كتاب Theory of Machines and Mechanisms

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Theory of Machines and Mechanisms
Fifth Edition
John J. Uicker, Jr.
Professor Emeritus of Mechanical Engineering
University of Wisconsin–Madison
Gordon R. Pennock
Associate Professor of Mechanical Engineering
Purdue University
Joseph E. Shigley
Late Professor Emeritus of Mechanical Engineering
The University of Michigan

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Contents
PREFACE xvii
ABOUT THE AUTHORS xxv
Part 1 KINEMATICS AND MECHANISMS 1
1 The World of Mechanisms 3
1.1 Introduction 3
1.2 Analysis and Synthesis 4
1.3 Science of Mechanics 4
1.4 Terminology, Definitions, and Assumptions 6
1.5 Planar, Spheric, and Spatial Mechanisms 10
1.6 Mobility 12
1.7 Characteristics of Mechanisms 17
1.8 Kinematic Inversion 32
1.9 Grashof’s Law 33
1.10 Mechanical Advantage 36
1.11 References 39
Problems 40
2 Position, Posture, and Displacement 48
2.1 Locus of a Moving Point 48
2.2 Position of a Point 51
2.3 Position Difference Between Two Points 53
2.4 Apparent Position of a Point 54
2.5 Absolute Position of a Point 55
2.6 Posture of a Rigid Body 56
2.7 Loop-Closure Equations 57
2.8 Graphic Posture Analysis 62
2.9 Algebraic Posture Analysis 69
2.10 Complex-Algebraic Solutions of Planar Vector Equations 73
2.11 Complex Polar Algebra 74
2.12 Posture Analysis Techniques 78
2.13 Coupler-Curve Generation 86
viiviii CONTENTS
2.14 Displacement of a Moving Point 89
2.15 Displacement Difference Between Two Points 89
2.16 Translation and Rotation 91
2.17 Apparent Displacement 92
2.18 Absolute Displacement 94
2.19 Apparent Angular Displacement 94
2.20 References 98
Problems 99
3 Velocity 105
3.1 Definition of Velocity 105
3.2 Rotation of a Rigid Body 106
3.3 Velocity Difference Between Points of a Rigid Body 109
3.4 Velocity Polygons; Velocity Images 111
3.5 Apparent Velocity of a Point in a Moving Coordinate System 119
3.6 Apparent Angular Velocity 126
3.7 Direct Contact and Rolling Contact 126
3.8 Systematic Strategy for Velocity Analysis 128
3.9 Algebraic Velocity Analysis 129
3.10 Complex-Algebraic Velocity Analysis 131
3.11 Method of Kinematic Coefficients 135
3.12 Instantaneous Centers of Velocity 145
3.13 Aronhold-Kennedy Theorem of Three Centers 147
3.14 Locating Instantaneous Centers of Velocity 149
3.15 Velocity Analysis Using Instant Centers 153
3.16 Angular-Velocity-Ratio Theorem 156
3.17 Relationships Between First-Order Kinematic Coefficients
and Instant Centers 157
3.18 Freudenstein’s Theorem 160
3.19 Indices of Merit; Mechanical Advantage 162
3.20 Centrodes 164
3.21 References 166
Problems 167
4 Acceleration 180
4.1 Definition of Acceleration 180
4.2 Angular Acceleration 183
4.3 Acceleration Difference Between Points of a Rigid Body 183
4.4 Acceleration Polygons; Acceleration Images 192
4.5 Apparent Acceleration of a Point in a Moving Coordinate System 196CONTENTS ix
4.6 Apparent Angular Acceleration 205
4.7 Direct Contact and Rolling Contact 206
4.8 Systematic Strategy for Acceleration Analysis 212
4.9 Algebraic Acceleration Analysis 213
4.10 Complex-Algebraic Acceleration Analysis 214
4.11 Method of Kinematic Coefficients 216
4.12 Euler-Savary Equation 225
4.13 Bobillier Constructions 230
4.14 Instantaneous Center of Acceleration 234
4.15 Bresse Circle (or de La Hire Circle) 235
4.16 Radius of Curvature of a Point Trajectory Using Kinematic
Coefficients 239
4.17 Cubic of Stationary Curvature 242
4.18 References 249
Problems 250
5 Multi-Degree-of-Freedom Mechanisms 258
5.1 Introduction 258
5.2 Posture Analysis; Algebraic Solution 262
5.3 Velocity Analysis; Velocity Polygons 263
5.4 Instantaneous Centers of Velocity 265
5.5 First-Order Kinematic Coefficients 268
5.6 Method of Superposition 273
5.7 Acceleration Analysis; Acceleration Polygons 276
5.8 Second-Order Kinematic Coefficients 278
5.9 Path Curvature of a Coupler Point Trajectory 285
5.10 Finite Difference Method 289
5.11 Reference 292
Problems 292
Part 2 DESIGN OF MECHANISMS 295
6 Cam Design 297
6.1 Introduction 297
6.2 Classification of Cams and Followers 298
6.3 Displacement Diagrams 300
6.4 Graphic Layout of Cam Profiles 303
6.5 Kinematic Coefficients of Follower 307
6.6 High-Speed Cams 312
6.7 Standard Cam Motions 313x CONTENTS
6.8 Matching Derivatives of Displacement Diagrams 323
6.9 Plate Cam with Reciprocating Flat-Face Follower 327
6.10 Plate Cam with Reciprocating Roller Follower 332
6.11 Rigid and Elastic Cam Systems 350
6.12 Dynamics of an Eccentric Cam 351
6.13 Effect of Sliding Friction 355
6.14 Dynamics of Disk Cam with Reciprocating Roller Follower 356
6.15 Dynamics of Elastic Cam Systems 359
6.16 Unbalance, Spring Surge, and Windup 362
6.17 References 363
Problems 363
7 Spur Gears 369
7.1 Terminology and Definitions 369
7.2 Fundamental Law of Toothed Gearing 372
7.3 Involute Properties 373
7.4 Interchangeable Gears; AGMA Standards 375
7.5 Fundamentals of Gear-Tooth Action 376
7.6 Manufacture of Gear Teeth 381
7.7 Interference and Undercutting 384
7.8 Contact Ratio 386
7.9 Varying Center Distance 388
7.10 Involutometry 389
7.11 Nonstandard Gear Teeth 393
7.12 Parallel-Axis Gear Trains 401
7.13 Determining Tooth Numbers 404
7.14 Epicyclic Gear Trains 405
7.15 Analysis of Epicyclic Gear Trains by Formula 407
7.16 Tabular Analysis of Epicyclic Gear Trains 417
7.17 References 421
Problems 421
8 Helical Gears, Bevel Gears, Worms, and Worm Gears 427
8.1 Parallel-Axis Helical Gears 427
8.2 Helical Gear Tooth Relations 428
8.3 Helical Gear Tooth Proportions 430
8.4 Contact of Helical Gear Teeth 431
8.5 Replacing Spur Gears with Helical Gears 432
8.6 Herringbone Gears 433
8.7 Crossed-Axis Helical Gears 434CONTENTS xi
8.8 Straight-Tooth Bevel Gears 436
8.9 Tooth Proportions for Bevel Gears 440
8.10 Bevel Gear Epicyclic Trains 440
8.11 Crown and Face Gears 443
8.12 Spiral Bevel Gears 443
8.13 Hypoid Gears 445
8.14 Worms and Worm Gears 445
8.15 Summers and Differentials 449
8.16 All-Wheel Drive Train 453
8.17 Note 455
Problems 455
9 Synthesis of Linkages 458
9.1 Type, Number, and Dimensional Synthesis 458
9.2 Function Generation, Path Generation, and Body Guidance 459
9.3 Two Finitely Separated Postures of a Rigid Body (N = 2) 460
9.4 Three Finitely Separated Postures of a Rigid Body (N = 3) 465
9.5 Four Finitely Separated Postures of a Rigid Body (N = 4) 474
9.6 Five Finitely Separated Postures of a Rigid Body (N = 5) 481
9.7 Precision Postures; Structural Error; Chebyshev Spacing 481
9.8 Overlay Method 483
9.9 Coupler-Curve Synthesis 485
9.10 Cognate Linkages; Roberts-Chebyshev Theorem 489
9.11 Freudenstein’s Equation 491
9.12 Analytic Synthesis Using Complex Algebra 495
9.13 Synthesis of Dwell Linkages 499
9.14 Intermittent Rotary Motion 500
9.15 References 504
Problems 504
10 Spatial Mechanisms and Robotics 507
10.1 Introduction 507
10.2 Exceptions to the Mobility Criterion 509
10.3 Spatial Posture-Analysis Problem 513
10.4 Spatial Velocity and Acceleration Analyses 518
10.5 Euler Angles 524
10.6 Denavit-Hartenberg Parameters 528
10.7 Transformation-Matrix Posture Analysis 530
10.8 Matrix Velocity and Acceleration Analyses 533
10.9 Generalized Mechanism Analysis Computer Programs 538xii CONTENTS
10.10 Introduction to Robotics 541
10.11 Topological Arrangements of Robotic Arms 542
10.12 Forward Kinematics Problem 543
10.13 Inverse Kinematics Problem 550
10.14 Inverse Velocity and Acceleration Analyses 553
10.15 Robot Actuator Force Analysis 558
10.16 References 561
Problems 562
Part 3 DYNAMICS OF MACHINES 567
11 Static Force Analysis 569
11.1 Introduction 569
11.2 Newton’s Laws 571
11.3 Systems of Units 571
11.4 Applied and Constraint Forces 573
11.5 Free-Body Diagrams 576
11.6 Conditions for Equilibrium 578
11.7 Two- and Three-Force Members 579
11.8 Four- and More-Force Members 589
11.9 Friction-Force Models 591
11.10 Force Analysis with Friction 594
11.11 Spur- and Helical-Gear Force Analysis 597
11.12 Straight-Tooth Bevel-Gear Force Analysis 604
11.13 Method of Virtual Work 608
11.14 Introduction to Buckling 611
11.15 Euler Column Formula 612
11.16 Critical Unit Load 615
11.17 Critical Unit Load and Slenderness Ratio 618
11.18 Johnson’s Parabolic Equation 619
11.19 References 645
Problems 646
12 Dynamic Force Analysis 658
12.1 Introduction 658
12.2 Centroid and Center of Mass 658
12.3 Mass Moments and Products of Inertia 663
12.4 Inertia Forces and d’Alembert’s Principle 666
12.5 Principle of Superposition 674
12.6 Planar Rotation about a Fixed Center 680CONTENTS xiii
12.7 Shaking Forces and Moments 682
12.8 Complex-Algebraic Approach 683
12.9 Equation of Motion from Power Equation 692
12.10 Measuring Mass Moment of Inertia 702
12.11 Transformation of Inertia Axes 705
12.12 Euler’s Equations of Motion 710
12.13 Impulse and Momentum 714
12.14 Angular Impulse and Angular Momentum 714
12.15 References 724
Problems 725
13 Vibration Analysis 743
13.1 Differential Equations of Motion 743
13.2 A Vertical Model 747
13.3 Solution of the Differential Equation 748
13.4 Step Input Forcing 752
13.5 Phase-Plane Representation 755
13.6 Phase-Plane Analysis 757
13.7 Transient Disturbances 760
13.8 Free Vibration with Viscous Damping 764
13.9 Damping Obtained by Experiment 766
13.10 Phase-Plane Representation of Damped Vibration 768
13.11 Response to Periodic Forcing 772
13.12 Harmonic Forcing 776
13.13 Forcing Caused by Unbalance 780
13.14 Relative Motion 781
13.15 Isolation 782
13.16 Rayleigh’s Method 785
13.17 First and Second Critical Speeds of a Shaft 787
13.18 Torsional Systems 793
13.19 References 795
Problems 796
14 Dynamics of Reciprocating Engines 804
14.1 Engine Types 804
14.2 Indicator Diagrams 811
14.3 Dynamic Analysis—General 814
14.4 Gas Forces 814
14.5 Equivalent Masses 816
14.6 Inertia Forces 818xiv CONTENTS
14.7 Bearing Loads in a Single-Cylinder Engine 821
14.8 Shaking Forces of Engines 824
14.9 Computation Hints 825
Problems 828
15 Balancing 830
15.1 Static Unbalance 830
15.2 Equations of Motion 831
15.3 Static Balancing Machines 834
15.4 Dynamic Unbalance 835
15.5 Analysis of Unbalance 837
15.6 Dynamic Balancing 846
15.7 Dynamic Balancing Machines 848
15.8 Field Balancing with a Programmable Calculator 851
15.9 Balancing a Single-Cylinder Engine 854
15.10 Balancing Multi-Cylinder Engines 858
15.11 Analytic Technique for Balancing Multi-Cylinder Engines 862
15.12 Balancing Linkages 868
15.13 Balancing of Machines 874
15.14 References 875
Problems 875
16 Flywheels, Governors, and Gyroscopes 885
16.1 Dynamic Theory of Flywheels 885
16.2 Integration Technique 887
16.3 Multi-Cylinder Engine Torque Summation 890
16.4 Classification of Governors 890
16.5 Centrifugal Governors 892
16.6 Inertia Governors 893
16.7 Mechanical Control Systems 894
16.8 Standard Input Functions 895
16.9 Solution of Linear Differential Equations 897
16.10 Analysis of Proportional-Error Feedback Systems 901
