Theory of Machines and Mechanisms

Cover......Page 1
Half title......Page 2
Title page......Page 4
Copyright......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 18
About the Authors......Page 26
PART 1 Kinematics and Mechanisms......Page 28
1.1 INTRODUCTION......Page 30
1.3 SCIENCE OF MECHANICS......Page 31
1.4 TERMINOLOGY, DEFINITIONS, AND ASSUMPTIONS......Page 33
1.5 PLANAR, SPHERIC, AND SPATIAL MECHANISMS......Page 37
1.6 MOBILITY......Page 39
1.7 CHARACTERISTICS OF MECHANISMS......Page 44
1.8 KINEMATIC INVERSION......Page 59
1.9 GRASHOF’S LAW......Page 60
1.10 MECHANICAL ADVANTAGE......Page 63
1.11 REFERENCES......Page 66
PROBLEMS......Page 67
2.1 LOCUS OF A MOVING POINT......Page 75
2.2 POSITION OF A POINT......Page 78
2.3 POSITION DIFFERENCE BETWEEN TWO POINTS......Page 80
2.4 APPARENT POSITION OF A POINT......Page 81
2.5 ABSOLUTE POSITION OF A POINT......Page 82
2.6 POSTURE OF A RIGID BODY......Page 83
2.7 LOOP-CLOSURE EQUATIONS......Page 84
2.8 GRAPHIC POSTURE ANALYSIS......Page 89
2.9 ALGEBRAIC POSTURE ANALYSIS......Page 96
2.10 COMPLEX-ALGEBRAIC SOLUTIONS OF PLANAR VECTOR EQUATIONS......Page 100
2.11 COMPLEX POLAR ALGEBRA......Page 101
2.12 POSTURE ANALYSIS TECHNIQUES......Page 105
2.13 COUPLER-CURVE GENERATION......Page 113
2.15 DISPLACEMENT DIFFERENCE BETWEEN TWO POINTS......Page 116
2.16 TRANSLATION AND ROTATION......Page 118
2.17 APPARENT DISPLACEMENT......Page 119
2.19 APPARENT ANGULAR DISPLACEMENT......Page 121
2.20 REFERENCES......Page 125
PROBLEMS......Page 126
3.1 DEFINITION OF VELOCITY......Page 132
3.2 ROTATION OF A RIGID BODY......Page 133
3.3 VELOCITY DIFFERENCE BETWEEN POINTS OF A RIGID BODY......Page 136
3.4 VELOCITY POLYGONS; VELOCITY IMAGES......Page 138
3.5 APPARENT VELOCITY OF A POINT IN A MOVING COORDINATE SYSTEM......Page 146
3.7 DIRECT CONTACT AND ROLLING CONTACT......Page 153
3.8 SYSTEMATIC STRATEGY FOR VELOCITY ANALYSIS......Page 155
3.9 ALGEBRAIC VELOCITY ANALYSIS......Page 156
3.10 COMPLEX-ALGEBRAIC VELOCITY ANALYSIS......Page 158
3.11 METHOD OF KINEMATIC COEFFICIENTS......Page 162
3.12 INSTANTANEOUS CENTERS OF VELOCITY......Page 172
3.13 ARONHOLD-KENNEDY THEOREM OF THREE CENTERS......Page 174
3.14 LOCATING INSTANTANEOUS CENTERS OF VELOCITY......Page 176
3.15 VELOCITY ANALYSIS USING INSTANT CENTERS......Page 180
3.16 ANGULAR-VELOCITY-RATIO THEOREM......Page 183
3.17 RELATIONSHIPS BETWEEN FIRST-ORDER KINEMATIC COEFFICIENTS AND INSTANT CENTERS......Page 184
3.18 FREUDENSTEIN’S THEOREM......Page 187
3.19 INDICES OF MERIT; MECHANICAL ADVANTAGE......Page 189
3.20 CENTRODES......Page 191
3.21 REFERENCES......Page 193
PROBLEMS......Page 194
4.1 DEFINITION OF ACCELERATION......Page 207
4.3 ACCELERATION DIFFERENCE BETWEEN POINTS OF A RIGID BODY......Page 210
4.4 ACCELERATION POLYGONS; ACCELERATION IMAGES......Page 219
4.5 APPARENT ACCELERATION OF A POINT IN A MOVING COORDINATE SYSTEM......Page 223
4.6 APPARENT ANGULAR ACCELERATION......Page 232
4.7 DIRECT CONTACT AND ROLLING CONTACT......Page 233
4.8 SYSTEMATIC STRATEGY FOR ACCELERATION ANALYSIS......Page 239
