Theory of Machines and Mechanisms – Third Edition

Theory of Machines and Mechanisms – Third Edition
اسم المؤلف
John J. Dicker, Gordon R. Pennock, Joseph E. Shigley
التاريخ
25 ديسمبر 2023
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371
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Theory of Machines and Mechanisms
Third Edition
John J. Dicker, Jr.
Professor 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
Contents
PREFACE XIII
ABOUT THE AUTHORS XVII
Part1 KINEMATICS AND MECHANISMS 1
1 The World of Mechanisms 3
1.1 Introduction 3
1.2 Analysis and Synthesis 4
1.3 The Science of Mechanics 4
1.4 Terminology, Definitions, and Assumptions 5
1.5 Planar, Spherical, and Spatial Mechanisms 10
1.6 Mobility II
1.7 Classification of Mechanisms 14
1.8 Kinematic Inversion 26
1.9 Grashof’s Law 27
1.10 Mechanical Advantage 29
Problems 31
2 Positionand Displacement 33
2.1 Locus of a Moving Point 33
2.2 Position of a Point 36
2.3 Position Difference Between Two Points 37
2.4 Apparent Position of a Point 38
2.5 Absolute Position of a Point 39
2.6 The Loop-Closure Equation 41
2.7 Graphic Position Analysis 45
2.8 Algebraic Position Analysis 51
2.9 Complex-Algebra Solutions of Planar Vector Equations 55
2.10 Complex Polar Algebra 57
2.11 Position Analysis Techniques 60
2.12 The Chace Solutions to Planar Vector Equations 64
2.13 Coupler-Curve Generation 68
2.14 Displacement of a Moving Point 70
2.15 Displacement Difference Between Two Points 71vi CONTENTS
2.16 Rotation and Translation 72
2.17 Apparent Displacement 74
2.18 Absolute Displacement 75
Problems 76
3 Velocity 79
3.1 Definition of Velocity 79
3.2 Rotation of a Rigid Body 80
3.3 Velocity Difference Between Points of a Rigid Body 82
3.4 Graphic Methods; Velocity Polygons 85
3.5 Apparent Velocity of a Point in a Moving Coordinate System 92
3.6 Apparent Angular Velocity 97
3.7 Direct Contact and Rolling Contact 98
3.8 Systematic Strategy for Velocity Analysis 99
3.9 Analytic Methods 100
3.10 Complex-Algebra Methods 101
3.11 The Method of Kinematic Coefficients 105
3.12 The Vector Method 116
3.13 Instantaneous Center of Velocity 117
3.14 The Aronhold-Kennedy Theorem of Three Centers 119
3.15 Locating Instant Centers of Velocity 120
3.16 Velocity Analysis Using Instant Centers 123
3.17 The Angular-Velocity-Ratio Theorem 126
3.18 Relationships Between First-Order Kinematic Coefficients and Instant Centers 127
3.19 Freudenstein’ s Theorem 129
3.20 Indices of Merit; Mechanical Advantage 130
3.21 Centrodes 133
Problems 135
4 Acceleration 141
4.1 Definition of Acceleration 141
4.2 Angular Acceleration 144
4.3 Acceleration Difference Between Points of a Rigid Body 144
4.4 Acceleration Polygons 151
4.5 Apparent Acceleration of a Point in a Moving Coordinate System 155
4.6 Apparent Angular Acceleration 163
4.7 Direct Contact and Rolling Contact 164
4.8 Systematic Strategy for Acceleration Analysis 167
4.9 Analytic Methods 168
4.10 Complex-Algebra Methods 169CONTENTS vii
4.11 The Method of Kinematic Coefficients 171
4.12 The Chace Solutions 175
4.13 The Instant Center of Acceleration 177
4.14 The Euler-Savary Equation 178
4.15 The Bobillier Constructions 183
4.16 Radius of Curvature of a Point Trajectory Using Kinematic Coefficients 187
4.17 The Cubic of Stationary Curvature 188
Problems 190
Part 2 DESIGN OF MECHANISMS 195
5 Carn Design 197
5.1 Introduction 197
5.2 Classification of Cams and Followers 198
5.3 Displacement Diagrams 200
5.4 Graphical Layout of Cam Profiles 203
5.5 Kinematic Coefficients of the Follower Motion 207
5.6 High-Speed Cams 211
5.7 Standard Cam Motions 212
5.8 Matching Derivatives of the Displacement Diagrams 222
5.9 Plate Cam with Reciprocating Flat-Face Follower 225
5.10 Plate Cam with Reciprocating Roller Follower 230
Problems 250
6 Spur Gears 252
6.1 Terminology and Definitions 252
6.2 Fundamental Law of Toothed Gearing 255
6.3 Involute Properties 256
6.4 Interchangeable Gears; AGMA Standards 257
6.5 Fundamentals of Gear-Tooth Action 259
6.6 The Manufacture of Gear Teeth 262
6.7 Interference and Undercutting 265
6.8 Contact Ratio 268
6.9 Varying the Center Distance 270
6.10 Involutometry 271
6.11 Nonstandard Gear Teeth 274
Problems 282
7 Helical Gears 286
7.1 Parallel-Axis Helical Gears 286
7.2 Helical Gear Tooth Relations 287viii CONTENTS
7.3 Helical Gear Tooth Proportions 289
7.4 Contact of Helical Gear Teeth 290
7.5 Replacing Spur Gears with Helical Gears 291
7.6 Herringbone Gears 292
7.7 Crossed-Axis Helical Gears 292
Problems 295
8 Bevel Gears 297
8.1 Straight-Tooth Bevel Gears 297
8.2 Tooth Proportions for Bevel Gears 301
8.3 Crown and Face Gears 302
8.4 Spiral Bevel Gears 303
8.5 Hypoid Gears 304
Problems 305
9 Worms and Worm Gears 306
9.1 Basics 306
Problems 310
10 Mechanism Trains 311
10.1 Parallel-Axis Gear Trains 311
10.2 Examples of Gear Trains 313
10.3 Determining Tooth Numbers 314
10.4 Epicyclic Gear Trains 315
10.5 Bevel Gear Epicyclic Trains 317
10.6 Analysis of Planetary Gear Trains by Formula 317
10.7 Tabular Analysis of Planetary Gear Trains 319