16.11 Introduction to Gyroscopes 905
16.12 Motion of a Gyroscope 906
16.13 Steady or Regular Precession 908
16.14 Forced Precession 911
16.15 References 917
Problems 917CONTENTS xv
APPENDIXES
APPENDIX A: Tables 919
Table 1 Standard SI Prefixes 919
Table 2 Conversion from US Customary Units to SI Units 920
Table 3 Conversion from SI Units to US Customary Units 920
Table 4 Properties of Areas 921
Table 5 Mass Moments of Inertia 922
Table 6 Involute Function 923
APPENDIX B: Answers to Selected Problems 925
INDEX 935
INDEX
Absolute:
Acceleration, 181
Displacement, 94
Motion, 32
Position, 55
System of units, 572
Velocity, 105
Acceleration:
Absolute, 181
Angular, 183
Apparent, 198
Angular, 183
Average, 180
Components of:
Centripetal component (see Normal, component
of acceleration)
Coriolis component, 199
Normal component, 182, 199
Rolling-contact component, 206
Tangential component, 183, 199
Definition, 180
Difference, 183
Image, 192
Instant center of, 234
Normal component of, 182
Pole, 234
Polygon, 192, 276
Rolling-contact component of, 206
Tangential component of, 183
Action, line of, 377
Actuator, linear, 18
ADAMS (Automatic Dynamic Analysis of
Mechanical Systems), 539
Adams, D. P., 504n
Addendum, 370
Circle, 370
Adjustments, 18
Advance stroke, 24
Advance-to-return ratio, 24
AGMA (American Gear Manufacturers Association),
375, 375n
Air-standard cycle, 811
Alford, H. H., 724n
Algebraic analysis, 213
Acceleration, 213
Dynamic force, 683
Loop-closure cases, 73
Posture, 78, 262
Static force, 569
Velocity, 128, 131
All wheel drive train, 453
Alwerdt, J. J., 421n
American Institute of Steel Construction (AISC), 617
Ampère, A. M., 5, 5n
Analysis:
Dynamic force, 658
Elastic body, 744
Rigid body, 570
Static force, 569
Angular:
Acceleration, 183
Apparent, 205
Bevel gears, 436
Displacement, 94
Impulse, 714
Momentum, 714
Velocity, 106
Apparent, 126
Ratio theorem, 156
Annular gear, 380
ANSI (American National Standards Institute), 76n
Answers to selected problems, 925
ANSYS, 539
Apparent:
Acceleration, 196, 198
Angular, 205
Displacement, 92, 106
Angular, 94
Position, 54
Velocity, 119
Angular, 126
Applied force, 573
Approach, 384
Angle, 384
Arc of, 384
Arc:
of Approach, 384
of Recess, 385
Area, properties of, 921
Area moment of inertia, 613, 615, 663
935936 INDEX
Arm of couple, 574
Aronhold, S. H., 148n
Aronhold-Kennedy theorem, 147
Aronhold theorem, 148n
Articulated arm, 542
Articulated connecting rod, 806
ATAN2(y,x), 76n
Automotive:
All wheel drive train, 453
Cruise-control, 905
Differential, 451
Limited slip, 452
Overhead valve arrangement, 350
Transmission, 404
Average:
Acceleration, 180
Velocity, 105
Axes:
Body-fixed, 524
Collineation, 161, 230
Instantaneous screw, 145n
Principal, 664
Spin, 907
Transformation of inertia, 705
Axial pitch, 447
Axodes, 165n
Back cone, 439
Backlash, 372
Baker, J. E., 561n
Balancing:
Definition, 830
Direct method, 843
Dynamic, 846
Field, 851
of Linkages, 868
Machines:
Mechanical compensation, 850
Nodal-Point, 848
Pivoted-cradle, 846
of Machines, 874
of Multi-cylinder engines, 858
Numeric analysis, 845
Scalar equations, 845
of Single-cylinder engines, 854
Static, 834
Ball, R. S., 145n, 167n
Ball-and-socket joint, 9
Ball’s point, 244
Barrel cam, 298
Base:
Circle:
of Cam, 304
of Gear, 377
Cylinder, 377
Link, 7
Pitch, 379
Basic units, 572
Beer, F. P., 645n, 724n
Bennett, G. T., 561n
Bennett linkage, 510
Berkhof, R. S., 868, 875n
Bernoulli, J., 608
Bevel gear, 427
Angular, 436
Epicyclic trains, 440
Forces on, 604
Spiral, 443
Straight-tooth, 436
Tooth proportions, 440
Zerol, 444
Beyer, R., 39n, 167n, 249n, 504n
Bhat, R. B., 795n
Binormal unit vector, 124
Bistable mechanism, 18
Bobillier constructions, 230
Bobillier theorem, 230
Body-fixed axes, 524
Body guidance, 459
Bohenberger, J. G. F., 917n
Bollinger, J. G., 917n
Bore-to-stroke ratio, 812
Bottema, O., 167n
Bottom dead center (BDC), 856
Branch defect, 483
Bresse circle, 235
Bricard linkage, 511
Bridgman, P. W., 795n
Buckling, 611
Burmester points, 481
Calahan, D. A., 561n
Cam:
Barrel, 298
Base circle, 304
Circle-arc, 312
Conjugate, 300
Constant-breadth, 300
Cylindric, 298
Definition of, 298
Disk, 298
Displacement diagram, 300
Dual, 300
Eccentric, 351
Elastic body, 350
End, 298
Face, 298INDEX 937
Follower:
Curved-shoe, 298
Flat-face, 298
Knife-edge, 298
Offset, 300
Oscillating, 300
Radial, 300
Reciprocating, 298
Roller, 298
Spheric-face, 298
Trace-point, 304
High-speed, 312
Inverse, 298
Motion:
Cycloidal, 302, 314
Dwell, 301
Eighth-order polynomial, 315
Half-return, 320
Half-rise, 319
Kinematic coefficients of, 307
Parabolic, 302, 311
Polydyne, 319
Return, 301
Rise, 300
Simple-harmonic, 302, 314
Uniform, 301
Nomenclature, 298
Plate, 298
Pressure angle, 332
Maximum, 333
Prime circle, 304
Profile, 303
Coordinates, 331
Graphic layout, 303
Radial, 298
Radius of curvature, 328
Rigid body, 350
Roller, size of, 336
Standard motions, 313
Tangent, 312
Types:
Barrel, 298
Circle-arc, 312
Conjugate, 300
Constant breadth, 300
Cylindric, 298
Disk, 298
Dual, 300
Eccentric, 351
End, 298
Face, 298
Inverse, 298
Plate, 298
Radial, 298
Tangent, 312
Wedge, 298
Undercut, 327, 335
Wedge, 298
Capek, K., 541
Cardan joint, 529
Cardan suspension, 905
Card factor, 812
Cartesian coordinates, 49
Cayley, A., 490n
Cayley diagram, 490
Center-distance modification, 394
Center of curvature, 183n, 225
Center of mass, 658
Center of percussion, 682
Center point, 475
Center point curve, 475
Centrifugal governors, 892
Centripetal component of acceleration (see Normal,
component of acceleration)
Centrode, 164
Fixed, 165
Moving, 165
Normal, 227
Tangent, 227
Centroid, 658
Definition, 660
Chace, M. A., 513, 539, 561n
Chace approach:
Loop-closure cases, 513
Posture analysis, 513
Chain, kinematic, 7
Chebychev, P. L., 489
Chebychev linkage, 31
Chebychev spacing, 481
Chen, F. Y., 363n
Chuang, J. C., 561n
Circle-arc cam, 312
Circle point, 474
Circle point curve, 475
Circling-point curve, 242
Circular:
Pitch, 369, 372
Normal, 428
Transverse, 428
Circumscribing circle, 471
Clamping mechanisms, 18
Classification of mechanism, 17
Clausen, W. E., 724n
Clearance, 370, 394
Closed kinematic chain, 7
Closed-loop control system, 894
Coefficient:
of Friction, 592938 INDEX
Coefficient: (continued)
Kinematic:
First-order, 135, 268
Second-order, 216, 278
of Speed fluctuation, 888
of Viscous damping, 745
Cognate linkages, 31, 489
Collineation axis, 161, 230
Complex algebraic analysis:
Acceleration, 213
Dynamic force, 683
Loop-closure cases, 73
Posture, 78
Velocity, 131
Complex polar algebra, 74
Components of acceleration:
Centripetal component (see Normal, component
of acceleration)
Coriolis component, 199
Normal component, 182
Rolling-contact component, 206
Tangential component, 183
Compound-closed chain, 7
Compound gear train, 404
Compression, 811
Ratio, 813
Computer programs, 538
Concurrency, point of, 582
Concurrent forces, 580
Conjugate:
Cams, 300
Points, 225
Profiles, 372
Connecting rod, 807
Articulated, 806
Force, 822
Master, 806
Connectors, 27
Conservation of:
Angular momentum, 717
Momentum, 714
Constant-breadth cam, 300
Constraint, 59
Force, 512, 573
General, 511
Redundant, 512
Contact:
Direct, 126
Gear teeth, 384
Helical gear teeth, 431
Path of, 384
Ratio, 386
Formula, 387
Helical gears
Axial, 431
Face, 431
Normal, 431
Total, 432
Transverse, 431
Rolling, 126
Acceleration, 206
Displacement, 95
Velocity, 126
Control systems, mechanical, 894
Conversion of units:
SI to U.S. customary, 920
U.S. customary to SI, 920
Coordinates, complex, 73
Coordinate systems, 52
Coplanar motion, 10
Coriolis component of acceleration, 199
Correction planes, 838
Costanzo, F., 645n, 724n
Coulomb friction, 592
Counterweight, 871
Couple, 574
Arm of, 574
Characteristics of, 574
Coupler curve, 29
Generation, 86
Synthesis, 485
Coupler point, 285
Couplings, 27
Crane, C., 561n
Crankpin force, 823
Crank-rocker linkage, 34
Advantages of, 460
Limit position of, 34
Spatial, 514
Spheric, 509
Synthesis, 460
Crankshaft, 808
Force, 823
Torque, 824
Crank-shaper linkage, 22
Critical damping, 832
Coefficient of, 832
Critical load, 612
Critical speed, 787
Critical unit load, 615
Crossed-axis helical gears, 433
Pitch diameters of, 433
Crossed posture, 68
Crown gear, 443
Crown rack, 444
Cubic of stationary curvature, 242
Degenerate forms, 244
Curvature, 182
Center of, 125
Radius of, 124INDEX 939
Curved-shoe follower, 298
Curve generator, 29
Curvilinear translation, 91n
Cycloid, definition, 302
Cycloidal cam motion, 302
Cylinder wall force, 823
Cylindric:
Cam, 298
Coordinates, 49
Pair, 10
DADS (Dynamic Analysis and Design
System), 539
D’Alembert, J., 668
D’Alembert principle, 666
Damping:
Coefficient, 745
Viscous, 745
Critical, 832
Factor, 743
Measurement of, 766
Ratio, 832
Viscous, 832
Dead-center posture, 37
Dedendum, 370
Circle, 370
Deformable body, 570
Analysis, 744
Degrees of freedom, 12
Lower Pairs, 9
Multiple, 258
de Jonge, A. E. R., 249n
de La Hire circle, 235
Denavit, J., 9, 39n, 167n, 249n, 489, 504n, 528, 561n
Denavit-Hartenberg parameters, 528
Derived unit, 572
Design, definition of, 297
Diagram:
Displacement, 300
Free-body, 576
Schematic, 7
Diametral pitch, 369
Normal, 429
Transverse, 429
Diesel-cycle engines, 804
Difference:
Displacement, 107
Position, 53
Velocity, 110
Differential, 449
Automotive, 451
All wheel drive train, 453
Limited slip, 452
TORSEN, 453
Worm gear, 453
Chinese, 451
Limited-slip, 453
Mechanism, 450
Screw, 18
Spur gear, 450
TORSEN, 453
Worm gear, 453
Dimensional synthesis, 458
Direct contact, 126
Direction cosines, 49
Disk cam, 298
Displacement, 89
Absolute, 94
Angular, 94
Apparent, 92
Apparent angular, 94
Definition, 89
Diagram, 300
Difference, 89
Virtual, 608
Volume, 813
Disturbance, 760
Transient, 760
Division by complex number, 76
Dobbs, H. H., 453
Double-crank linkage (see drag-link linkage)
Double-helical gear, 433
Double-rocker linkage, 35, 37
Drag-link linkage, 27
Driver, 6
Dual number, 513
Duffie, N. A., 917n
Duffy, J., 561n
Dunkerley’s method, 789
Dwell linkages, 499
Synthesis of, 499
Dwell motion, 301
Dynamic balancing, 846
Dynamic balancing machines, 848
Dynamic equilibrium, 658
Dynamic force analysis, 658
Dynamics:
Cam systems, 351
Definition, 4
Reciprocating engines, 804
Eccentric cam, 351
Eccentricity in cam system, 333
Edge mill, 913
Eighth-order polynomial cam motion, 315
Eisenberg, E. R., 645n
Elastic-body analysis, 744940 INDEX
Elliptical gears, 166
Elliptic-trammel linkage, 623
End effecter, 542
Engine, 804
Bearing loads in single-cylinder, 821
Crank arrangement, 805
Cycle, 804
Diesel-cycle, 804
Firing order, 805
Five-cylinder, 806
Four-cylinder, 859
Indicator, 811
In line, 805
Opposed piston, 806
Otto-cycle, 804
Radial, 807
Shaking force, 824
Single cylinder, 854
Six cylinder, 808
Three-cylinder, 805
Two-cylinder, 858
Types, 804
V-type, 805
Epicyclic gear, 405
