249-250
Infinitesimal stability, 479
Inside unit vector, 80
Instant center of zero acceleration, 150
Instant center of zero velocity, 133, 147Index 755
Intake stroke, 529
Integration algorithms, 688
Intermediate body, 608
Inverse matrix, 40
Involute curve, 578
Involute function, 579-581
Involute rack, 591
J
Joint, 3
Joint forces, 716
Jourdain’s principle, 243
K
Kane’s equations, 242, 243, 263, 415, 422, 435
Kane, T. R., 416, 460
Kinematic chain, 4
Kinematics, 1, 2, 57, 241
Kinetic energy, 327
Kinetics, 163, 241
Kronecker’s delta function, 24, 38, 42
Krylov and Bogoliuboff method, 463
L
Lagrange multiplier, 224
Lagrange’s equations, 242, 262, 423, 435
Lagrange’s form of d’Alembert’s principle, 243, 416
Lagrangian, 242, 424
Lanchester balancing mechanism, 525
Law of action and reaction, 717
Law of conjugate action, 576
Linear impulse, 279
Linear momentum, 280
Linear oscillator equation, 246, 439
Linear rise function, 551
Line of action, 578
Line of centers, 585
Line of contact, 584
Logarithmic decrement, 471
Loop closure equation, 137
Lower body arrays, 605
M
Machine, 3
Magnitude of a vector, 5, 15, 27
Mass, 2, 10, 241
Mass center, 177
Mass center locations (common shapes), 735
Mass density, 10
Mass-spring system, 336
Matrix, 39
Matrix inverse, 40
Maximum moment of inertia, 223
Mechanism, 3
Mesh, 575
Minimum moment of inertia, 223
Minimum moments, 175
Minor, 40
Mobile robot, 661
Modes of vibration, 455
Module, 583
Moment, 10, 163
Moment of inertia, 200, 743
Moment of momentum, 282
Momentum, 280
Motion on a circle, 66
Motion on a plane, 68
Multi-arm robot, 662
Multibody system, 258, 605
Muscle forces, 716
N
Natural modes of vibration, 456
Newton, I., 241
Newton’s laws, 2, 241, 285, 287
Nonholonomic constraint, 357
Nonlinear vibrations, 458
Normal pitch, 585
N-rod pendulum, 260, 433
O
Oblique impact, 306
Open-chain system, 606
Open-tree system, 606
Orientation angles, 79
Orientation of a vector, 5, 15
Orientation of bodies, 77, 84
Orthogonal complement arrays, 687, 689
Orthogonal matrix, 40
Orthogonal transformation, 42, 77
Outside unit vector, 80
P
Parabolic rise function, 557
Parallel axis theorem, 206, 207
Parallelogram law, 16
Partial angular velocity, 359, 667
Partial angular velocity array, 639
Partial velocity, 359756 Dynamics of Mechanical Systems
Partial velocity arrays, 651
Particle, 3, 57
Passive forces, 2, 177, 184, 244, 377, 680
Period, 440
Permutation symbol, 30
Perturbation, 479
Phase, 440
Pinion, 539
Pinion gear, 574, 597
Pitch circle, 576
Pitch point, 582
Pivoting, 107
Planar joint, 4
Planar motion, 128
Planetary gear system, 593
Planet gear, 593
Plastic collision, 304
Position, 58
Position vector, 8
Potential energy, 389
Power, 10, 327
Power stroke, 529
Power transmission, 573
Pressure, 10
Pressure angle, 542, 578
Pressure line, 578, 584
Principal axis of inertia, 208, 215
Principal moment of inertia, 208, 209
Principal unit vector, 209
Principle of angular momentum, 289
Principle of linear momentum, 285
Product of inertia, 200, 743
Projectile motion, 251
Projection of a vector, 24, 28, 31
Pure rolling, 107
Pythagorean theorem, 7
R
Reciprocating machines, balancing of, 520
Reduction of a force system, 171
Redundant robots, 661, 684
Reference frame, 3, 6, 41
Relative acceleration, 63, 97
Relative orientation angles, 137, 142
Relative velocity, 61, 97
Resultant, 16, 165
Right-hand rule, 29
Rigid body, 3
Ring gear, 594
Rise of cam follower, 543
Robot, 663
Robot arm, 663
Rod pendulum, 255, 380, 396, 418, 425
Rolling, 106
Rolling circular disk, 267
Rolling disk, 107, 357, 385, 399, 421, 488
Root circle, 581
Rotating pinned rod, 263
Rotating unit vectors, 63
Rotation, 129, 130
Routh-Hurwitz stability criteria, 505
Row–column product of matrices, 39
Row matrix, 39
S
Scalar, 5, 9, 15
Scalar product, 23, 27
Scalar triple product, 33
Screw joint, 4
Second-moment vectors, 199
Sense of a vector, 5, 15
Simple angular velocity, 83, 87, 665
Simple chains, 4
Simple pendulum, 245, 324, 333, 365, 379, 395, 417,
424, 445, 459, 479
Singularity functions, 553
Singular matrix, 39
Sinistral vectors, 30
Sinusoidal rise function, 560
Sliding joint, 4
Sliding vector, 15
Solver, 688
Space, 2, 3
Speed, 63, 64
Spherical coordinate system, 7
Spherical joint, 4
Spiral angle, 597
Spiral bevel gears, 597
Spring forces, 178
Spur gear, 4, 581
Stability, 479
Static balancing, 513
Statics, 1
Stress, 10
Stroke, 528
Substitution symbol, 38
Summation convention, 37
Sun gear, 593
Symmetric matrix, 39
System of forces, 165
T
Tensor, 204
Thrust bearing, 110
Time, 2
Torque, 10, 170
Transformation matrices, 78, 609, 663, 704
Transformation matrix derivatives, 612, 668
Translation, 129
Transmission, 540, 573
Transpose of a matrix, 39Index 757
Triple-rod pendulum, 260, 429
Tzu, Mo, 242
U
Units, 9
Unit vector, 6, 15
Universal joint, 4
Unstable system, 482
V
Vector, 5, 15
Vector characteristics, 5, 57
Vector components, 16, 19
Vector differentiation, 57
Vector multiplication, 23, 28
Vector product, 28, 33
Vector space, 5
Vector subtraction, 17
Vector triple product, 33
Velocity, 5, 10, 59
Vibration, 439
Virtual work, 242
W
Weight, 177
Wheel rolling over a step, 302, 341
Whole-body model, 701, 703
Work, 321
Work-energy, 242
Work-energy principles, 329
Worm gears, 597
Worm wheel, 598
Wrench, 173
Z
Zero force systems, 170
Zero vector, 6, 15

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