10.8 Adders and Differentials 323
10.9 All Wheel Drive Train 327
Problems 329
11 Synthesisof Linkages 332
11.1 Type, Number, and Dimensional Synthesis 332
11.2 Function Generation, Path Generation, and Body Guidance 333
11.3 Two-Position Synthesis of Slider-Crank Mechanisms 333
11.4 Two-Position Synthesis of Crank-and-Rocker Mechanisms 334
11.5 Crank-Rocker Mechanisms with Optimum Transmission Angle 335
11.6 Three-Position Synthesis 338
11.7 Four-Position Synthesis; Point-Precision Reduction 339
. 11.8 Precision Positions; Structural Error; Chebychev Spacing 341
11.9 The Overlay Method 34311.10 Coupler-Curve Synthesis 344
11.11 Cognate Linkages; The Roberts-Chebychev Theorem 348
11.l2 Bloch’s Method of Synthesis 350
11.I3 Freudenstein’s Equation 352
11.I4 Analytic Synthesis Using Complex Algebra 356
11.15 Synthesis of Dwell Mechanisms 360
II.I 6 Intermittent Rotary Motion 361
Problems 366
12 Spatial Mechanisms 368
12.1 Introduction 368
12.2 Exceptions in the Mobility of Mechanisms 369
12.3 The Position-Analysis Problem 373
12.4 Velocity and Acceleration Analyses 378
12.5 The Eulerian Angles 384
12.6 The Denavit-Hartenberg Parameters 387
12.7 Transformation-Matrix Position Analysis 389
12.8 Matrix Velocity and Acceleration Analyses 392
12.9 Generalized Mechanism Analysis Computer Programs 397
Problems 400
13 Robotics 403
13.1 Introduction 403
13.2 Topological Arrangements of Robotic Arms 404
13.3 Forward Kinematics 407
13.4 Inverse Position Analysis 411
13.5 Inverse Velocity and Acceleration Analyses 414
13.6 Robot Actuator Force Analyses 418
Problems 421
Part 3 DYNAMICS OF MACHINES 423
14 Static;: ForceAnalysis 425
14.1 Introduction 425
14.2 Newton’s Laws 427
14.3 Systems of Units 428
14.4 Applied and Constraint Forces 429
14.5 Free-Body Diagrams 432
14.6 Conditions for Equilibrium 433
14.7 Two- and Three-Force Members 435
14.8 Four-Force Members 443
CONTENTSx CONTENTS
14.9 Friction-Force Models 445
14.10 Static Force Analysis with Friction 448
14.11 Spur- and Helical-Gear Force Analysis 451
14.12 Straight- Bevel-Gear Force Analysis 457
14.13 The Method of Virtual Work 461
Problems 464
15 Dynamic ForceAnalysis (Planar) 470
15.1 Introduction 470
15.2 Centroid and Center of Mass 470
15.3 Mass Moments and Products of Inertia 475
15.4 Inertia Forces and D’ Alembert’s Principle 478
15.5 The Principle of Superposition 485
15.6 Planar Rotation About a Fixed Center 489
15.7 Shaking Forces and Moments 492
15.8 Complex Algebra Approach 492
15.9 Equation of Motion 502
Problems 511
16 Dynamic ForceAnalysis(Spatial) 515
16.1 Introduction 515
16.2 Measuring Mass Moment of Inertia 515
16.3 Transformation of Inertia Axes 519
16.4 Euler’s Equations of Motion 523
16.5 Impulse and Momentum 527
16.6 Angular Impulse and Angular Momentum 528
Problems 538
17 Vibration Analysis 542
17.1 Differential Equations of Motion 542
17.2 A Vertical Model 546
17.3 Solution of the Differential Equation 547
17.4 Step Input Forcing 551
17.5 Phase-Plane Representation 553
17.6 Phase-Plane Analysis 555
17.7 Transient Disturbances 559
17.8 Free Vibration with Viscous Damping 563
17.9 Damping Obtained by Experiment 565
17.10 Phase-Plane Representation of Damped Vibration 567
17.11 Response to Periodic Forcing 571
17.12 Harmonic Forcing 574CONTENTS xi
17.13 Forcing Caused by Unbalance 579
17.14 Relative Motion 580
17.15 Isolation 580
17.16 Rayleigh’s Method 583
17.17 First and Second Critical Speeds of a Shaft 586
17.18 Torsional Systems 592
Problems 594
18 Dynamics of Reciprocating Engines 598
18.1 Engine Types 598
18.2 Indicator Diagrams 603
18.3 Dynamic Analysis-General 606
18.4 Gas Forces 606
18.5 Equivalent Masses 609
18.6 Inertia Forces 610
18.7 Bearing Loads in a Single-Cylinder Engine 613
18.8 Crankshaft Torque 616
18.9 Engine Shaking Forces 616
18.10 Computation Hints 617
Problems 620
19 Balancing 621
19.1 Static Unbalance 621
19.2 Equations of Motion 622
19.3 Static Balancing Machines 624
19.4 Dynamic Unbalance 626
19.5 Analysis of Unbalance 627
19.6 Dynamic Balancing 635
19.7 Balancing Machines 638
19.8 Field Balancing with a Programmable Calculator 640
19.9 Balancing a Single-Cylinder Engine 643
19.10 Balancing Multicylinder Engines 647
19.11 Analytical Technique for Balancing Multicylinder Reciprocating Engines 651
19.12 Balancing Linkages 656
19.13 Balancing of Machines 661
Problems 663
20 Cam Dynamics 665
20.1 Rigid- and Elastic-Body Cam Systems 665
20.2 Analysis of an Eccentric Cam 666
20.3 Effect of Sliding Friction 670xii CONTENTS
20.4 Analysis of Disk Cam with Reciprocating Roller Follower 671
20.5 Analysis of Elastic Cam Systems 673
20.6 Unbalance, Spring Surge, and Windup 675
Problems 676
21 Flywheels 678
21.1 Dynamic Theory 678
21.2 Integration Technique 680
21.3 Multicylinder Engine Torque Summation 682
Problems 683
22 Governors 685
22.1 Classification 685
22.2 Centrifugal Governors 686
22.3 Inertia Governors 687
22.4 Mechanical Control Systems 687
22.5 Standard Input Functions 689
22.6 Solution of Linear Differential Equations 690
22.7 Analysis of Proportional-Error Feedback Systems 695