Epicyclic gear train types, 407
Formula analysis, 407
Tabular analysis, 417
Equation of motion, 692
Euler’s, 710
Equilibrium, 578
Conditions, 578
Dynamic, 578, 597
Static, 578
Equivalent:
Gear, 430
Mass, 816
Erdman, A. G., 504n, 561n
Error:
Graphic, 482
Mechanical, 482
Structural, 482
Escapements, 18
Graham’s, 19
Euler, L., 4, 4n, 39n, 917n
Euler angles, 524
Euler column formula, 612
Euler equation, 75
Euler-Savary equation, 225, 230
Euler’s equations of motion, 710
Exhaust, 805
Expansion, 811
Extreme positions of crank-rocker linkage, 34
Extreme values of velocity, 161
Face cam, 298
Face gear, 443
Face width:
of Cam follower, 330
of Helical gears, 431
of Worm gear, 448
Fagerstrom, W. B., 851n
Feedback control system, 894
Ferguson, J., 419n
Ferguson’s paradox, 419
Fillet, 370
Fine adjustments, 18
Finite difference method, 287
Finitely separated postures of a rigid body, 460
Center point, 468
Circle point, 474
Five posture synthesis, 481
Four posture synthesis, 474
Center point curve, 475
Circle point curve, 475
Opposite pole quadrilateral, 475
Pole, 462
Pole Triangle, 465
Two posture synthesis, 460
Crank-and-rocker linkage, 460
Slider-crank linkage, 460
Three posture synthesis, 465
Firing order, 805
First-order kinematic coefficients, 135
Relationship to instant centers of velocity, 157
Fisher, F. E., 724n
Five-bar linkage, 258
Geared, 259
Five-cylinder engine, 806
Fixed centrode, 164–165
Flat-face follower, 298, 306
Flat pair, 10
Flip-flop mechanism, 18
Float in cam systems, 353
Flywheels, 885
Follower, 6
Force, 570
Applied, 573
Characteristics of, 573
Constraint, 573
External, 576
Friction, 591–592
Indeterminate, 512
Inertia, 666
Internal, 576
Polygon, 582
Transmitted, 598
Unit of, 569
Vector, 570INDEX 941
Force analysis:
Analytic, 583
of Bevel gears, 604
with Friction, 594
Graphic, 580
of Helical gears, 597
of Robot actuators, 558
of Spur gears, 597
Forced precession, 911
Form cutter, 381
Forward kinematics, 543
Foster, D. E., 167n
Foucault, L., 905
Four-bar linkage, 21
Algebraic posture analysis, 72
Analysis of, 67
Angular velocity relations, 156
Inversions of, 33
Spatial, 510
Spheric, 510
Four-circle method, 235
Four-cylinder engine, 859
Four-force member, 589
Four-stroke engine cycle, 805
Frame, 7
Free-body diagram, 576
Freedom:
Degrees of, 12
Idle, 511
Free vector, 575
Free vibration, 764
with viscous damping, 764
Frequency, 743
Freudenstein, F., 167n, 504n, 561n
Freudenstein’s equation, 491
Freudenstein’s theorem, 160
Friction, 591–592
Angle, 593
Coefficient of, 592
Coulomb, 592
Force, 592
Force models, 591–592
Sliding, 355, 592
Static, 592
Viscous, 593
Full depth, 376
Full-return cam motion, 316
Full-rise cam motion, 314
Function generation, 459
Fundamental law of toothed gearing, 372
Ganter, M. A., 363n
Gantry robot, 542
Gas force, 814
Gas law, 811
Gear, 369
Differentials, 449
Graphical layout, 377
Manufacture, 381
Tooth action, 376
Tooth sizes, 375
Tooth terminology, 370
TORSEN, 413
Train:
Compound, 404
Epicyclic, 405
Analysis by formula, 407
Analysis by table, 417
Bevel gear, 440
Planetary, 406
Tabular analysis, 417
Reverted, 404
Series connected, 403
Type of:
Annular, 380
Bevel, 427
Angular, 436
Spiral, 443
Straight-tooth, 436
Tooth proportions, 440
Crossed-axis helical, 433
Crown, 443
Double-helical, 433
Elliptical, 166
Epicyclic, 405
Face, 443
Helical, 427
Herringbone, 433
Hypoid, 445
Internal, 380
Miter, 436
Planet, 406
Ring, 451
Spiral, 433
Spur, 369
Sun, 406
Worm, 427
Zerol bevel, 444
Worm:
Differential, 453
Geared five-bar linkage, 259
Generalized mechanism analysis programs, 538
Generating cutter, 381
Generating line, 372
Generators:
Curve, 29
Function, 459
Straight-line, 31
Geneva mechanism, 20942 INDEX
Geneva wheel, 20
Gleasman, V., 413
Globular pair, 10
Goldberg, M., 561n
Goldberg linkage, 511
Goodman, T. P., 504n
Gough, V. E., 561n
Governors, 890
Centrifugal, 892
Electronic, 905
Inertia, 893
Graham’s escapement, 19
Graphic error, 482
Grashof’s law, 33
Gravitational system of units, 572
Gravity, standard, 572
Gray, G. L., 645n, 724n
Grodzinsky, P., 504n
Grübler, M. F, 39n
Grübler’s criterion, 14
Gustavson, R. E., 504n, 561n
Gyration, radius of, 616, 664
Gyroscope:
Definition of, 905
Motion of, 906
Gyroscopic moment, 911
Hain, K., 167n, 249n, 485n, 504n
Half-cycloidal cam motion, 321
Half-harmonic cam motion, 319
Hall, A. S., Jr., 161n, 167n, 249n, 504n
Hand and thrust relations of helical gears, 433
Harmonic forcing, 776
Harmonic motion, 314
Harrisberger, L., 509, 561n
Hartenberg, R. S., 9, 39n, 249n, 489, 504n, 528, 561n
Hartmann construction, 227
Haug, E. J., 539, 561n
Helical gears:
Contact ratio:
Axial, 431
Face, 431
Normal, 431
Total, 432
Transverse, 431
Crossed-axis:
Hand and thrust relations, 433
Tooth proportions, 435
Double, 433
Equivalent pitch radius, 429
Face width, 431
Forces on, 599
Helix angle, 428
Overlap, 432
Parallel-axis, 427
Tooth proportions, 430
Pitch:
Axial, 428
Normal circular, 428
Normal diametral, 429
Transverse circular, 428
Transverse diametral, 429
Pressure angle:
Normal, 429
Transverse, 429
Replacing spur gears with, 432
Helical motion, 50
Helical pair, 9
Helix angle, 428
Herringbone gears, 433
Hertz, H. R., 751n
Hesitation mechanisms, 29
Hesitation motion, 506
Higher pair, 8
Hindley worm, 446
Hinkle, R. T., 489, 504n
Hirschhorn, J., 249n, 504n
Hob, 342
Hobbing, 342
Hodges, H., 455
Holowenko, A. R., 39n
Holzer tabulation method, 795
Hooke universal joint, 28, 529
Hrones, J. A., 30, 39n
Hrones and Nelson atlas, 30
Humpage’s reduction gear, 440
Hunt, K. H., 504n, 561n
Hypoid gears, 445
Idle freedom, 511
Idler, 403
Image:
Acceleration, 192
Point, 468
Pole, 468
Velocity, 114
Imaginary-mass method of balancing, 856
IMP (Integrated Mechanisms Program), 539
Impulse, 714
Angular, 714
Indeterminate force, 512
Indexing mechanisms, 20
Indicator:
Diagram, 811
Engine, 811
Indices of merit, 162
Inertia:
Axes, principal, 664
Axes, transformation of, 705INDEX 943
Definition, 570
Force, 666
in Engines, 818
Governors, 893
Primary, 820
Secondary, 820
Mass moment of, 663, 922
Mass product of, 663
Measurement of, 702
Tensor, 664
Torque, 820
Inflection circle, 228
Inflection pole, 228
Influence coefficients, 787
In-line engine, 805
Instantaneous:
Acceleration, 180
Center:
of Acceleration, 234
Four-circle method of locating, 235
of Velocity, 145
Locating, 149
in Multi-degree-of-freedom planar
linkages, 265
Number of, 147
Relationship to first-order kinematic
coefficients, 157
Use for velocity analysis, 153
Screw Axis, 145n
Velocity, 105
Integration by Simpson’s rule, 887
Interference, 384
Internal gear, 380
International Standards Organization (ISO), 76n
International System (SI) of units, 572
Inverse:
Acceleration analysis, 553
Cam, 298
Kinematics, 550
Velocity analysis, 553
Inversion:
Kinematic, 32
Involute:
Curve, 374
Function, 390, 923
Generation of, 374
Helicoid, 427
Properties, 372
Involutometry, 390
Isolation, 782
Jacobian, 164
Jamming, 37
Jerk, 311
Johnson, J. B., 618n
Johnson parabolic equation, 618
Johnston, E. R., 724n
Johnston, E. R., Jr., 645n
Joint, types of:
Balanced, 584
Cardan, 529
Hooke, 529
Turning, 9
Universal, 529
Wrapping, 10
see also Pair, Types of, Lower
Jump, in cam systems, 353
Jump speed, 353
KAM (Kinematic Analysis Method), 539
Kaufman, R. E., 541, 561n
Kennedy, A. B. W., 6n, 39n, 148n
Kennedy circle, 148
Kennedy’s theorem, 148
Kinematic chain, kind, 7
Kinematic coefficients:
First-order, 135
Relationship to instant centers, 157
Velocity analysis, 135
Rolling contact condition, 143
Second-Order, 216
Acceleration analysis, 216
Relationship to radius and center of curvature,
239
Kinematic inversion, 32
Kinematic pair, 6
Kinematics:
Definition, 5
Direct, 543
Forward, 543
Inverse, 550
Kinematic synthesis, 458
Kinetic energy, 693
Kinetics, definition, 5
KINSYN (KINematic SYNthesis), 540
Kloomak, M., 363n
Knife-edge follower, 298
Kota, S., 504n
Kraige, L. G., 724n
Krause, R., 160, 167n
Kuenzel, H., 504n
Kutzbach, K., 39n
Kutzbach mobility criterion, 12
Law of gearing, 372
Lead, 448
Lead angle, 447944 INDEX
Lévai, Z. L., 421n
Lévai epicyclic gear train types, 407
Lever, 18
Lichty, L. C., 875n
Lift, 301
Limited slip differential, 452
Limit posture, 37
LINCAGES, 540
Line:
of Action, 377
of Centers, 372
Coordinates, 555
Linear actuators, 18
Linearity, 135
Linear system, 134
Link:
Binary, 7
Definition of, 6
Function of, 6
Ternary, 7
Linkage:
Balancing of, 868
Definition, 10
Planar, 10
Quick-return, 21
Types of:
Bennett, 510
Bricard, 511
Chebychev, 31
Cognate, 489
Crank-rocker, 21
Crank-shaper, 22
Differential screw, 18
Double-crank, 35
Double-rocker, 35
Drag-link, 35
Dwell, 499
Five-bar, 258
Four-bar, 21
Geared five-bar, 259
Geneva, 20
Goldberg, 511
Maltese cross, 20
Pantograph, 32
Peaucillier inversor, 31
Quick return, 21
Reuleaux coupling, 28
Roberts’, 31
RSSR, 514
Scotch-yoke, 22, 151
Scott-Russell, 32
Six-bar, 22
Slider-crank, 22
Isosceles, 460
Offset, 22
Sliding-block, 78
Spatial four-link, 508
Spheric, 11
Wanzer needle-bar, 23
Watt’s, 31
Whitworth, 22
Wobble plate, 510
Locational devices, 18
Location of a point, 48
Locus, 48
Logarithmic decrement, 767
Long-and-short-addendum system, 400
Loop-closure equation, 57
Cases of, 66, 513
Lowen, G. G., 868, 875n
Lower pair, 8
Machine, definition of, 6
Maleev, V. L., 875n
Maltese cross, 20
Manipulator, 258
Mass:
Center of, 660
Definition, 570
Equivalent, 816
Moment of inertia, 663, 922
Product of inertia, 663
Unit of, 572
Master connecting rod, 806
Matter, definition, 570
Matthew, G. K., 363n
Maxwell’s reciprocity theorem, 788
Mean effective pressure, 812
Mechanical:
Advantage, 36
Compensation balancing method, 850
Control systems, 894
Efficiency, 812
Error, 482
Mechanics:
Definition of, 4
Divisions of, 4
Mechanism:
Analysis, computer, 538
Definition of, 6
Trains, 401
Types of (see also Linkage, Types of)
Bistable, 18
Cam, 21
Cam-and-follower, 97
Clamping, 18
Escapement, 18
Fine adjustment, 18INDEX 945
Flip-flop, 18
Indexing, 20
Linear actuator, 18
Locational, 18
Oscillator, 20
Planar, 10
Quick-return, 21
Rack and pinion, 97
Ratchet, 18
Reciprocating, 21
Reversing, 27
Rocking, 20
Snap-action, 18
Spatial, 11
Stop, pause, hesitation, 29
Straight-line, 31
Swinging, 20
Toggle, 18
Mehmke, R., 114, 167n
Meriam, J. L., 724n
Merit indices, 162
M’Ewan, E., 504n
Milling of gear teeth, 381
Mischke, C. R., 98n, 421n, 504n, 645n, 795n
Miter gears, 436
Mobility, 12
Exceptions to criteria, 13
Kutzbach criterion, 12
Module, 371
Molian, S., 363n
Moment:
of a Couple, 574
Gyroscopic, 911
of Impulse, 715
of Inertia:
Area, 613, 615
Mass, 663
Measurement, 702
Polygon, 838
Shaking, 682
Vector, 575
Momentum, 714
Angular, 714
Movability, definition, 12n
Moving centrode, 165
Moving point:
Acceleration of, 181
Displacement of, 93
Locus of, 48
Velocity of, 105
MSC Working Model, 539
Muffley, R. V., 363n
Müller, R., 167n
Multi-degree of freedom, 258
NASTRAN, 539