4.9 ALGEBRAIC ACCELERATION ANALYSIS......Page 240
4.10 COMPLEX-ALGEBRAIC ACCELERATION ANALYSIS......Page 241
4.11 METHOD OF KINEMATIC COEFFICIENTS......Page 243
4.12 EULER-SAVARY EQUATION......Page 252
4.13 BOBILLIER CONSTRUCTIONS......Page 257
4.14 INSTANTANEOUS CENTER OF ACCELERATION......Page 261
4.15 BRESSE CIRCLE (OR DE LA HIRE CIRCLE)......Page 262
4.16 RADIUS OF CURVATURE OF A POINT TRAJECTORY USING KINEMATIC COEFFICIENTS......Page 266
4.17 CUBIC OF STATIONARY CURVATURE......Page 269
4.18 REFERENCES......Page 276
PROBLEMS......Page 277
5.1 INTRODUCTION......Page 285
5.2 POSTURE ANALYSIS; ALGEBRAIC SOLUTION......Page 289
5.3 VELOCITY ANALYSIS; VELOCITY POLYGONS......Page 290
5.4 INSTANTANEOUS CENTERS OF VELOCITY......Page 292
5.5 FIRST-ORDER KINEMATIC COEFFICIENTS......Page 295
5.6 METHOD OF SUPERPOSITION......Page 300
5.7 ACCELERATION ANALYSIS; ACCELERATION POLYGONS......Page 303
5.8 SECOND-ORDER KINEMATIC COEFFICIENTS......Page 305
5.9 PATH CURVATURE OF A COUPLER POINT TRAJECTORY......Page 312
5.10 FINITE DIFFERENCEMETHOD......Page 316
PROBLEMS......Page 319
PART 2 Design of Mechanisms......Page 322
6.1 INTRODUCTION......Page 324
6.2 CLASSIFICATION OF CAMS AND FOLLOWERS......Page 325
6.3 DISPLACEMENT DIAGRAMS......Page 327
6.4 GRAPHIC LAYOUT OF CAM PROFILES......Page 330
6.5 KINEMATIC COEFFICIENTS OF FOLLOWER......Page 334
6.6 HIGH-SPEED CAMS......Page 339
6.7 STANDARD CAMMOTIONS......Page 340
6.8 MATCHING DERIVATIVES OF DISPLACEMENT DIAGRAMS......Page 350
6.9 PLATE CAM WITH RECIPROCATING FLAT-FACE FOLLOWER......Page 354
6.10 PLATE CAM WITH RECIPROCATING ROLLER FOLLOWER......Page 359
6.11 RIGID AND ELASTIC CAM SYSTEMS......Page 377
6.12 DYNAMICS OF AN ECCENTRIC CAM......Page 378
6.13 EFFECT OF SLIDING FRICTION......Page 382
6.14 DYNAMICS OF DISK CAM WITH RECIPROCATING ROLLER FOLLOWER......Page 383
6.15 DYNAMICS OF ELASTIC CAM SYSTEMS......Page 386
6.16 UNBALANCE, SPRING SURGE, AND WINDUP......Page 389
PROBLEMS......Page 390
7.1 TERMINOLOGY AND DEFINITIONS......Page 396
7.2 FUNDAMENTAL LAW OF TOOTHED GEARING......Page 399
7.3 INVOLUTE PROPERTIES......Page 400
7.4 INTERCHANGEABLE GEARS; AGMA STANDARDS......Page 402
7.5 FUNDAMENTALS OF GEAR-TOOTH ACTION......Page 403
7.6 MANUFACTURE OF GEAR TEETH......Page 408
7.7 INTERFERENCE AND UNDERCUTTING......Page 411
7.8 CONTACT RATIO......Page 413
7.9 VARYING CENTER DISTANCE......Page 415
7.10 INVOLUTOMETRY......Page 416
7.11 NONSTANDARD GEAR TEETH......Page 420
7.12 PARALLEL-AXIS GEAR TRAINS......Page 428
7.13 DETERMINING TOOTH NUMBERS......Page 431
7.14 EPICYCLIC GEAR TRAINS......Page 432
7.15 ANALYSIS OF EPICYCLIC GEAR TRAINS BY FORMULA......Page 434
7.16 TABULAR ANALYSIS OF EPICYCLIC GEAR TRAINS......Page 444
PROBLEMS......Page 448
8.1 PARALLEL-AXIS HELICAL GEARS......Page 454
8.2 HELICAL GEAR TOOTH RELATIONS......Page 455
8.3 HELICAL GEAR TOOTH PROPORTIONS......Page 457
8.4 CONTACT OF HELICAL GEAR TEETH......Page 458
8.5 REPLACING SPUR GEARS WITH HELICAL GEARS......Page 459
8.6 HERRINGBONE GEARS......Page 460