23 Gyroscopes 699
23.1 Introduction 699
23.2 The Motion of a Gyroscope 700
23.3 Steady or Regular Precession 701
23.4 Forced Precession 704
Problems 711
APPENDIXES
ApPENDIX A: TABLES
Table 1 Standard SI Prefixes 712
Table 2 Conversion from U.S. Customary Units to SI Units 713
Table 3 Conversion from SI Units to U.S. Customary Units 713
Table 4 Properties of Areas 714
Table 5 Mass Moments ofInertia 715
Table 6 Involute Function 716
ApPENDIX B: ANSWERS TO SELECTED PROBLEMS 718
INDEX 725
Index
Absolute Second, 210 Apparent position, 38-39
Acceleration, 142 of Spatial Mechanisms, 396-397 Equation, 39
Coordinate system, 40 Tangential component of, 143 Apparent velocity, 93-94
Displacement, 75 Action, line of, 256, 259 Angular, 97-98
Motion,26 Actuator, linear, 14 Equation, 97
Position, 39–40 ADAMS (Automatic Dynamic Analysis Equation, 93
System of units, 428 of Mechanical Systems), 398 Applied force, 429
Velocity, 80 Addendum, 253, 254 Approach
Acceleration,141-193 Circle, 259 Angle, 265-266
Absolute, 142 Adder and differential mechanisms, 323 Arc of, 265-266, 268
Angular, 144 Adjustments, 14 Arc
Apparent, 155-163 Advance stroke, 18-20 of Approach, 265-266, 268
Angular, 163 AGMA (American Gear Manufacturers of Recess, 266, 268
Equation, 163 Association), 257, 257n Area moment of inertia, 714
Equation, 158 Air-standard cycle, 604 Arm of couple, 430
Average, 141 Alvord, H. H., 517n Aronhold,135n
Cam follower, 210-211 All wheel drive train, 327-328 Aronhold-Kennedy theorem, 119-120
Centripetal component of. Amplitude of vibration, 550 Articulated arm, 404, 405
See Normal component Analysis, 4 Automotive
Components of Dynamic force, 470-514 All wheel drive train, 327-328
Centripetal component. Elastic body, 5, 427, 665 Cruise-control,698
See Normal component Rigid body, 5, 426, 665 Differential,325-328
Coriolis component, 158-163, 168 Static force, 425–463 Limited slip, 326
Normal component, 143, 146-155, Angular Suspension, 398
157-163, 168 Acceleration, 144 Overhead valve arrangement, 666
Rolling-contact component, Apparent acceleration, 163 Transmission, 313
164-167, 168 Apparent velocity, 97-98 Average
Tangential component, 143, Displacement, 80-81, 83 Acceleration, 141
146-155, 158-163, 168 Impulse, 528-538 Velocity, 79
Coriolis component of, 143, Momentum, 528-538, 701, 703-704 Axes, principal, 475
146-155, 157-163, 168 Velocity, 82 Axial pitch, 287-288
Definition of, 141 Ratio theorem, 126 Axodes, 135n
Difference, 145-150 Angular bevel gears, 297
Equation, 148 Annular gear, 262 Back cone, 300
Image, 153 ANSI (American National Standards Backlash, 255
Instant center of, 177-178 Institute), 257n Balancing, 621-664
Normal component of, 143, 157 Answers to selected problems, 718-724 Definition of, 621
Polygon,151-155 ANSYS,397 Direct method of, 633-635
Relations Apparent acceleration, 155-163 Dynamic, 635-638
of Four-bar linkage, 148-151 Angular, 163 Field,640-643
of Slider-crank mechanism, Equation, 163 of Linkages, 656-661
160-163,607 Equation, 158 Machines, 624-626
Rolling-contact component of, Apparent displacement, 74-75 Mechanical compensation,
164-165 Equation, 74 639-640
725726 INDEX
Balancing (continued)
Nodal-Point, 638-639
Pivoted-cradle, 636, 638
of Machines, 661-662
of Multicylinder engines, 647-651,
651-656
of Single-cylinder engines, 643-647
Static, 624-626
Ball, R. S., 135n
Ball’s point, 189
Ball-and-socket joint, 9
Barrel cam, 198, 199
Base
Circle, 259
of Cam, 203
of Gear, 256
Cylinder, 256
Link,7
Pitch,261
Basic units, 428
Beer, F. P., 447n
Bennett’s mechanism, 371, 372
Berkhoff, R. S., 656n
Bernoulli, J., 461
Bevel gear, 297-305
Epicyclic trains, 317
Forces on, 457-460
Spiral, 303-304
Zerol, 303-304
Beyer, R. A., 365n
Bhat, R. B., 593n
Bistable mechanism, 15
Bloch, S. Sch., 350, 365n
Bloch’s method of synthesis, 350-352
Bobillier constructions, 183-187
Bobillier theorem, 183
Body-fixed axes, 384
Body guidance, 333
Bore-stroke ratio, 605
Bottom dead center (BDC), 646
Branch defect, 343
Bricard linkage, 372
Bridgman, P. W, 545n
Brodell, R. J., 365n
Calahan, D. A., 398n
Cam, 17-18, 198
Definition of, 198
Displacement diagram, 200-203
Dynamics, 665-676
Elastic body, 665
Follower, 17-18
Curved-shoe, 198, 199
Flat-face, 198-200
Knife-edge, 198, 199
Offset, 198, 199
Oscillating, 198-200
Radial, 198
Reciprocating, 198-200
Roller, 198-200
Spherical-face, 198
Forces, 667
Layout, 203-206
Pressure angle, 231-232
Maximum, 232
Profile, 203-206
Coordinates, 229, 240
Rigid-body, 665
Roller, size of, 234-239
Shaft torque, 668
Standard motions, 212-221
Types of
Barrel, 198, 199
Circle-arc, 211-212
Conjugate, 200
Constant breadth, 200
Cylindric, 198
Disk, 198
Dual, 200
End,198
Face, 198, 199
Inverse, 198
Plate, 198, 199
Radial, 198
Tangent, 211-212
Wedge, 198, 199
Card factor, 605
Cardan
Joint, 22, 370, 388-389
Suspension, 699-700
Cartesian coordinates, 34
Cayley, A, 349, 365n
Cayley diagram, 349
Center of mass, 470-474
Center of percussion, 491, 609
Centrifugal governors, 686
Centripetal component of acceleration.