Natural frequency, 743
Damped, 766
Neale, M. J., 645n
Nelson, G. L., 30
Newton (unit), 572
Newton, I., 645n
Newton-Raphson method, 70
Newton’s laws, 571
Newton’s notation, 745
Nodal-point balancing method, 848
Normal:
Component of acceleration, 182
Unit vector, 124
Notation, complex-rectangular, 74
Offset circle, 305
Offset follower, 300
Open kinematic chain, 7
Open posture, 68
Opposed-piston engine, 806
Opposite pole quadrilateral, 475
Order defect, 483
Orlandea, N., 539, 561n
Oscillating follower, 300
Osculating circles, 225
Osculating plane, 124
Ostenfeld, A., 618n
Otto-cycle engine, 804
Overconstrained, 13
Overdrive unit, 420
Overlay method, 483
Pair:
Types of (see also Joint, types of)
Higher, 8
Lower, 8
Cylindric, 10
Flat, 10
Helical, 9
Prismatic, 9
Revolute, 9
Spheric, 10
Wrapping, 10
Variable, 8
Pantograph linkage, 32
Parabolic motion, 302
Parallel-axis formula, 664
Parallel-axis helical gears, 427
Parker, J. W., 917n
Particle, definition, 50
Particle motion, equation of, 50946 INDEX
Path:
Coordinates, 51
Curvature, 285
Generation, 459
Point, 89
Pause mechanisms, 29
Pawl, 19
Peaucillier inversor, 31
Pendulum:
Equation of, 702
Three-string, 704
Torsional, 702
Trifilar, 704
Pennock, G. R., 167n, 421n, 561n
Percussion, center of, 682
Periodic forcing, 772
Response to, 772
Period of vibration, 743
Phase, of motion, 751
Phase angle, 751
Phase plane:
Analysis, 757
Method, 757
Representation, 755
Phasor, 750
Phillips, J., 512n, 561n
Pinion, 369
Pin joint (see Pair, Types of, Lower, Revolute)
Piston acceleration, 814
Piston-pin force, 823
Pitch:
Angle, 438
Axial, 428, 447
Base, 379
Circle, 369
Circular, 369
Normal, 428
Transverse, 428
Curve, of cam, 304
Diametral, 369
Normal, 429
Transverse, 429
Point, 372
Radius, equivalent, 429
Surface, of bevel gear, 437–438
Pivoted-cradle method of balancing, 846
Planar:
Linkage, 10
Mechanism, 10
Motion, 51
Pair, 10
Rotation about fixed center, 680
Vector equations, 64
Plane of couple, 574
Planet:
Carrier, 406
Gear, 406
Planetary gear train, 406
Force analysis, 602
Plate cam, 298
Plesha, M. E., 645n, 724n
Plücker coordinates, 555
Point:
Acceleration:
Absolute, 181
Apparent, 196
Difference, 183
Definition, 50
Displacement:
Absolute, 89, 94
Apparent, 92
Difference, 89
Pitch, 372
Position:
Absolute, 55
Apparent, 54
Difference, 53
Velocity:
Absolute, 105
Apparent, 119
Difference, 109
Polar notation, 73
Pole, 462
Pole triangle, 465
Polode, 165n
Polydyne cam, 319
Polygon:
Acceleration, 192
Force, 582
Moment, 838
Velocity, 113, 263
Pose, of rigid body, 57
Position:
Absolute, 55
Apparent, 54
Difference, 53
Rigid body, 56
Posture:
Analysis:
Algebraic, 69, 262
Graphic, 62
of Spatial mechanism, 513
Techniques, 78
Precision, 481
Rigid body, 56
Potential energy, 694
Power equation, 692
Power stroke, 805INDEX 947
Precession:
Forced, 911
Regular, 908
Steady, 908
Precision postures, 481
Prefixes, standard SI, 919
Preload on cam, 351
Pressure, mean effective, 812
Pressure angle, 164
Maximum, 333
Normal, 429
Transverse, 429
Pressure line, 377
Prime circle, 304
Principal axes, 664
Principle of superposition, 674
Prismatic pair, 9
Products of inertia, 663
Pro/ENGINEER Mechanism Dynamics, 539
Programs, computer, 538
Proportional-error feedback systems, 901
Quadrant, 76n
Quaternion, 513
Quick-return mechanism, 21
Rack, 19
Radcliffe, C. W., 504n
Radial cam, 298
Radial cam follower, 300
Radial engine, 807
Radius:
of curvature, 182
of cam profile
charts for minimum, 337
equation, 328
of gyration, 616
Rapson’s slide, 220
Ratchets, 18
Rathbone, T. C., 795, 875n
Ravani, B., 561n
Raven, F. H., 167n
Raven’s method:
for Acceleration, 213
for Posture, 74
for Velocity, 131
Rayleigh, Baron, 795n
Rayleigh-Ritz equation, 787
Rayleigh’s method, 785
Recess:
Angle, 384
Arc of, 385
Reciprocating:
Engines, dynamics of, 804
Follower, 298
Linkages, 23
Reciprocity, Maxwell’s theorem, 788
RECSYN (RECtified SYNthesis), 540
Rectangular notation, 74
Rectilinear motion, 51
Rectilinear translation, 91n
Redundant constraint, 512
Reference system, 48
Regular precession, 908
Relative motion, 32, 781
Resonance, 743
Response curve, 744
Return, motion of cam, 301
Reuleaux, F., 6, 6n
Reuleaux coupling, 28
Reverted gear train, 404
Revolute, 9
Rigid body, 570
Cam, 350
Posture, 56
Rotation of, 106
Velocity difference between, 109
Rise, motion of cam, 300
Roberts, S., 489n
Roberts-Chebychev theorem, 489
Roberts linkage, 31
Robot, 541
Robotics, 541
Robot Institute of America (RIA), 542
Roller follower, 298, 305
Rolling contact, 126
Acceleration, 206
Displacement, 95
Velocity, 126
Rosenauer, N., 167n, 249n
Rotation:
About a fixed center, 680
of crossed-helical gears, 433
Definition, 91
of Rigid body, 106
Roth, B., 167n
Rothbart, H. A., 504n
Roulettes, 165n
RSSR linkage, 511
Sandor, G. N., 504n
Sankar, T. S., 795n
SCARA robot, 542
Scarborough, J. B., 917n
Scotch-yoke linkage, 22, 151
Scott-Russell linkage, 32
Screw:
Axis, instantaneous, 145n948 INDEX
Screw: (continued)
Differential, 19
Pair (see Pair, Types of, Lower, Helical)
Second harmonic forces, 857
Second-order kinematic coefficients, 216
Relationship to radius of and center of
curvature, 239
Shaking:
Forces, 682
Engine, 824
Moments, 682
Shaping, 381
Sheth, P. N., 539, 561n
Shigley, J. E., 421n, 504n, 645n, 795n
SI (System International), 572
Conversion to U.S. customary units, 920
Prefixes, 919
Units, 572
Simple-closed chain, 7
Simple gear train, 404
Simple-harmonic cam motion, 302
Simpson’s rule integration, 887
Single cylinder engine, 821
Single plane balancers, 834
Six-bar linkage, 22
Skew curve, 51
Slenderness ratio, 616
Slider-crank linkage:
Algebraic posture analysis, 69
Analysis of, 66
Inversions of, 33
Limit positions, 22
Offset, 27
Synthesis, 460
Synthesis of, 27
Sliding connectors, 28
Sliding friction, 355, 592
Snap-action mechanism, 18
Soni, A. H., 504n
Spatial:
Four-link mechanism, 513
Graphic analysis, 514
Mechanism, 507
Motion, 51
Seven-link, 508
Speed fluctuation, coefficient of, 888
Speed ratio, 402
Spheric:
Coordinates, 49
Joint, 10
Linkage, 509
Mechanism, 507
Spheric-face follower, 298
Spheric-slide oscillator, 510
Spin axis, 907
Spiral angle, 444
Spiral gears, 433
Spring:
Rate, 351
Stiffness, 745
Surge, 362
Spur gears, 369
Forces on, 598
Standard gear tooth proportions, 375
Standard gravity, 532
Starting transient, 774
Statically indeterminate force, 512
Static balancing machines, 834
Static force analysis, 569
Static friction, 592
Statics, definition, 4
Static unbalance, 830
Stationary curvature, 242
Steady precession, 908
Steady-state vibration, 744
Step input forcing, 752
Stevensen, E. N., Jr., 504n, 856, 874n, 875n
Stevensen’s rule, 857
Stiction, 597
Stoddart, D. A., 363n
Stop mechanisms, 29
Straight-line generators, 31
Straight-tooth bevel gears, 436
Forces on, 604
Strong„ R. T., 561n
Structural error, 482
Structure:
Definition, 6
Statically indeterminate, 13
Strutt, J. W., 795n
Stub tooth, 376
Suction stroke, 805
Suh, C. H., 504n
Summing mechanism, 449
Sun gear, 406
Superposition, 273
Principle of, 674
Swashplate, 708
Synthesis:
Coupler-curve, 485
Definition, 4
Dimensional, 458
Kinematic, 458
of Linkages, 458
Number, 458
Type, 458
Tabular analysis of epicyclic gear trains, 417
Tangent cam, 312INDEX 949
Tangential component of acceleration, 183
Tao, D. C., 249n, 504n
Ternary link, 7
Tesar, D., 363n
Thearle, E. L., 795, 875n
Theorem of Mehmke, 114
Three cylinder engine, 805
Three-force member, 579
Three-string pendulum, 704
Toggle:
Mechanism, 18
Posture, 37
Tooth proportions:
Bevel gears, 440
Helical gears, 430
Spur gears, 376
Tooth sizes, 371
Tooth thickness, 370
Top dead center (TDC), 856
Torfason, L. E., 18, 39n
Torque characteristics of engines, 810
TORSEN differential, 413
Torsional pendulum, 702
Torsional system, 793
Trace point, 304
Train value, 402
Transfer formula, 664
Transformation matrix, 513
Transient disturbances, 760
Transient vibration, 744
Translation:
Curvilinear, 91n
Definition, 91
Rectilinear, 91n
Transmissibility, 782
Transmission, automotive, 404
Transmission angle, 37, 73
Extremes of, 73
Transmitted force, 598
Tredgold’s approximation, 439
Trifilar pendulum, 704
True toggle mechanism, 18
Turning pair (see Pair, Types of, Lower, Revolute)
Two-cylinder engine, 858
Two-force member, 579
Two-stroke engine cycle, 805
Type synthesis, 458
Uicker, J. J., Jr, 363n, 539, 561n
Unbalance:
Analysis of, 837
in Cam systems, 362
Dynamic, 835
Forcing caused by, 780
Static, 830
Units of, 846
Undercutting:
in Cam systems, 327
Elimination of, 330
in Gear systems, 384
Uniform motion, 301
Units:
Conversion:
SI to U.S. customary, 920
U.S. customary to SI, 920
Systems of, 571
Unit vector:
Binormal, 124
Normal, 124
Tangent, 124
Universal joint, 28
Vector:
Addition, 62
Angular momentum, 715
Approach to rotor balancing, 839
Graphical operations, 62
Loop-closure cases, 66
Subtraction, 62
Tetrahedron equation, 513
Solutions, 513
Type of:
Absolute acceleration, 181
Absolute displacement, 89, 94
Absolute position, 55
Absolute velocity, 105
Acceleration, 181
Acceleration difference, 183
Apparent acceleration, 196
Apparent displacement, 92
Apparent position, 54
Apparent velocity, 119
Displacement, 89
Displacement difference, 89
Force, 573
Moment, 574
Position, 55
Position difference, 53
Unit, 52
Velocity, 105
Velocity difference, 109
Velocity, 105
Absolute, 105
Analysis:
of Four-bar linkage, 115
Graphic, 111
Inverse, 553950 INDEX
Velocity, (continued)
of Offset slider-crank linkage, 118
Polygons, 263
of Spatial mechanism, 518
Systematic strategy for, 128
Using instantaneous centers, 153
Angular, 106
Apparent, 119
Average, 105
Condition for rolling contact, 126
Definition, 105
Difference, 109
Image, 114
Size of, 114
Instantaneous, 105
Instantaneous centers of, 145
Locating, 150
in Multi-degree-of-freedom planar linkages, 265
Using, 153
Matrix, 533
Poles, 165n, 225
Polygon, 113, 263
Ratio, Angular, 156
Vibration:
Definition, 743
Forced, 743
Free, 743
Isolation, 782
Phase-plane representation of, 768
Virtual displacement, 608
Virtual-rotor method of balancing, 856
Virtual work, 608
Viscous damping:
Coefficient of, 745
Free vibration with, 764
V-type engine, 805
Waldron, K. J., 504n, 561n
Wanzer. R. M., 23
Wanzer needle-bar linkage, 23
WATT Mechanism Design Tool, 540
Watt’s linkage, 31
Wedge cam, 298
Weight, definition, 570
Weight/mass controversy, 572, 572n
Whitworth linkage, 22
Whole depth, 372
Willis, A. H., 249n
Willis, R. W., 917n
Windup, 362
Wobble-plate mechanism, 510
Working stroke, 22
Worm, 427
Worm gear, 427, 446
Worm gear differential, 453
Wrapping pair, 10
Wrist-pin force, 816
Yang, A. T., 561n
Young’s modulus, 612
Zerol bevel gear, 444

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كتاب Theory of Machines and Mechanisms - صفحة 2 761752

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Theory of Machines and Mechanisms
Fifth Edition
John J. Uicker, Jr.