8.7 CROSSED-AXIS HELICAL GEARS......Page 461
8.8 STRAIGHT-TOOTH BEVEL GEARS......Page 463
8.10 BEVEL GEAR EPICYCLIC TRAINS......Page 467
8.12 SPIRAL BEVEL GEARS......Page 470
8.14 WORMS ANDWORM GEARS......Page 472
8.15 SUMMERS AND DIFFERENTIALS......Page 476
8.16 ALL-WHEEL DRIVE TRAIN......Page 480
PROBLEMS......Page 482
9.1 TYPE, NUMBER, AND DIMENSIONAL SYNTHESIS......Page 485
9.2 FUNCTION GENERATION, PATH GENERATION, AND BODY GUIDANCE......Page 486
9.3 TWO FINITELY SEPARATED POSTURES OF A RIGID BODY (N = 2)......Page 487
9.4 THREE FINITELY SEPARATED POSTURES OF A RIGID BODY (N = 3)......Page 492
9.5 FOUR FINITELY SEPARATED POSTURES OF A RIGID BODY (N = 4)......Page 501
9.7 PRECISION POSTURES; STRUCTURAL ERROR; CHEBYSHEV SPACING......Page 508
9.8 OVERLAY METHOD......Page 510
9.9 COUPLER-CURVE SYNTHESIS......Page 512
9.10 COGNATE LINKAGES; ROBERTS-CHEBYSHEV THEOREM......Page 516
9.11 FREUDENSTEIN’S EQUATION......Page 518
9.12 ANALYTIC SYNTHESIS USING COMPLEX ALGEBRA......Page 522
9.13 SYNTHESIS OF DWELL LINKAGES......Page 526
9.14 INTERMITTENT ROTARY MOTION......Page 527
PROBLEMS......Page 531
10.1 INTRODUCTION......Page 534
10.2 EXCEPTIONS TO THE MOBILITY CRITERION......Page 536
10.3 SPATIAL POSTURE-ANALYSIS PROBLEM......Page 540
10.4 SPATIAL VELOCITY AND ACCELERATION ANALYSES......Page 545
10.5 EULER ANGLES......Page 551
10.6 DENAVIT-HARTENBERG PARAMETERS......Page 555
10.7 TRANSFORMATION-MATRIX POSTURE ANALYSIS......Page 557
10.8 MATRIX VELOCITY AND ACCELERATION ANALYSES......Page 560
10.9 GENERALIZED MECHANISM ANALYSIS COMPUTER PROGRAMS......Page 565
10.10 INTRODUCTION TO ROBOTICS......Page 568
10.11 TOPOLOGICAL ARRANGEMENTS OF ROBOTIC ARMS......Page 569
10.12 FORWARD KINEMATICS PROBLEM......Page 570
10.13 INVERSE KINEMATICS PROBLEM......Page 577
10.14 INVERSE VELOCITY AND ACCELERATION ANALYSES......Page 580
10.15 ROBOT ACTUATOR FORCE ANALYSIS......Page 585
10.16 REFERENCES......Page 588
PROBLEMS......Page 589
PART 3 Dynamics of Machines......Page 594
11.1 INTRODUCTION......Page 596
11.3 SYSTEMS OF UNITS......Page 598
11.4 APPLIED AND CONSTRAINT FORCES......Page 600
11.5 FREE-BODY DIAGRAMS......Page 603
11.6 CONDITIONS FOR EQUILIBRIUM......Page 605
11.7 TWO- AND THREE-FORCE MEMBERS......Page 606
11.8 FOUR- AND MORE-FORCE MEMBERS......Page 616
11.9 FRICTION-FORCE MODELS......Page 618
11.10 FORCE ANALYSIS WITH FRICTION......Page 621
11.11 SPUR- AND HELICAL-GEAR FORCE ANALYSIS......Page 624
11.12 STRAIGHT-TOOTH BEVEL-GEAR FORCE ANALYSIS......Page 631
11.13 METHOD OF VIRTUAL WORK......Page 635
11.14 INTRODUCTION TO BUCKLING......Page 638
11.15 EULER COLUMN FORMULA......Page 639
11.16 CRITICAL UNIT LOAD......Page 642
11.17 CRITICAL UNIT LOAD AND SLENDERNESS RATIO......Page 645
11.18 JOHNSON’S PARABOLIC EQUATION......Page 646
11.19 REFERENCES......Page 672
PROBLEMS......Page 673
12.2 CENTROID AND CENTER OF MASS......Page 685
12.3 MASS MOMENTS AND PRODUCTS OF INERTIA......Page 690
12.4 INERTIA FORCES AND D’ALEMBERT’S PRINCIPLE......Page 693
12.5 PRINCIPLE OF SUPERPOSITION......Page 701