See Normal component
of acceleration
Centrode, 133-134
Fixed, 133
Moving, 133
Normal, 134
Tangent, 134
Centroid,472
of Area, 472
Definition of, 472
Chace, M. A., 64n, 373n, 374,
398,398n
Chace approach, 374
Acceleration analysis, 175-177
Position analysis, 64-68, 374
Velocity analysis, 116-117
Chain, kinematic, 6, 26
Chebychev linkage, 24-25
Chebychev spacing, 341-343
Chen, F. Y., 241n
Circle-arc cam, 211-212
Circling-point curve, 188
Circular
Frequency, 549-550, 623
Pitch, 254
Normal,287-288
Transverse, 287-288
Clamping mechanism, 14-15,41
Classification of mechanisms, 14-26
Clearance, 253, 255
Closed chain, 7
Closed-loop control system, 687-688
Coefficient
of Friction, 447
Kinematic, 105-117
First-order, 115
Second-order, 172
of Speed fluctuation, 681
of Viscous damping, 544
Cognate linkage, 23, 348-350
Collineation axis, 130
Complex algebra, 55-57,101-105,
169-171,356-360,492-502
Components of acceleration
Centripetal component.
See Normal component
Coriolis component, 158
Normal component, 143, 146, 157
Rolling-contact component, 164-165
Tangential component, 143, 146, 158
Compound-closed chain, 7
Compound gear train, 313
Compression, 599
Ratio, 605
Computer programs, 397-399
Concurrency, point of, 438
Concurrent forces, 436
Conjugate
Cams, 200INDEX 727
Points, 179 Position analysis, 54-55 Denavit-Hartenberg parameters,
Profiles, 255 Spatial, 375-384 387-389,407
Connecting rod, 54 Spherical, 370 Derived unit, 428
Articulated, 600 Synthesis, 334-338 Design, definition of
Force, 614-616 Crankshaft, 60 I Diagram
Master, 600 Two-throw, 648 Displacement, 200-203
Connector, 21-22 Force, 614-616 Free-body, 432-433
Conservation of angular Torque, 616 Schematic, 6
momentum, 530 Crank-shaper mechanism, 17, 19-20 Diametral pitch, 252
Conservation of momentum, 528 Critical damping, 563, 623 Normal, 287-288
Constant-breadth cam, 200 Critical damping coefficient, 563, 623 Transverse, 287-288
Constraint, 42 Critical speed, 586-591, 623 Diesel cycle, 598-599
General, 372 Crossed-axis helical gears, 292-294 Differential, automotive, 325-326
Redundant, 372 Pitch diameters of, 292-294 All wheel drive train, 327-328
Constraint force, 429 Crossed linkage, 51, 68 Limited slip, 326
Contact Crown gear, 302-303 TORSEN,326
Direct, 98-99 Crown rack, 303-304 Worm gear, 326
of Gear teeth, 265-268 Cubic of stationary curvature, 188-189 Differential equation of motion,
of Helical gear teeth, 290 Curvature, 143 542-546
Path of, 267 Center of, 93, 179 Solution of, 547-551
Ratio, 269 Radius of, 93, 143, 179 Differential mechanisms, 323-327
Formula, 269 Curve generator, 23, 68-70 Differential screw, 15
of Helical gears Curved-shoe follower, 198, 199 Dimensional synthesis, 332
Axial, 290 Curvilinear translation, 73 Direct contact, 98-99, 164-167
Face, 290 Cycloid, definition, 164 Direction cosines, 34, 385
Normal, 290 Cycloidal motion, 202, 216-217 Disk cam, 198
Total, 290 Derivatives of, 213-214, 216-217 Displacement, 70-75
Transverse, 290 Cylinder wall force, 614-616 Absolute, 75
Rolling, 98-99, 111, 168 Cylindric Angular, 80-81, 83
Control systems, mechanical, 687-698 Cam, 198 Apparent, 74-75
Conversion of units Coordinates, 34 Definition, 70-71
SI to U.S. customary, 713 Pair, 8,9 Diagram, 200-203
U.S. customary to SI, 713 Difference, 71-72, 83
Coordinate systems, 38-39, 74-75, DADS (Dynamic Analysis and Design Virtual, 461
93-94, 155-163 System), 398 Volume, 605
Coordinates, complex, 55-57 D’ Alembert’s principle, 479 Disturbance, 559
Coplanar motion, 10 Damping Division, by complex number, 58
Coriolis component of acceleration, 158 Coefficient, 623 Dobbs, H. H., 327, 328
Correction planes, 628-636, 641-643 Critical, 563, 623 Double-crank linkage.