Professor Emeritus of Mechanical Engineering
University of Wisconsin–Madison
Gordon R. Pennock
Associate Professor of Mechanical Engineering
Purdue University
Joseph E. Shigley
Late Professor Emeritus of Mechanical Engineering
The University of Michigan

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Contents
PREFACE xvii
ABOUT THE AUTHORS xxv
Part 1 KINEMATICS AND MECHANISMS 1
1 The World of Mechanisms 3
1.1 Introduction 3
1.2 Analysis and Synthesis 4
1.3 Science of Mechanics 4
1.4 Terminology, Definitions, and Assumptions 6
1.5 Planar, Spheric, and Spatial Mechanisms 10
1.6 Mobility 12
1.7 Characteristics of Mechanisms 17
1.8 Kinematic Inversion 32
1.9 Grashof’s Law 33
1.10 Mechanical Advantage 36
1.11 References 39
Problems 40
2 Position, Posture, and Displacement 48
2.1 Locus of a Moving Point 48
2.2 Position of a Point 51
2.3 Position Difference Between Two Points 53
2.4 Apparent Position of a Point 54
2.5 Absolute Position of a Point 55
2.6 Posture of a Rigid Body 56
2.7 Loop-Closure Equations 57
2.8 Graphic Posture Analysis 62
2.9 Algebraic Posture Analysis 69
2.10 Complex-Algebraic Solutions of Planar Vector Equations 73
2.11 Complex Polar Algebra 74
2.12 Posture Analysis Techniques 78
2.13 Coupler-Curve Generation 86
viiviii CONTENTS
2.14 Displacement of a Moving Point 89
2.15 Displacement Difference Between Two Points 89
2.16 Translation and Rotation 91
2.17 Apparent Displacement 92
2.18 Absolute Displacement 94
2.19 Apparent Angular Displacement 94
2.20 References 98
Problems 99
3 Velocity 105
3.1 Definition of Velocity 105
3.2 Rotation of a Rigid Body 106
3.3 Velocity Difference Between Points of a Rigid Body 109
3.4 Velocity Polygons; Velocity Images 111
3.5 Apparent Velocity of a Point in a Moving Coordinate System 119
3.6 Apparent Angular Velocity 126
3.7 Direct Contact and Rolling Contact 126
3.8 Systematic Strategy for Velocity Analysis 128
3.9 Algebraic Velocity Analysis 129
3.10 Complex-Algebraic Velocity Analysis 131
3.11 Method of Kinematic Coefficients 135
3.12 Instantaneous Centers of Velocity 145
3.13 Aronhold-Kennedy Theorem of Three Centers 147
3.14 Locating Instantaneous Centers of Velocity 149
3.15 Velocity Analysis Using Instant Centers 153
3.16 Angular-Velocity-Ratio Theorem 156
3.17 Relationships Between First-Order Kinematic Coefficients
and Instant Centers 157
3.18 Freudenstein’s Theorem 160
3.19 Indices of Merit; Mechanical Advantage 162
3.20 Centrodes 164
3.21 References 166
Problems 167
4 Acceleration 180
4.1 Definition of Acceleration 180
4.2 Angular Acceleration 183
4.3 Acceleration Difference Between Points of a Rigid Body 183
4.4 Acceleration Polygons; Acceleration Images 192
4.5 Apparent Acceleration of a Point in a Moving Coordinate System 196CONTENTS ix
4.6 Apparent Angular Acceleration 205
4.7 Direct Contact and Rolling Contact 206
4.8 Systematic Strategy for Acceleration Analysis 212
4.9 Algebraic Acceleration Analysis 213
4.10 Complex-Algebraic Acceleration Analysis 214
4.11 Method of Kinematic Coefficients 216
4.12 Euler-Savary Equation 225
4.13 Bobillier Constructions 230
4.14 Instantaneous Center of Acceleration 234
4.15 Bresse Circle (or de La Hire Circle) 235
4.16 Radius of Curvature of a Point Trajectory Using Kinematic
Coefficients 239
4.17 Cubic of Stationary Curvature 242
4.18 References 249
Problems 250
5 Multi-Degree-of-Freedom Mechanisms 258
5.1 Introduction 258
5.2 Posture Analysis; Algebraic Solution 262
5.3 Velocity Analysis; Velocity Polygons 263
5.4 Instantaneous Centers of Velocity 265
5.5 First-Order Kinematic Coefficients 268
5.6 Method of Superposition 273
5.7 Acceleration Analysis; Acceleration Polygons 276
5.8 Second-Order Kinematic Coefficients 278
5.9 Path Curvature of a Coupler Point Trajectory 285
5.10 Finite Difference Method 289
5.11 Reference 292
Problems 292
Part 2 DESIGN OF MECHANISMS 295
6 Cam Design 297
6.1 Introduction 297
6.2 Classification of Cams and Followers 298
6.3 Displacement Diagrams 300
6.4 Graphic Layout of Cam Profiles 303
6.5 Kinematic Coefficients of Follower 307
6.6 High-Speed Cams 312
6.7 Standard Cam Motions 313x CONTENTS
6.8 Matching Derivatives of Displacement Diagrams 323
6.9 Plate Cam with Reciprocating Flat-Face Follower 327
6.10 Plate Cam with Reciprocating Roller Follower 332
6.11 Rigid and Elastic Cam Systems 350
6.12 Dynamics of an Eccentric Cam 351
6.13 Effect of Sliding Friction 355
6.14 Dynamics of Disk Cam with Reciprocating Roller Follower 356
6.15 Dynamics of Elastic Cam Systems 359
6.16 Unbalance, Spring Surge, and Windup 362
6.17 References 363
Problems 363
7 Spur Gears 369
7.1 Terminology and Definitions 369
7.2 Fundamental Law of Toothed Gearing 372
7.3 Involute Properties 373
7.4 Interchangeable Gears; AGMA Standards 375
7.5 Fundamentals of Gear-Tooth Action 376
7.6 Manufacture of Gear Teeth 381
7.7 Interference and Undercutting 384
7.8 Contact Ratio 386
7.9 Varying Center Distance 388
7.10 Involutometry 389
7.11 Nonstandard Gear Teeth 393
7.12 Parallel-Axis Gear Trains 401
7.13 Determining Tooth Numbers 404
7.14 Epicyclic Gear Trains 405
7.15 Analysis of Epicyclic Gear Trains by Formula 407
7.16 Tabular Analysis of Epicyclic Gear Trains 417
7.17 References 421
Problems 421
8 Helical Gears, Bevel Gears, Worms, and Worm Gears 427
8.1 Parallel-Axis Helical Gears 427
8.2 Helical Gear Tooth Relations 428
8.3 Helical Gear Tooth Proportions 430
8.4 Contact of Helical Gear Teeth 431
8.5 Replacing Spur Gears with Helical Gears 432
8.6 Herringbone Gears 433
8.7 Crossed-Axis Helical Gears 434CONTENTS xi
8.8 Straight-Tooth Bevel Gears 436
8.9 Tooth Proportions for Bevel Gears 440
8.10 Bevel Gear Epicyclic Trains 440
8.11 Crown and Face Gears 443
8.12 Spiral Bevel Gears 443
8.13 Hypoid Gears 445
8.14 Worms and Worm Gears 445
8.15 Summers and Differentials 449
8.16 All-Wheel Drive Train 453
8.17 Note 455
Problems 455
9 Synthesis of Linkages 458
9.1 Type, Number, and Dimensional Synthesis 458
9.2 Function Generation, Path Generation, and Body Guidance 459
9.3 Two Finitely Separated Postures of a Rigid Body (N = 2) 460
9.4 Three Finitely Separated Postures of a Rigid Body (N = 3) 465
9.5 Four Finitely Separated Postures of a Rigid Body (N = 4) 474
9.6 Five Finitely Separated Postures of a Rigid Body (N = 5) 481
9.7 Precision Postures; Structural Error; Chebyshev Spacing 481
9.8 Overlay Method 483
9.9 Coupler-Curve Synthesis 485
9.10 Cognate Linkages; Roberts-Chebyshev Theorem 489
9.11 Freudenstein’s Equation 491
9.12 Analytic Synthesis Using Complex Algebra 495
9.13 Synthesis of Dwell Linkages 499
9.14 Intermittent Rotary Motion 500
9.15 References 504
Problems 504
10 Spatial Mechanisms and Robotics 507
10.1 Introduction 507
10.2 Exceptions to the Mobility Criterion 509
10.3 Spatial Posture-Analysis Problem 513
10.4 Spatial Velocity and Acceleration Analyses 518
10.5 Euler Angles 524
10.6 Denavit-Hartenberg Parameters 528
10.7 Transformation-Matrix Posture Analysis 530
10.8 Matrix Velocity and Acceleration Analyses 533
10.9 Generalized Mechanism Analysis Computer Programs 538xii CONTENTS
10.10 Introduction to Robotics 541
10.11 Topological Arrangements of Robotic Arms 542
10.12 Forward Kinematics Problem 543
10.13 Inverse Kinematics Problem 550
10.14 Inverse Velocity and Acceleration Analyses 553
10.15 Robot Actuator Force Analysis 558
10.16 References 561
Problems 562
Part 3 DYNAMICS OF MACHINES 567
11 Static Force Analysis 569
11.1 Introduction 569
11.2 Newton’s Laws 571
11.3 Systems of Units 571
11.4 Applied and Constraint Forces 573
11.5 Free-Body Diagrams 576
11.6 Conditions for Equilibrium 578
11.7 Two- and Three-Force Members 579
11.8 Four- and More-Force Members 589
11.9 Friction-Force Models 591
11.10 Force Analysis with Friction 594
11.11 Spur- and Helical-Gear Force Analysis 597
11.12 Straight-Tooth Bevel-Gear Force Analysis 604
11.13 Method of Virtual Work 608
11.14 Introduction to Buckling 611
11.15 Euler Column Formula 612
11.16 Critical Unit Load 615
11.17 Critical Unit Load and Slenderness Ratio 618
11.18 Johnson’s Parabolic Equation 619
11.19 References 645
Problems 646
12 Dynamic Force Analysis 658
12.1 Introduction 658
12.2 Centroid and Center of Mass 658
12.3 Mass Moments and Products of Inertia 663
12.4 Inertia Forces and d’Alembert’s Principle 666
12.5 Principle of Superposition 674
12.6 Planar Rotation about a Fixed Center 680CONTENTS xiii
12.7 Shaking Forces and Moments 682
12.8 Complex-Algebraic Approach 683
12.9 Equation of Motion from Power Equation 692
12.10 Measuring Mass Moment of Inertia 702
12.11 Transformation of Inertia Axes 705
12.12 Euler’s Equations of Motion 710
12.13 Impulse and Momentum 714
12.14 Angular Impulse and Angular Momentum 714
12.15 References 724
Problems 725
13 Vibration Analysis 743
13.1 Differential Equations of Motion 743
13.2 A Vertical Model 747
13.3 Solution of the Differential Equation 748
13.4 Step Input Forcing 752
13.5 Phase-Plane Representation 755
13.6 Phase-Plane Analysis 757
13.7 Transient Disturbances 760
13.8 Free Vibration with Viscous Damping 764
13.9 Damping Obtained by Experiment 766
13.10 Phase-Plane Representation of Damped Vibration 768
13.11 Response to Periodic Forcing 772
13.12 Harmonic Forcing 776
13.13 Forcing Caused by Unbalance 780
13.14 Relative Motion 781
13.15 Isolation 782
13.16 Rayleigh’s Method 785
13.17 First and Second Critical Speeds of a Shaft 787
13.18 Torsional Systems 793
13.19 References 795
Problems 796
14 Dynamics of Reciprocating Engines 804
14.1 Engine Types 804
14.2 Indicator Diagrams 811
14.3 Dynamic Analysis—General 814
14.4 Gas Forces 814
14.5 Equivalent Masses 816
14.6 Inertia Forces 818xiv CONTENTS
14.7 Bearing Loads in a Single-Cylinder Engine 821
14.8 Shaking Forces of Engines 824
14.9 Computation Hints 825
Problems 828
15 Balancing 830
15.1 Static Unbalance 830
15.2 Equations of Motion 831
15.3 Static Balancing Machines 834
15.4 Dynamic Unbalance 835
15.5 Analysis of Unbalance 837
15.6 Dynamic Balancing 846
15.7 Dynamic Balancing Machines 848
15.8 Field Balancing with a Programmable Calculator 851
15.9 Balancing a Single-Cylinder Engine 854
15.10 Balancing Multi-Cylinder Engines 858
15.11 Analytic Technique for Balancing Multi-Cylinder Engines 862
15.12 Balancing Linkages 868
15.13 Balancing of Machines 874
15.14 References 875
Problems 875
16 Flywheels, Governors, and Gyroscopes 885
16.1 Dynamic Theory of Flywheels 885
16.2 Integration Technique 887
16.3 Multi-Cylinder Engine Torque Summation 890
16.4 Classification of Governors 890
16.5 Centrifugal Governors 892
16.6 Inertia Governors 893
16.7 Mechanical Control Systems 894
16.8 Standard Input Functions 895
16.9 Solution of Linear Differential Equations 897
16.10 Analysis of Proportional-Error Feedback Systems 901
16.11 Introduction to Gyroscopes 905