12.6 PLANAR ROTATION ABOUT A FIXED CENTER......Page 707
12.7 SHAKING FORCES AND MOMENTS......Page 709
12.8 COMPLEX-ALGEBRAIC APPROACH......Page 710
12.9 EQUATION OF MOTION FROM POWER EQUATION......Page 719
12.10 MEASURING MASS MOMENT OF INERTIA......Page 729
12.11 TRANSFORMATION OF INERTIA AXES......Page 732
12.12 EULER’S EQUATIONS OF MOTION......Page 737
12.14 ANGULAR IMPULSE AND ANGULAR MOMENTUM......Page 741
12.15 REFERENCES......Page 751
PROBLEMS......Page 752
13.1 DIFFERENTIAL EQUATIONS OF MOTION......Page 770
13.2 A VERTICAL MODEL......Page 774
13.3 SOLUTION OF THE DIFFERENTIAL EQUATION......Page 775
13.4 STEP INPUT FORCING......Page 779
13.5 PHASE-PLANE REPRESENTATION......Page 782
13.6 PHASE-PLANE ANALYSIS......Page 784
13.7 TRANSIENT DISTURBANCES......Page 787
13.8 FREE VIBRATION WITH VISCOUS DAMPING......Page 791
13.9 DAMPING OBTAINED BY EXPERIMENT......Page 793
13.10 PHASE-PLANE REPRESENTATION OF DAMPED VIBRATION......Page 795
13.11 RESPONSE TO PERIODIC FORCING......Page 799
13.12 HARMONIC FORCING......Page 803
13.13 FORCING CAUSED BY UNBALANCE......Page 807
13.14 RELATIVE MOTION......Page 808
13.15 ISOLATION......Page 809
13.16 RAYLEIGH’S METHOD......Page 812
13.17 FIRST AND SECOND CRITICAL SPEEDS OF A SHAFT......Page 814
13.18 TORSIONAL SYSTEMS......Page 820
13.19 REFERENCES......Page 822
PROBLEMS......Page 823
14.1 ENGINE TYPES......Page 831
14.2 INDICATOR DIAGRAMS......Page 838
14.4 GAS FORCES......Page 841
14.5 EQUIVALENT MASSES......Page 843
14.6 INERTIA FORCES......Page 845
14.7 BEARING LOADS IN A SINGLE-CYLINDER ENGINE......Page 848
14.8 SHAKING FORCES OF ENGINES......Page 851
14.9 COMPUTATION HINTS......Page 852
PROBLEMS......Page 855
15.1 STATIC UNBALANCE......Page 857
15.2 EQUATIONS OF MOTION......Page 858
15.3 STATIC BALANCING MACHINES......Page 861
15.4 DYNAMIC UNBALANCE......Page 862
15.5 ANALYSIS OF UNBALANCE......Page 864
15.6 DYNAMIC BALANCING......Page 873
15.7 DYNAMIC BALANCING MACHINES......Page 875
15.8 FIELD BALANCING WITH A PROGRAMMABLE CALCULATOR......Page 878
15.9 BALANCING A SINGLE-CYLINDER ENGINE......Page 881
15.10 BALANCING MULTI-CYLINDER ENGINES......Page 885
15.11 ANALYTIC TECHNIQUE FOR BALANCING MULTI-CYLINDER ENGINES......Page 889
15.12 BALANCING LINKAGES......Page 895
15.13 BALANCING OF MACHINES......Page 901
PROBLEMS......Page 902
16.1 DYNAMIC THEORY OF FLYWHEELS......Page 912
16.2 INTEGRATION TECHNIQUE......Page 914
16.4 CLASSIFICATION OF GOVERNORS......Page 917
16.5 CENTRIFUGAL GOVERNORS......Page 919
16.6 INERTIA GOVERNORS......Page 920
16.7 MECHANICAL CONTROL SYSTEMS......Page 921
16.8 STANDARD INPUT FUNCTIONS......Page 922
16.9 SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS......Page 924
16.10 ANALYSIS OF PROPORTIONAL-ERROR FEEDBACK SYSTEMS......Page 928
16.11 INTRODUCTION TO GYROSCOPES......Page 932
16.12 MOTION OF A GYROSCOPE......Page 933
16.13 STEADY OR REGULAR PRECESSION......Page 935
16.14 FORCED PRECESSION......Page 938
PROBLEMS......Page 944
Appendix A: Tables......Page 946
Appendix B......Page 952
INDEX......Page 962