Coulomb friction, 446-448 Factor, 542 See drag-link mechanism
Counterweight, 658-660 Phase angle, 567 Double-helical gear, 292
Couple, 430 Ratio, 564, 623 Double-rocker mechanism, 27,77
Characteristics of, 430 Dead-Center Position, 77 Drag-link mechanism, 21, 27
Coupler, 54 Dedendum, 253, 254 Driver, 6
Coupler curve, 23-24, 68-70, 344-348 Circle, 260 Dual number, 373
Coupling, 21-22 Deformable body, 427, 543 Dunkerley’s Method, 587-588
Crane, floating, 466 Degrees of freedom, 11-14,369 Dwell mechanism, 360-361
Crankpin force, 614-616 Of Lower Pairs, 9 Dwell motion, 200
Crank-rocker mechanism, 17,27, deJonge, A. E. R., 178n Dynamic equilibrium, 435
54-55,334-335 Denavit, J., 8n, 14n, 132n, 178n, 189n, Dynamic force analysis
Advantages of, 334 348, 365n, 372n, 373n, 387n, Planar, 470-514
Limit position, 77, 334 387-389,407 Spatial, 515-541728 INDEX
Dynamics Euler’s equations of motion, 523-527 Forcing, 551-553, 571-579
of Cam systems, 665-676 Euler’s theorem, 72 Form cutter, 263
Definition,4 Exhaust, 599 Forward kinematics, 407–411
of Reciprocating engine, 598-620 Expansion, 599 Foucault, L., 699
Extreme positions of crank-rocker Four-bar linkage, 17,41
Eccentric cam, 666-670 linkage, 334 Analysis of, 50-51, 105-108,304-305
Eccentricity in Cam system, 229, 231 Extreme values of velocity, 130 Angular velocity relations, 305
Edge mill, 707-710 Inversions of, 27-29
Eighth-order polynomial cam Face cam, 198, 199 Spatial, 375-384
motion, 214-215, 216-217 Face gear, 302-303 Spherical,370
Derivatives of, 214-215, 216-217 Face width, 253 Four-circle method, 178
Elastic-body analysis, 427, 543, 665 of Cam follower, 228 Four-force member, 443–445
Ellipse, equation of, 288 of Helical gears, 290 Four-stroke engine cycle, 599
Elliptical gear, 134 Fagerstrom, W. B., 640n, 643 Frame, 7, 26
End effecter, 404 Feedback control system, 687-688 Free-body, 432–433
Engine Ferguson’s paradox, 321 Freedom
Bearing loads in single-cylinder, Fillet, 261 Degrees of, II, 369
613-616 Fine adjustment, 14 Idle, 372
Crank arrangement, 600 Firing order, 599 Free vector, 432
Cycle, 598-599 First-order kinematic coefficients, 115 Frequency, 543
Firing order, 599 Fisher, FE., 517n Freudenstein, F, 129n, 332n, 365n, 373n
Five-cylinder, 599-600 Five-cylinder engine, 599-600 Freudenstein’s equation, 352-353
Four-cylinder, 648 Fixed centrode, 133 Freudenstein’s theorem, 129-130
In line, 599 Flat pair, 9 Friction
Opposed piston, 599 Flat-face follower. 198-200 Angle, 447
Radial, 600 Flip-flop mechanism, 15 Coefficient of, 447
Shaking force, 616-617 Float in cam systems, 667 Coulomb, 446–448, 670
Single cylinder, 613-616 Flyball governor, 541 Force models, 445–448
Six cylinder, 650 Flywheels, 678-683 Force, 446
Three-cylinder, 599, 649 Follower, 6, 17-18 Sliding, 447, 670
V-type, 599-600 Motion, derivatives of, 207, 211-225 Static, 446–447
Various types, 598-603, 650-651 Force,426 Viscous, 446, 448
Epicyclic gear, 315 Applied, 429, 432 Full depth, 258
Epicyclic gear train types, 316 Characteristics of, 426, 430 Full-rise cam motion, 215
Equation of motion, 427, 502-510, Constraint, 429 Full-return cam motion, 215
523-527,542-546,622-624 Definition, 426 Function generation, 333
Equilibrium External, 432 Function generator, 26
Dynamic, 435 Friction, 446
Static, 433 Indeterminate, 373 Ganter, M. A., 235-239
Equivalent gear, 288, 301 Inertia, 610-613 Gantry robot, 406
Equivalent mass, 609-610 Internal, 432 Gas force, 606-609
Erdman, A. G., 356, 365n, 399n Polygon, 438 Gas law, 604
Error, 341-343 Transmitted, 452 Gear, 252
Graphical, 341 Unit of, 428 Graphical layout, 259-262
Mechanical, 341 Vector, 430 Manufacture, 262-265
Structural, 341 Force analysis Tooth action, 259-262
Escapement, 15-16 Analytic, 438–439 Train, 311-328
Graham’s, 15-16 of Bevel gears, 457–460 Compound, 313
Euler, L., 4, 4n, 699 graphical, 436–438 Planetary, 315
Euler equation, 57 of Helical gears, 451–456 Reverted,313
Euler-Savary equation, 178-183 of Robot actuator, 418–420 Series connected, 311-315
Eulerian angles, 384-387 Forced precession, 704-710 Epicyclic, 315INDEX 729
Analysis by formula, 317-319 Gravity, 429 Horsepower equation, 604
Bevel gear, 317 Gravity, standard, 429 Hrones, J. A., 23n
Differentials, 323-327 Grodzinsky, P., 365n Hrones-Nelson atlas, 23, 23n,
TORSEN, 326 Griibler’s criterion, 13 360–361,364