16.12 Motion of a Gyroscope 906
16.13 Steady or Regular Precession 908
16.14 Forced Precession 911
16.15 References 917
Problems 917CONTENTS xv
APPENDIXES
APPENDIX A: Tables 919
Table 1 Standard SI Prefixes 919
Table 2 Conversion from US Customary Units to SI Units 920
Table 3 Conversion from SI Units to US Customary Units 920
Table 4 Properties of Areas 921
Table 5 Mass Moments of Inertia 922
Table 6 Involute Function 923
APPENDIX B: Answers to Selected Problems 925
INDEX 935
INDEX
Absolute:
Acceleration, 181
Displacement, 94
Motion, 32
Position, 55
System of units, 572
Velocity, 105
Acceleration:
Absolute, 181
Angular, 183
Apparent, 198
Angular, 183
Average, 180
Components of:
Centripetal component (see Normal, component
of acceleration)
Coriolis component, 199
Normal component, 182, 199
Rolling-contact component, 206
Tangential component, 183, 199
Definition, 180
Difference, 183
Image, 192
Instant center of, 234
Normal component of, 182
Pole, 234
Polygon, 192, 276
Rolling-contact component of, 206
Tangential component of, 183
Action, line of, 377
Actuator, linear, 18
ADAMS (Automatic Dynamic Analysis of
Mechanical Systems), 539
Adams, D. P., 504n
Addendum, 370
Circle, 370
Adjustments, 18
Advance stroke, 24
Advance-to-return ratio, 24
AGMA (American Gear Manufacturers Association),
375, 375n
Air-standard cycle, 811
Alford, H. H., 724n
Algebraic analysis, 213
Acceleration, 213
Dynamic force, 683
Loop-closure cases, 73
Posture, 78, 262
Static force, 569
Velocity, 128, 131
All wheel drive train, 453
Alwerdt, J. J., 421n
American Institute of Steel Construction (AISC), 617
Ampère, A. M., 5, 5n
Analysis:
Dynamic force, 658
Elastic body, 744
Rigid body, 570
Static force, 569
Angular:
Acceleration, 183
Apparent, 205
Bevel gears, 436
Displacement, 94
Impulse, 714
Momentum, 714
Velocity, 106
Apparent, 126
Ratio theorem, 156
Annular gear, 380
ANSI (American National Standards Institute), 76n
Answers to selected problems, 925
ANSYS, 539
Apparent:
Acceleration, 196, 198
Angular, 205
Displacement, 92, 106
Angular, 94
Position, 54
Velocity, 119
Angular, 126
Applied force, 573
Approach, 384
Angle, 384
Arc of, 384
Arc:
of Approach, 384
of Recess, 385
Area, properties of, 921
Area moment of inertia, 613, 615, 663
935936 INDEX
Arm of couple, 574
Aronhold, S. H., 148n
Aronhold-Kennedy theorem, 147
Aronhold theorem, 148n
Articulated arm, 542
Articulated connecting rod, 806
ATAN2(y,x), 76n
Automotive:
All wheel drive train, 453
Cruise-control, 905
Differential, 451
Limited slip, 452
Overhead valve arrangement, 350
Transmission, 404
Average:
Acceleration, 180
Velocity, 105
Axes:
Body-fixed, 524
Collineation, 161, 230
Instantaneous screw, 145n
Principal, 664
Spin, 907
Transformation of inertia, 705
Axial pitch, 447
Axodes, 165n
Back cone, 439
Backlash, 372
Baker, J. E., 561n
Balancing:
Definition, 830
Direct method, 843
Dynamic, 846
Field, 851
of Linkages, 868
Machines:
Mechanical compensation, 850
Nodal-Point, 848
Pivoted-cradle, 846
of Machines, 874
of Multi-cylinder engines, 858
Numeric analysis, 845
Scalar equations, 845
of Single-cylinder engines, 854
Static, 834
Ball, R. S., 145n, 167n
Ball-and-socket joint, 9
Ball’s point, 244
Barrel cam, 298
Base:
Circle:
of Cam, 304
of Gear, 377
Cylinder, 377
Link, 7
Pitch, 379
Basic units, 572
Beer, F. P., 645n, 724n
Bennett, G. T., 561n
Bennett linkage, 510
Berkhof, R. S., 868, 875n
Bernoulli, J., 608
Bevel gear, 427
Angular, 436
Epicyclic trains, 440
Forces on, 604
Spiral, 443
Straight-tooth, 436
Tooth proportions, 440
Zerol, 444
Beyer, R., 39n, 167n, 249n, 504n
Bhat, R. B., 795n
Binormal unit vector, 124
Bistable mechanism, 18
Bobillier constructions, 230
Bobillier theorem, 230
Body-fixed axes, 524
Body guidance, 459
Bohenberger, J. G. F., 917n
Bollinger, J. G., 917n
Bore-to-stroke ratio, 812
Bottema, O., 167n
Bottom dead center (BDC), 856
Branch defect, 483
Bresse circle, 235
Bricard linkage, 511
Bridgman, P. W., 795n
Buckling, 611
Burmester points, 481
Calahan, D. A., 561n
Cam:
Barrel, 298
Base circle, 304
Circle-arc, 312
Conjugate, 300
Constant-breadth, 300
Cylindric, 298
Definition of, 298
Disk, 298
Displacement diagram, 300
Dual, 300
Eccentric, 351
Elastic body, 350
End, 298
Face, 298INDEX 937
Follower:
Curved-shoe, 298
Flat-face, 298
Knife-edge, 298
Offset, 300
Oscillating, 300
Radial, 300
Reciprocating, 298
Roller, 298
Spheric-face, 298
Trace-point, 304
High-speed, 312
Inverse, 298
Motion:
Cycloidal, 302, 314
Dwell, 301
Eighth-order polynomial, 315
Half-return, 320
Half-rise, 319
Kinematic coefficients of, 307
Parabolic, 302, 311
Polydyne, 319
Return, 301
Rise, 300
Simple-harmonic, 302, 314
Uniform, 301
Nomenclature, 298
Plate, 298
Pressure angle, 332
Maximum, 333
Prime circle, 304
Profile, 303
Coordinates, 331
Graphic layout, 303
Radial, 298
Radius of curvature, 328
Rigid body, 350
Roller, size of, 336
Standard motions, 313
Tangent, 312
Types:
Barrel, 298
Circle-arc, 312
Conjugate, 300
Constant breadth, 300
Cylindric, 298
Disk, 298
Dual, 300
Eccentric, 351
End, 298
Face, 298
Inverse, 298
Plate, 298
Radial, 298
Tangent, 312
Wedge, 298
Undercut, 327, 335
Wedge, 298
Capek, K., 541
Cardan joint, 529
Cardan suspension, 905
Card factor, 812
Cartesian coordinates, 49
Cayley, A., 490n
Cayley diagram, 490
Center-distance modification, 394
Center of curvature, 183n, 225
Center of mass, 658
Center of percussion, 682
Center point, 475
Center point curve, 475
Centrifugal governors, 892
Centripetal component of acceleration (see Normal,
component of acceleration)
Centrode, 164
Fixed, 165
Moving, 165
Normal, 227
Tangent, 227
Centroid, 658
Definition, 660
Chace, M. A., 513, 539, 561n
Chace approach:
Loop-closure cases, 513
Posture analysis, 513
Chain, kinematic, 7
Chebychev, P. L., 489
Chebychev linkage, 31
Chebychev spacing, 481
Chen, F. Y., 363n
Chuang, J. C., 561n
Circle-arc cam, 312
Circle point, 474
Circle point curve, 475
Circling-point curve, 242
Circular:
Pitch, 369, 372
Normal, 428
Transverse, 428
Circumscribing circle, 471
Clamping mechanisms, 18
Classification of mechanism, 17
Clausen, W. E., 724n
Clearance, 370, 394
Closed kinematic chain, 7
Closed-loop control system, 894
Coefficient:
of Friction, 592938 INDEX
Coefficient: (continued)
Kinematic:
First-order, 135, 268
Second-order, 216, 278
of Speed fluctuation, 888
of Viscous damping, 745
Cognate linkages, 31, 489
Collineation axis, 161, 230
Complex algebraic analysis:
Acceleration, 213
Dynamic force, 683
Loop-closure cases, 73
Posture, 78
Velocity, 131
Complex polar algebra, 74
Components of acceleration:
Centripetal component (see Normal, component
of acceleration)
Coriolis component, 199
Normal component, 182
Rolling-contact component, 206
Tangential component, 183
Compound-closed chain, 7
Compound gear train, 404
Compression, 811
Ratio, 813
Computer programs, 538
Concurrency, point of, 582
Concurrent forces, 580
Conjugate:
Cams, 300
Points, 225
Profiles, 372
Connecting rod, 807
Articulated, 806
Force, 822
Master, 806
Connectors, 27
Conservation of:
Angular momentum, 717
Momentum, 714
Constant-breadth cam, 300
Constraint, 59
Force, 512, 573
General, 511
Redundant, 512
Contact:
Direct, 126
Gear teeth, 384
Helical gear teeth, 431
Path of, 384
Ratio, 386
Formula, 387
Helical gears
Axial, 431
Face, 431
Normal, 431
Total, 432
Transverse, 431
Rolling, 126
Acceleration, 206
Displacement, 95
Velocity, 126
Control systems, mechanical, 894
Conversion of units:
SI to U.S. customary, 920
U.S. customary to SI, 920
Coordinates, complex, 73
Coordinate systems, 52
Coplanar motion, 10
Coriolis component of acceleration, 199
Correction planes, 838
Costanzo, F., 645n, 724n
Coulomb friction, 592
Counterweight, 871
Couple, 574
Arm of, 574
Characteristics of, 574
Coupler curve, 29
Generation, 86
Synthesis, 485
Coupler point, 285
Couplings, 27
Crane, C., 561n
Crankpin force, 823
Crank-rocker linkage, 34
Advantages of, 460
Limit position of, 34
Spatial, 514
Spheric, 509
Synthesis, 460
Crankshaft, 808
Force, 823
Torque, 824
Crank-shaper linkage, 22
Critical damping, 832
Coefficient of, 832
Critical load, 612
Critical speed, 787
Critical unit load, 615
Crossed-axis helical gears, 433
Pitch diameters of, 433
Crossed posture, 68
Crown gear, 443
Crown rack, 444
Cubic of stationary curvature, 242
Degenerate forms, 244
Curvature, 182
Center of, 125
Radius of, 124INDEX 939
Curved-shoe follower, 298
Curve generator, 29
Curvilinear translation, 91n
Cycloid, definition, 302
Cycloidal cam motion, 302
Cylinder wall force, 823
Cylindric:
Cam, 298
Coordinates, 49
Pair, 10
DADS (Dynamic Analysis and Design
System), 539
D’Alembert, J., 668
D’Alembert principle, 666
Damping:
Coefficient, 745
Viscous, 745
Critical, 832
Factor, 743
Measurement of, 766
Ratio, 832
Viscous, 832
Dead-center posture, 37
Dedendum, 370
Circle, 370
Deformable body, 570
Analysis, 744
Degrees of freedom, 12
Lower Pairs, 9
Multiple, 258
de Jonge, A. E. R., 249n
de La Hire circle, 235
Denavit, J., 9, 39n, 167n, 249n, 489, 504n, 528, 561n
Denavit-Hartenberg parameters, 528
Derived unit, 572
Design, definition of, 297
Diagram:
Displacement, 300
Free-body, 576
Schematic, 7
Diametral pitch, 369
Normal, 429
Transverse, 429
Diesel-cycle engines, 804
Difference:
Displacement, 107
Position, 53
Velocity, 110
Differential, 449
Automotive, 451
All wheel drive train, 453
Limited slip, 452
TORSEN, 453
Worm gear, 453
Chinese, 451
Limited-slip, 453
Mechanism, 450
Screw, 18
Spur gear, 450
TORSEN, 453
Worm gear, 453
Dimensional synthesis, 458
Direct contact, 126
Direction cosines, 49
Disk cam, 298
Displacement, 89
Absolute, 94
Angular, 94
Apparent, 92
Apparent angular, 94
Definition, 89
Diagram, 300
Difference, 89
Virtual, 608
Volume, 813
Disturbance, 760
Transient, 760
Division by complex number, 76
Dobbs, H. H., 453
Double-crank linkage (see drag-link linkage)
Double-helical gear, 433
Double-rocker linkage, 35, 37
Drag-link linkage, 27
Driver, 6
Dual number, 513
Duffie, N. A., 917n
Duffy, J., 561n
Dunkerley’s method, 789
Dwell linkages, 499
Synthesis of, 499
Dwell motion, 301
Dynamic balancing, 846
Dynamic balancing machines, 848
Dynamic equilibrium, 658
Dynamic force analysis, 658
Dynamics:
Cam systems, 351
Definition, 4
Reciprocating engines, 804
Eccentric cam, 351
Eccentricity in cam system, 333
Edge mill, 913
Eighth-order polynomial cam motion, 315
Eisenberg, E. R., 645n
Elastic-body analysis, 744940 INDEX
Elliptical gears, 166
Elliptic-trammel linkage, 623
End effecter, 542
Engine, 804
Bearing loads in single-cylinder, 821
Crank arrangement, 805
Cycle, 804
Diesel-cycle, 804
Firing order, 805
Five-cylinder, 806
Four-cylinder, 859
Indicator, 811
In line, 805
Opposed piston, 806
Otto-cycle, 804
Radial, 807
Shaking force, 824
Single cylinder, 854
Six cylinder, 808
Three-cylinder, 805
Two-cylinder, 858
Types, 804
V-type, 805
Epicyclic gear, 405