Worm gear, 326 Gustavson, R. E., 365n Humpage’s reduction gear, 317
Tabular analysis, 319-323 Gyration, radius of, 476 Hunt, K. H., 365n, 415n
Type of Gyroscope, 699-710 Hypoid gears, 304-305
Annular, 262 Definition of, 699
Bevel, 297-305 Motion of, 700–701 Idle freedom, 372
Angular, 297 Gyroscopic torque, 704-710 Idler, 312
Spiral, 303-304 Images, properties of, 91,153
Straight-tooth, 297-301 Hain, K., 178n, 188n, 332n, 365n Imaginary coordinates, 55-57
Crossed-axis helical, 292-294 Half earn motions, 2I7-221 Imaginary mass method of
Crown, 302-303 Half-cycloidal earn motion, 219-221 balancing, 644-651
Double-helical, 292 Equations, 219-221 IMP (Integrated Mechanisms
Elliptical, 134 Half-harmonic earn motion, 217-219 Program), 398
Epicyclic, 315 Equations, 217-219 Impulse, 527-528
Face, 302-303 Hall, A. S., Jr., 130n, 178n, 189n, 365n Indexing mechanism, 16-17,44
Helical, 286-295 Hand and thrust relations of helical Indeterminate force, 373
Herringbone, 292 gears, 293 Indicator, 603
Hypoid,304-305 Harmonic forcing, 574-579 Diagram, 602, 603-606, 617-619
Internal, 262 Harmonic motion, 213, 215-216 Engine, 603
Miter, 297, 298 Harmonics, 646 Inertia
Planet, 315 Harrisberger, L., 369, 369n, 370, Axes, principal, 475
Ring, 324-325 372,372n Axes, transformation of, 519-523
Spiral, 292 Hartenberg, R. S., 8n, 14n, 178n, 189n, Definition, 426
Spur, 252 348, 365n, 372n, 373n, 387n, Force, 478–480
Sun, 315 387-389 in Engines, 610–613
Worm, 306-309 Hartmann construction, 179-180 Primary, 612, 644
Zerol, 303-304 Haug, E. J., 398, 398n Secondary, 612, 644
General constraint, 372 Helical gears, 286-295 Governors, 687
Generating cutter, 263 Crossed-axis, 292-295 Mass moment of, 475
Generating line, 256 Hand and thrust relations, 293 Mass product of, 475
Generators Tooth proportions, 294 Measurement of, 515-519
Curve, 23, 68-70 Forces on, 452–453 Tensor, 475
Function, 26 Parallel-axis, 286-292 Torque, 612-613
Straight-line, 24 Tooth proportions, 289 Inflection circle, 181
Geneva wheel, 16-17,44,361-364 Helical motion, 35 Inflection pole, 181
Gleasman, V., 326 Helical pair, 8, 9 Influence coefficients, 586
Globular pair, 8, 9 Helix angle, 287 In-line engine, 599
Goldberg mechanism, 372 Herringbone gears, 292 Instant center
Goodman, T. P., 178n, 332n Hesitation motion, 22 of Acceleration, 177-178
Governors, 685-698 Higher pair, 8-9 Definition, 118
Centrifugal, 686 Hinkle, R. T., 348 Number of, 119
Electronic, 685 Hirschhorn, J., 365n Use of, 123-126
Flyball,541 Hob, 264, 265 of Velocity, 117-119
Flywheels, 678-683 Hobbing, 264, 265 Instantaneous
Inertia, 687 Hodges, H., 328 Acceleration, 141
Graham’s escapement, 15-16 Holowenko, A. R., 19 Velocity,79
Graphical error, 341 Holzer tabular method, 593 Integration by Simpson’s rule, 680-681
Grashof’s law, 18, 27-29 Hooke universal joint, 22, 370, 388-389 Interference, 266-267
Gravitational system of units, 428 Horsepower characteristics, 452 Reduction of, 267-268730 INDEX
Internal gear, 262 Kinetics, definition, 5 Goldberg, 372
International System (SI of units), KINSYN (KINematic Maltese cross, 44
428-429,713 SYNthesis), 399 Oscillating-slider, 402
Inverse Kloomak, M., 215n, 241n Pantagraph,25
Acceleration analysis, 416-417 Knife-edge follower, 198, 199 Parallelogram, 137
Cam, 198 Kota, S., 356, 365n Peaucillier inversor, 25
Position analysis, 411-414 Krause, R., 129n RGGR,375-384
Velocity analysis, 414-416 Kuenzel, H., 332n, 365n Reuleaux coupling, 22
Inversion Kutzbach mobility criterion, 12-14,369 Roberts’, 24-25
Kinematic, 26 Scotch-yoke, 17, 19, 139
for Synthesis, 338 Law of gearing, 255-256 Scott-Russell, 25
Involute Lead, 308 Six-bar, 17, 19, 22-23
Curve. 255-257 Lead angle, 309 Slider-crank, 51-54, 333
Function, 272, 716-717 Levai epicyclic gear train types, 316 Isosceles, 333
Generation of, 256 Levai, Z. L., 315 Offset, 333
Helicoid, 286-287 Lever, 14 Sliding-block, 60-64
Isolation, 580-583 Lichty, L. C, 644n Spherical, 10
Lift, 15, 200 Wanzer needle-bar, 19
Jacobian, 171n, 397 Limit position, 77, 78 Watt’s, 24-25
Jamming, 30 Limited slip differential, 326 Whitworth, 18-20
Jerk, 210 LINCAGES,399 Wobble plate, 370
Johnston, E. R., Jr., 447n Line Location of a point, 33-36
Joint, types of, 8-9 of Action, 256, 259 Locational device, 14
Balanced, 440 of Centers, 124-126, 259 Locus, 33-35
Cardan, 22, 388~389 Coordinates, 415 Logarithmic decrement, 565-566
Hooke’s, 22, 388-389 Linear actuator, 14 Long-and-short-addendum
Turning, 8 Linear system, 105,485 system, 281-282
Universal, 22 Linearity, 105,485 Loop-closure
Wrapping, 9 Link Equation, 41-44, 373
See also, Pair, types of, lower Binary, 6 Cases of, 374
Jump, in cam systems, 667 Definition of, 6 Lowen, G. G., 656n
Jump speed, 667 Function of, 6 Lower pair, 8
Ternary, 6
KAM (Kinematic Analysis Method), 397 Linkage Machine, definition of, 5n, 5-6
Kaufman. R. E., 399 Definition Maleev, M. L., 644n
Kennedy, A. B. W., 5n Planar Maltese cross, 44, 361
Kennedy theorem, 119-120, 135n Quick-return, 16-20 Manipulator, 403
Kinematic chain, kind, 6-7, 26 Synthesis of Mass
Kinematic coefficients, 105-117, Types of Center of, 470-474
207-211 Bennett’s, 371, 372 Definition, 426
First order, 105-117 Bricard,372 Moment of inertia, 715
Relationship to instant Chebychev,24-25 Unit of, 428-429
centers, 127-129 Cognate, 348-350 Matter, definition, 426
Second Order. 171-175 Crank-rocker, 17, 27-28, 54-55, Matthew, G. K., 212n
Relationship to radius and center 77,334-338 Maxwell’s reciprocity
of curvature, 187-188 Crank-shaper, 17, 19-20 theorem, 586-587
Kinematic inversion, 26 Crossed-bar, 137 Mechanical
Kinematic pair, 6 Differential screw, 15 Advantage, 29, 130-133
Kinematic synthesis, 332-365 Double-crank, 28 of Cam system
Kinematics Double-rocker, 27-28, 77 Compensation balancing method,
Definition, 5 Drag-link, 21, 27-28 639-640
Forward, 407-41 I Four-bar, 17,54-55,371-372 Efficiency, 605
Inverse, 41 ]-417 Geneva, 16-17, 44 Error, 341INDEX 731
Mechanics of Momentum, 528-538 Flat. See Planar
Definition of, 4 Vector, 430-431 Globular. See Spheric
Divisions of, 4-5 Momentum, 527-528 Helical, 8, 9
Mechanism Angular, 701, 703-704 Pin. See Revolute
Analysis, computer, 397-399 Movability, definition, 11n Planar, 8, 9
Definition of, 5-7 Moving centrode, 133 Prismatic, 8, 9
Trains, 311 Moving point Revolute, 8, 9
Types of Acceleration of, 141-144 Screw. See Helical
Bistable, 15 Displacement of, 70-71 Spheric, 8, 9
Carn,17-18 Locus of, 33-35 Variable, 8
Clamping, 14 Velocity of, 79 Pantagraph linkage, 25
Dwell, 360-361 MSC Working Model, 399 Parabolic motion, 201,208-210
Escapement, 15-16 Muffley, R. v., 215n, 241n Parallel-axis formula, 476
Fine adjustment, 14 Muller, 707-710 Parallelogram linkage, 137
Flip-flop, 15 Particle, definition, 35, 426
Indexing, 16-17,44 NASTRAN, 397 Particle motion, equation of, 471
Linear actuator, 14 Natural frequency, 542, 549, 623 Path, of a point, 35
Locational, 14 Damped, 564 Path generation, 333
Offset, 17, 19,78 Neale, M. J., 447n Pawl,15-16
Oscillator, 16 Nelson, G. L., 23n Peaucellier inversor, 25
Planar 10 Newton,!., 427 Pendulum
Quick~return, 16,20,78 Newton (unit), 428-429 Equation of, 516
Ratchet, 15-16 Newton~Raphson method, 53 Mill,711
Reciprocating, 17, 19 Newton slaws, 427 Torsional,516-517
Reversing,21 Newton’s.notation,544 Trifilar, 517-519
Rocking,16 Nodal-pomt balancmg method, 638-639 Percussion, center of, 491, 609
Snap-action, 14-15 Normal component of acceleratIOn, 143, Performance curve, 543
Spatial, 10-11,368-373 . 146-155,157-163,168 Period of vibration, 542
Spatial four-link, 371-372 NotatIOn, complex-rectangular, 55-56 Periodic forcing, 571-574
Stop,pause, hesitation, 22 Number synthesIs, 332 Phase angle, 550, 623
Straight-line, 24-25 Offset circle, 204 Phase, of motion, 7
Swinging, 16 Offset follower 198 199 204 Phase plane, 555
Toggle, 15 Offset mechani~m 17 19 78 333 Phase plane method, 553-559
See. also. Linkage, Types of Open kinematic chain: 7′ , Phasor, 549
Mechamcalcontrol systems, Opposed-piston engine, 599 Phll~IPS,1., 373, 373n
687-698 Order defect 343 Pm Jomt, 8, 9
M’Ewan, E., 365n Orlandea N’ 398 398n Pinion, 252
Meritindices, 130-133 Oscillati~g i~llow’er, 198-200 Piston acceleration, 607
Millingof gear teeth, 263 Oscillating-slider linkage, 402 Piston-pin force, 614-616
Mischke,C. R., 14n, 53n, 258n, 272n, Oscillator mechanism, 16 Pitch
. 365n, 426n, 591n, 593n Osculating plane, 93 An~le, 297-299
Mitergears, 297, 298 Otto cycle, 598-599 AXlal,287-288
Mobility, l1n, 11-14,369 Overconstrained 373 Base, 261
Exceptions to criteria, 369-373 Overdrive unit 322-323 Circle, 252, 253
Model,44 Overlay meth;d, 343-344 Circular, 253-254
Module, 254 Normal, 287-288
Molian, S., 241n Pair, 6-9 Transverse, 287-288