Epicyclic gear train types, 407
Formula analysis, 407
Tabular analysis, 417
Equation of motion, 692
Euler’s, 710
Equilibrium, 578
Conditions, 578
Dynamic, 578, 597
Static, 578
Equivalent:
Gear, 430
Mass, 816
Erdman, A. G., 504n, 561n
Error:
Graphic, 482
Mechanical, 482
Structural, 482
Escapements, 18
Graham’s, 19
Euler, L., 4, 4n, 39n, 917n
Euler angles, 524
Euler column formula, 612
Euler equation, 75
Euler-Savary equation, 225, 230
Euler’s equations of motion, 710
Exhaust, 805
Expansion, 811
Extreme positions of crank-rocker linkage, 34
Extreme values of velocity, 161
Face cam, 298
Face gear, 443
Face width:
of Cam follower, 330
of Helical gears, 431
of Worm gear, 448
Fagerstrom, W. B., 851n
Feedback control system, 894
Ferguson, J., 419n
Ferguson’s paradox, 419
Fillet, 370
Fine adjustments, 18
Finite difference method, 287
Finitely separated postures of a rigid body, 460
Center point, 468
Circle point, 474
Five posture synthesis, 481
Four posture synthesis, 474
Center point curve, 475
Circle point curve, 475
Opposite pole quadrilateral, 475
Pole, 462
Pole Triangle, 465
Two posture synthesis, 460
Crank-and-rocker linkage, 460
Slider-crank linkage, 460
Three posture synthesis, 465
Firing order, 805
First-order kinematic coefficients, 135
Relationship to instant centers of velocity, 157
Fisher, F. E., 724n
Five-bar linkage, 258
Geared, 259
Five-cylinder engine, 806
Fixed centrode, 164–165
Flat-face follower, 298, 306
Flat pair, 10
Flip-flop mechanism, 18
Float in cam systems, 353
Flywheels, 885
Follower, 6
Force, 570
Applied, 573
Characteristics of, 573
Constraint, 573
External, 576
Friction, 591–592
Indeterminate, 512
Inertia, 666
Internal, 576
Polygon, 582
Transmitted, 598
Unit of, 569
Vector, 570INDEX 941
Force analysis:
Analytic, 583
of Bevel gears, 604
with Friction, 594
Graphic, 580
of Helical gears, 597
of Robot actuators, 558
of Spur gears, 597
Forced precession, 911
Form cutter, 381
Forward kinematics, 543
Foster, D. E., 167n
Foucault, L., 905
Four-bar linkage, 21
Algebraic posture analysis, 72
Analysis of, 67
Angular velocity relations, 156
Inversions of, 33
Spatial, 510
Spheric, 510
Four-circle method, 235
Four-cylinder engine, 859
Four-force member, 589
Four-stroke engine cycle, 805
Frame, 7
Free-body diagram, 576
Freedom:
Degrees of, 12
Idle, 511
Free vector, 575
Free vibration, 764
with viscous damping, 764
Frequency, 743
Freudenstein, F., 167n, 504n, 561n
Freudenstein’s equation, 491
Freudenstein’s theorem, 160
Friction, 591–592
Angle, 593
Coefficient of, 592
Coulomb, 592
Force, 592
Force models, 591–592
Sliding, 355, 592
Static, 592
Viscous, 593
Full depth, 376
Full-return cam motion, 316
Full-rise cam motion, 314
Function generation, 459
Fundamental law of toothed gearing, 372
Ganter, M. A., 363n
Gantry robot, 542
Gas force, 814
Gas law, 811
Gear, 369
Differentials, 449
Graphical layout, 377
Manufacture, 381
Tooth action, 376
Tooth sizes, 375
Tooth terminology, 370
TORSEN, 413
Train:
Compound, 404
Epicyclic, 405
Analysis by formula, 407
Analysis by table, 417
Bevel gear, 440
Planetary, 406
Tabular analysis, 417
Reverted, 404
Series connected, 403
Type of:
Annular, 380
Bevel, 427
Angular, 436
Spiral, 443
Straight-tooth, 436
Tooth proportions, 440
Crossed-axis helical, 433
Crown, 443
Double-helical, 433
Elliptical, 166
Epicyclic, 405
Face, 443
Helical, 427
Herringbone, 433
Hypoid, 445
Internal, 380
Miter, 436
Planet, 406
Ring, 451
Spiral, 433
Spur, 369
Sun, 406
Worm, 427
Zerol bevel, 444
Worm:
Differential, 453
Geared five-bar linkage, 259
Generalized mechanism analysis programs, 538
Generating cutter, 381
Generating line, 372
Generators:
Curve, 29
Function, 459
Straight-line, 31
Geneva mechanism, 20942 INDEX
Geneva wheel, 20
Gleasman, V., 413
Globular pair, 10
Goldberg, M., 561n
Goldberg linkage, 511
Goodman, T. P., 504n
Gough, V. E., 561n
Governors, 890
Centrifugal, 892
Electronic, 905
Inertia, 893
Graham’s escapement, 19
Graphic error, 482
Grashof’s law, 33
Gravitational system of units, 572
Gravity, standard, 572
Gray, G. L., 645n, 724n
Grodzinsky, P., 504n
Grübler, M. F, 39n
Grübler’s criterion, 14
Gustavson, R. E., 504n, 561n
Gyration, radius of, 616, 664
Gyroscope:
Definition of, 905
Motion of, 906
Gyroscopic moment, 911
Hain, K., 167n, 249n, 485n, 504n
Half-cycloidal cam motion, 321
Half-harmonic cam motion, 319
Hall, A. S., Jr., 161n, 167n, 249n, 504n
Hand and thrust relations of helical gears, 433
Harmonic forcing, 776
Harmonic motion, 314
Harrisberger, L., 509, 561n
Hartenberg, R. S., 9, 39n, 249n, 489, 504n, 528, 561n
Hartmann construction, 227
Haug, E. J., 539, 561n
Helical gears:
Contact ratio:
Axial, 431
Face, 431
Normal, 431
Total, 432
Transverse, 431
Crossed-axis:
Hand and thrust relations, 433
Tooth proportions, 435
Double, 433
Equivalent pitch radius, 429
Face width, 431
Forces on, 599
Helix angle, 428
Overlap, 432
Parallel-axis, 427
Tooth proportions, 430
Pitch:
Axial, 428
Normal circular, 428
Normal diametral, 429
Transverse circular, 428
Transverse diametral, 429
Pressure angle:
Normal, 429
Transverse, 429
Replacing spur gears with, 432
Helical motion, 50
Helical pair, 9
Helix angle, 428
Herringbone gears, 433
Hertz, H. R., 751n
Hesitation mechanisms, 29
Hesitation motion, 506
Higher pair, 8
Hindley worm, 446
Hinkle, R. T., 489, 504n
Hirschhorn, J., 249n, 504n
Hob, 342
Hobbing, 342
Hodges, H., 455
Holowenko, A. R., 39n
Holzer tabulation method, 795
Hooke universal joint, 28, 529
Hrones, J. A., 30, 39n
Hrones and Nelson atlas, 30
Humpage’s reduction gear, 440
Hunt, K. H., 504n, 561n
Hypoid gears, 445
Idle freedom, 511
Idler, 403
Image:
Acceleration, 192
Point, 468
Pole, 468
Velocity, 114
Imaginary-mass method of balancing, 856
IMP (Integrated Mechanisms Program), 539
Impulse, 714
Angular, 714
Indeterminate force, 512
Indexing mechanisms, 20
Indicator:
Diagram, 811
Engine, 811
Indices of merit, 162
Inertia:
Axes, principal, 664
Axes, transformation of, 705INDEX 943
Definition, 570
Force, 666
in Engines, 818
Governors, 893
Primary, 820
Secondary, 820
Mass moment of, 663, 922
Mass product of, 663
Measurement of, 702
Tensor, 664
Torque, 820
Inflection circle, 228
Inflection pole, 228
Influence coefficients, 787
In-line engine, 805
Instantaneous:
Acceleration, 180
Center:
of Acceleration, 234
Four-circle method of locating, 235
of Velocity, 145
Locating, 149
in Multi-degree-of-freedom planar
linkages, 265
Number of, 147
Relationship to first-order kinematic
coefficients, 157
Use for velocity analysis, 153
Screw Axis, 145n
Velocity, 105
Integration by Simpson’s rule, 887
Interference, 384
Internal gear, 380
International Standards Organization (ISO), 76n
International System (SI) of units, 572
Inverse:
Acceleration analysis, 553
Cam, 298
Kinematics, 550
Velocity analysis, 553
Inversion:
Kinematic, 32
Involute:
Curve, 374
Function, 390, 923
Generation of, 374
Helicoid, 427
Properties, 372
Involutometry, 390
Isolation, 782
Jacobian, 164
Jamming, 37
Jerk, 311
Johnson, J. B., 618n
Johnson parabolic equation, 618
Johnston, E. R., 724n
Johnston, E. R., Jr., 645n
Joint, types of:
Balanced, 584
Cardan, 529
Hooke, 529
Turning, 9
Universal, 529
Wrapping, 10
see also Pair, Types of, Lower
Jump, in cam systems, 353
Jump speed, 353
KAM (Kinematic Analysis Method), 539
Kaufman, R. E., 541, 561n
Kennedy, A. B. W., 6n, 39n, 148n
Kennedy circle, 148
Kennedy’s theorem, 148
Kinematic chain, kind, 7
Kinematic coefficients:
First-order, 135
Relationship to instant centers, 157
Velocity analysis, 135
Rolling contact condition, 143
Second-Order, 216
Acceleration analysis, 216
Relationship to radius and center of curvature,
239
Kinematic inversion, 32
Kinematic pair, 6
Kinematics:
Definition, 5
Direct, 543
Forward, 543
Inverse, 550
Kinematic synthesis, 458
Kinetic energy, 693
Kinetics, definition, 5
KINSYN (KINematic SYNthesis), 540
Kloomak, M., 363n
Knife-edge follower, 298
Kota, S., 504n
Kraige, L. G., 724n
Krause, R., 160, 167n
Kuenzel, H., 504n
Kutzbach, K., 39n
Kutzbach mobility criterion, 12
Law of gearing, 372
Lead, 448
Lead angle, 447944 INDEX
Lévai, Z. L., 421n
Lévai epicyclic gear train types, 407
Lever, 18
Lichty, L. C., 875n
Lift, 301
Limited slip differential, 452
Limit posture, 37
LINCAGES, 540
Line:
of Action, 377
of Centers, 372
Coordinates, 555
Linear actuators, 18
Linearity, 135
Linear system, 134
Link:
Binary, 7
Definition of, 6
Function of, 6
Ternary, 7
Linkage:
Balancing of, 868
Definition, 10
Planar, 10
Quick-return, 21
Types of:
Bennett, 510
Bricard, 511
Chebychev, 31
Cognate, 489
Crank-rocker, 21
Crank-shaper, 22
Differential screw, 18
Double-crank, 35
Double-rocker, 35
Drag-link, 35
Dwell, 499
Five-bar, 258
Four-bar, 21
Geared five-bar, 259
Geneva, 20
Goldberg, 511
Maltese cross, 20
Pantograph, 32
Peaucillier inversor, 31
Quick return, 21
Reuleaux coupling, 28
Roberts’, 31
RSSR, 514
Scotch-yoke, 22, 151
Scott-Russell, 32
Six-bar, 22
Slider-crank, 22
Isosceles, 460
Offset, 22
Sliding-block, 78
Spatial four-link, 508
Spheric, 11
Wanzer needle-bar, 23
Watt’s, 31
Whitworth, 22
Wobble plate, 510
Locational devices, 18
Location of a point, 48
Locus, 48
Logarithmic decrement, 767
Long-and-short-addendum system, 400
Loop-closure equation, 57
Cases of, 66, 513
Lowen, G. G., 868, 875n
Lower pair, 8
Machine, definition of, 6
Maleev, V. L., 875n
Maltese cross, 20
Manipulator, 258
Mass:
Center of, 660
Definition, 570
Equivalent, 816
Moment of inertia, 663, 922
Product of inertia, 663
Unit of, 572
Master connecting rod, 806
Matter, definition, 570
Matthew, G. K., 363n
Maxwell’s reciprocity theorem, 788
Mean effective pressure, 812
Mechanical:
Advantage, 36
Compensation balancing method, 850
Control systems, 894
Efficiency, 812
Error, 482
Mechanics:
Definition of, 4
Divisions of, 4
Mechanism:
Analysis, computer, 538
Definition of, 6
Trains, 401
Types of (see also Linkage, Types of)
Bistable, 18
Cam, 21
Cam-and-follower, 97
Clamping, 18
Escapement, 18
Fine adjustment, 18INDEX 945
Flip-flop, 18
Indexing, 20
Linear actuator, 18
Locational, 18
Oscillator, 20
Planar, 10
Quick-return, 21
Rack and pinion, 97
Ratchet, 18
Reciprocating, 21
Reversing, 27
Rocking, 20
Snap-action, 18
Spatial, 11
Stop, pause, hesitation, 29
Straight-line, 31
Swinging, 20
Toggle, 18
Mehmke, R., 114, 167n
Meriam, J. L., 724n
Merit indices, 162
M’Ewan, E., 504n
Milling of gear teeth, 381
Mischke, C. R., 98n, 421n, 504n, 645n, 795n
Miter gears, 436
Mobility, 12
Exceptions to criteria, 13
Kutzbach criterion, 12
Module, 371
Molian, S., 363n
Moment:
of a Couple, 574
Gyroscopic, 911
of Impulse, 715
of Inertia:
Area, 613, 615
Mass, 663
Measurement, 702
Polygon, 838
Shaking, 682
Vector, 575
Momentum, 714
Angular, 714
Movability, definition, 12n
Moving centrode, 165
Moving point:
Acceleration of, 181
Displacement of, 93
Locus of, 48
Velocity of, 105
MSC Working Model, 539
Muffley, R. V., 363n
Müller, R., 167n
Multi-degree of freedom, 258
NASTRAN, 539
Natural frequency, 743
Damped, 766
Neale, M. J., 645n
Nelson, G. L., 30
Newton (unit), 572
Newton, I., 645n
Newton-Raphson method, 70
Newton’s laws, 571
Newton’s notation, 745
Nodal-point balancing method, 848
Normal:
Component of acceleration, 182
Unit vector, 124
Notation, complex-rectangular, 74
Offset circle, 305
Offset follower, 300
Open kinematic chain, 7
Open posture, 68
Opposed-piston engine, 806
Opposite pole quadrilateral, 475
Order defect, 483
Orlandea, N., 539, 561n
Oscillating follower, 300
Osculating circles, 225
Osculating plane, 124
Ostenfeld, A., 618n
Otto-cycle engine, 804
Overconstrained, 13
Overdrive unit, 420
Overlay method, 483
Pair:
Types of (see also Joint, types of)
Higher, 8
Lower, 8
Cylindric, 10
Flat, 10
Helical, 9
Prismatic, 9
Revolute, 9
Spheric, 10
Wrapping, 10
Variable, 8
Pantograph linkage, 32
Parabolic motion, 302
Parallel-axis formula, 664
Parallel-axis helical gears, 427
Parker, J. W., 917n
Particle, definition, 50
Particle motion, equation of, 50946 INDEX
Path:
Coordinates, 51
Curvature, 285
Generation, 459
Point, 89
Pause mechanisms, 29
Pawl, 19
Peaucillier inversor, 31
Pendulum:
Equation of, 702
Three-string, 704
Torsional, 702
Trifilar, 704
Pennock, G. R., 167n, 421n, 561n
Percussion, center of, 682
Periodic forcing, 772
Response to, 772
Period of vibration, 743
Phase, of motion, 751
Phase angle, 751
Phase plane:
Analysis, 757
Method, 757
Representation, 755
Phasor, 750
Phillips, J., 512n, 561n
Pinion, 369
Pin joint (see Pair, Types of, Lower, Revolute)
Piston acceleration, 814
Piston-pin force, 823
Pitch:
Angle, 438
Axial, 428, 447
Base, 379
Circle, 369
Circular, 369
Normal, 428
Transverse, 428
Curve, of cam, 304
Diametral, 369
Normal, 429
Transverse, 429
Point, 372
Radius, equivalent, 429
Surface, of bevel gear, 437–438
Pivoted-cradle method of balancing, 846
Planar:
Linkage, 10
Mechanism, 10
Motion, 51
Pair, 10
Rotation about fixed center, 680
Vector equations, 64
Plane of couple, 574
Planet:
Carrier, 406
Gear, 406
Planetary gear train, 406
Force analysis, 602
Plate cam, 298
Plesha, M. E., 645n, 724n
Plücker coordinates, 555
Point:
Acceleration:
Absolute, 181
Apparent, 196
Difference, 183
Definition, 50
Displacement:
Absolute, 89, 94
Apparent, 92
Difference, 89
Pitch, 372
Position:
Absolute, 55
Apparent, 54
Difference, 53
Velocity:
Absolute, 105
Apparent, 119
Difference, 109
Polar notation, 73
Pole, 462
Pole triangle, 465
Polode, 165n
Polydyne cam, 319
Polygon:
Acceleration, 192
Force, 582
Moment, 838
Velocity, 113, 263
Pose, of rigid body, 57
Position:
Absolute, 55
Apparent, 54
Difference, 53
Rigid body, 56
Posture:
Analysis:
Algebraic, 69, 262
Graphic, 62
of Spatial mechanism, 513
Techniques, 78
Precision, 481
Rigid body, 56
Potential energy, 694
Power equation, 692
Power stroke, 805INDEX 947
Precession:
Forced, 911
Regular, 908
Steady, 908
Precision postures, 481
Prefixes, standard SI, 919
Preload on cam, 351
Pressure, mean effective, 812
Pressure angle, 164
Maximum, 333
Normal, 429
Transverse, 429
Pressure line, 377
Prime circle, 304
Principal axes, 664
Principle of superposition, 674
Prismatic pair, 9
Products of inertia, 663
Pro/ENGINEER Mechanism Dynamics, 539
Programs, computer, 538
Proportional-error feedback systems, 901
Quadrant, 76n
Quaternion, 513
Quick-return mechanism, 21
Rack, 19
Radcliffe, C. W., 504n
Radial cam, 298
Radial cam follower, 300
Radial engine, 807
Radius:
of curvature, 182
of cam profile
charts for minimum, 337
equation, 328
of gyration, 616
Rapson’s slide, 220
Ratchets, 18
Rathbone, T. C., 795, 875n
Ravani, B., 561n
Raven, F. H., 167n
Raven’s method:
for Acceleration, 213
for Posture, 74
for Velocity, 131
Rayleigh, Baron, 795n
Rayleigh-Ritz equation, 787
Rayleigh’s method, 785
Recess:
Angle, 384
Arc of, 385
Reciprocating:
Engines, dynamics of, 804
Follower, 298
Linkages, 23
Reciprocity, Maxwell’s theorem, 788
RECSYN (RECtified SYNthesis), 540
Rectangular notation, 74
Rectilinear motion, 51
Rectilinear translation, 91n
Redundant constraint, 512
Reference system, 48
Regular precession, 908
Relative motion, 32, 781
Resonance, 743
Response curve, 744
Return, motion of cam, 301
Reuleaux, F., 6, 6n
Reuleaux coupling, 28
Reverted gear train, 404
Revolute, 9
Rigid body, 570
Cam, 350
Posture, 56
Rotation of, 106
Velocity difference between, 109
Rise, motion of cam, 300
Roberts, S., 489n
Roberts-Chebychev theorem, 489
Roberts linkage, 31
Robot, 541
Robotics, 541
Robot Institute of America (RIA), 542
Roller follower, 298, 305
Rolling contact, 126
Acceleration, 206
Displacement, 95
Velocity, 126
Rosenauer, N., 167n, 249n
Rotation:
About a fixed center, 680
of crossed-helical gears, 433
Definition, 91
of Rigid body, 106
Roth, B., 167n
Rothbart, H. A., 504n
Roulettes, 165n
RSSR linkage, 511
Sandor, G. N., 504n
Sankar, T. S., 795n
SCARA robot, 542
Scarborough, J. B., 917n
Scotch-yoke linkage, 22, 151
Scott-Russell linkage, 32
Screw:
Axis, instantaneous, 145n948 INDEX
Screw: (continued)
Differential, 19
Pair (see Pair, Types of, Lower, Helical)
Second harmonic forces, 857
Second-order kinematic coefficients, 216
Relationship to radius of and center of
curvature, 239
Shaking:
Forces, 682
Engine, 824
Moments, 682
Shaping, 381
Sheth, P. N., 539, 561n
Shigley, J. E., 421n, 504n, 645n, 795n
SI (System International), 572
Conversion to U.S. customary units, 920
Prefixes, 919
Units, 572
Simple-closed chain, 7
Simple gear train, 404
Simple-harmonic cam motion, 302
Simpson’s rule integration, 887
Single cylinder engine, 821
Single plane balancers, 834
Six-bar linkage, 22
Skew curve, 51
Slenderness ratio, 616
Slider-crank linkage:
Algebraic posture analysis, 69
Analysis of, 66
Inversions of, 33
Limit positions, 22
Offset, 27
Synthesis, 460
Synthesis of, 27
Sliding connectors, 28
Sliding friction, 355, 592
Snap-action mechanism, 18
Soni, A. H., 504n
Spatial:
Four-link mechanism, 513
Graphic analysis, 514
Mechanism, 507
Motion, 51
Seven-link, 508
Speed fluctuation, coefficient of, 888
Speed ratio, 402
Spheric:
Coordinates, 49
Joint, 10
Linkage, 509
Mechanism, 507
Spheric-face follower, 298
Spheric-slide oscillator, 510
Spin axis, 907
Spiral angle, 444
Spiral gears, 433
Spring:
Rate, 351
Stiffness, 745
Surge, 362
Spur gears, 369
Forces on, 598
Standard gear tooth proportions, 375
Standard gravity, 532
Starting transient, 774
Statically indeterminate force, 512
Static balancing machines, 834
Static force analysis, 569
Static friction, 592
Statics, definition, 4
Static unbalance, 830
Stationary curvature, 242
Steady precession, 908
Steady-state vibration, 744
Step input forcing, 752
Stevensen, E. N., Jr., 504n, 856, 874n, 875n
Stevensen’s rule, 857
Stiction, 597
Stoddart, D. A., 363n
Stop mechanisms, 29
Straight-line generators, 31
Straight-tooth bevel gears, 436
Forces on, 604
Strong„ R. T., 561n
Structural error, 482
Structure:
Definition, 6
Statically indeterminate, 13
Strutt, J. W., 795n
Stub tooth, 376
Suction stroke, 805
Suh, C. H., 504n
Summing mechanism, 449
Sun gear, 406
Superposition, 273
Principle of, 674
Swashplate, 708
Synthesis:
Coupler-curve, 485
Definition, 4
Dimensional, 458
Kinematic, 458
of Linkages, 458
Number, 458
Type, 458
Tabular analysis of epicyclic gear trains, 417
Tangent cam, 312INDEX 949
Tangential component of acceleration, 183
Tao, D. C., 249n, 504n
Ternary link, 7
Tesar, D., 363n
Thearle, E. L., 795, 875n
Theorem of Mehmke, 114
Three cylinder engine, 805
Three-force member, 579
Three-string pendulum, 704
Toggle:
Mechanism, 18
Posture, 37
Tooth proportions:
Bevel gears, 440
Helical gears, 430
Spur gears, 376
Tooth sizes, 371
Tooth thickness, 370
Top dead center (TDC), 856
Torfason, L. E., 18, 39n
Torque characteristics of engines, 810
TORSEN differential, 413
Torsional pendulum, 702
Torsional system, 793
Trace point, 304
Train value, 402
Transfer formula, 664
Transformation matrix, 513
Transient disturbances, 760
Transient vibration, 744
Translation:
Curvilinear, 91n
Definition, 91
Rectilinear, 91n
Transmissibility, 782
Transmission, automotive, 404
Transmission angle, 37, 73
Extremes of, 73
Transmitted force, 598
Tredgold’s approximation, 439
Trifilar pendulum, 704
True toggle mechanism, 18
Turning pair (see Pair, Types of, Lower, Revolute)
Two-cylinder engine, 858
Two-force member, 579
Two-stroke engine cycle, 805
Type synthesis, 458
Uicker, J. J., Jr, 363n, 539, 561n
Unbalance:
Analysis of, 837
in Cam systems, 362
Dynamic, 835
Forcing caused by, 780
Static, 830
Units of, 846
Undercutting:
in Cam systems, 327
Elimination of, 330
in Gear systems, 384
Uniform motion, 301
Units:
Conversion:
SI to U.S. customary, 920
U.S. customary to SI, 920
Systems of, 571
Unit vector:
Binormal, 124
Normal, 124
Tangent, 124
Universal joint, 28
Vector:
Addition, 62
Angular momentum, 715
Approach to rotor balancing, 839
Graphical operations, 62
Loop-closure cases, 66
Subtraction, 62
Tetrahedron equation, 513
Solutions, 513
Type of:
Absolute acceleration, 181
Absolute displacement, 89, 94
Absolute position, 55
Absolute velocity, 105
Acceleration, 181
Acceleration difference, 183
Apparent acceleration, 196
Apparent displacement, 92
Apparent position, 54
Apparent velocity, 119
Displacement, 89
Displacement difference, 89
Force, 573
Moment, 574
Position, 55
Position difference, 53
Unit, 52
Velocity, 105
Velocity difference, 109
Velocity, 105
Absolute, 105
Analysis:
of Four-bar linkage, 115
Graphic, 111
Inverse, 553950 INDEX
Velocity, (continued)
of Offset slider-crank linkage, 118
Polygons, 263
of Spatial mechanism, 518
Systematic strategy for, 128
Using instantaneous centers, 153
Angular, 106
Apparent, 119
Average, 105
Condition for rolling contact, 126
Definition, 105
Difference, 109
Image, 114
Size of, 114
Instantaneous, 105
Instantaneous centers of, 145
Locating, 150
in Multi-degree-of-freedom planar linkages, 265
Using, 153
Matrix, 533
Poles, 165n, 225
Polygon, 113, 263
Ratio, Angular, 156
Vibration:
Definition, 743
Forced, 743
Free, 743
Isolation, 782
Phase-plane representation of, 768
Virtual displacement, 608
Virtual-rotor method of balancing, 856
Virtual work, 608
Viscous damping:
Coefficient of, 745
Free vibration with, 764
V-type engine, 805
Waldron, K. J., 504n, 561n
Wanzer. R. M., 23
Wanzer needle-bar linkage, 23
WATT Mechanism Design Tool, 540
Watt’s linkage, 31
Wedge cam, 298
Weight, definition, 570
Weight/mass controversy, 572, 572n
Whitworth linkage, 22
Whole depth, 372
Willis, A. H., 249n
Willis, R. W., 917n
Windup, 362
Wobble-plate mechanism, 510
Working stroke, 22
Worm, 427
Worm gear, 427, 446
Worm gear differential, 453
Wrapping pair, 10
Wrist-pin force, 816
Yang, A. T., 561n
Young’s modulus, 612
Zerol bevel gear, 444

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