Moment Definition of, 6 Curve, of cam, 203
of a Couple, 430-431 Types of Definitions, 252-255
of Impulse, 528-538 Higher, 8-9 Diametral, 252
of Inertia, 475 See Joint, types of Normal, 287-288
Area,714 Lower, 8-9 Transverse, 287-288
Mass, 715 Cylindric, 8,9 Point, 256732 INDEX
Pitch (continued) Limit, 77, 78 Rayleigh-Ritz equation, 585
Radius, equivalent, 288-289 Vector, 36 Real coordinates, 55-57
Surface, of bevel gear, 297-299 Pound force, 428 Recess
Pivoted-cradle method of balancing, Power equation, 502, 604 Arc of, 266, 268
636-638 Power stroke, 599 Angle, 266
Planar Power, units of, 452 Reciprocating
Linkage, 10 Precession,701-71O Engine, dynamics of, 598-620
Mechanism, 10,45 Forced, 704-710 Follower, 198-200
Motion, 35 Regular, 701-704 Mechanism, 17, 19
Pair, 8-9 Steady, 701-704 Rectangular notation, 55
Rotation about fixed center, 489-491 Precision positions, 341-343 Rectilinear motion, 35,144
Vector equations, 46-47 Prefixes, standard SI, 712 Redundant constraint, 372
Plane of couple, 430 Preload on cam, 666 Reference system, 33
Planet Pressure angle, 231,258-259 Regular precession, 701-704
Carrier, 315 Equation of, 231 Relative motion, 26,99-100,167-168
Gear, 315 Maximum, 232 Resonance, 542, 573
Planetary train, 315 Normal, 287-288 Response curve, 543
Force analysis, 455-456 Transverse, 287-288 Return, motion of cam, 200
Plate cam, 198, 199 Pressure line, 259 Return stroke, 18-20
PlUcker coordinates, 415 Pressure, mean effective, 604, 605 Reuleaux, E, 5n
Point Prime circle, 203 Reuleaux coupling, 22
Mathematical meaning, 35 Principal axes, 475 Reversing mechanism, 21
Moving Principia, Newton’s, 427 Reverted gear train, 313
Displacement of, 70-71 Prismatic pair, 8, 9 Revolute, 8, 9
Locus of Products of inertia, 475 RGGR linkage, 375-384
Position, 36 Programs, computer, 397-399 Rigid body, 5, 426
Absolute, 39-40 Pro/MECHANICA Motion Simulation Rigidity, assumption of, 5, 426-427
Apparent, 38-39 Package, 399 Ring gear
Difference, 37-38 Rise, motion of cam, 200
Pitch, 256 Quaternion, 373 rig ratio, 607
Point-position reduction, 339-340 Quick-return mechanism, 16, 18-20 Roberts, S., 365n
Polar notation, 55 Roberts-Chebychev theorem, 348-350
Pole, 135n Rack, 261 Roberts’ mechanism, 24-25
Polodes, 135n Rack cutter, 264 Robot, 26, 403
Polydyne cam, 215 Radcliffe, C. w., 365n • Robotics, 403-407
Polygon Radial engine, 600 Roll center, 140
Acceleration, 151-155 Radial follower, 198 Roller follower, 198-200
Force, 438 Radius Roller radius, 234-239
Velocity, 85-91 of Curvature, 143 Rolling contact, 98-99,164-167,168
Polynomial cam motion, 215 of Cam profile, 227-228, 233-234 Root-finding technique, 53
Polytropic exponent, 604 Equation, 233-234 Rosenauer, N., 129n, 178n
Position Minimum, 235-239 Rotation
Absolute, 39-40 of Gyration, 476 Definition, 72-73
Analysis, 60-64 Rapson’s slide, 192 of Helical gears, 293
Algebraic, 51-55, 376-378 Ratchet, 15-16 Rothbart, H. A., 332n
Graphic, 45-51,375-376 Rathbone, T. c., 641, 641n Roulettes, 135n
of Spatial mechanisms, 373-378, Raven, F. H., 102, 134n
389-392 Raven’s method Sandor, G. N., 332n, 356, 365n
Techniques, 60-64, 373-374 for Acceleration, 169-171 Sankar, T. S., 593n
Apparent, 38-39 for Position, 62-64 SCARA robot, 405
Difference, 37 for Velocity, 101-105 Schematic diagram, 6
Equation, 37 Rayleigh, Baron, 584, 584n Scotch-yoke mechanism, 17, 19, 101
Dead-center, 77 Rayleigh’s method, 583-586 Scott-Russell mechanism, 25INDEX 733
Screw Spiral gears, 292 Three-force member, 435–443
Differential, 15 Spring Thrust, of helical gearing, 292-293
Axis, instantaneous, 117n Rate, 666 Time ratio, 20, 334
Pair, 8-9 Stiffness, 666 Toggle
Shaking Surge, 675-676 Mechanism, 15
Forces, 492, 616-617 Spur gears, 252 Position, 30,131-132
Moments, 492 Forces on, 451–452 Tooth proportions
Shaping, 263, 264 Standard gravity, 429 for Spur gears, 258
Sheth, P. N., 398, 398n Standard gear tooth for Bevel gears, 301-302
Shigley,J. E., 14n, 258n, 365n, 426n, proportions, 257-258 for Helical gears, 289, 294
591n,593n Starting transient, 572 Tooth sizes, 254
SI (System International) Static balancing machines, 624-626 Tooth thickness, 253, 273
Conversion to U.S. customary Static force analysis, 425–463 Top dead center (TDC), 646
units, 713 Static friction, 446–447 Torfason, L. E., 14n
Prefixes, 712 Statically indeterminate force, 373 Torque characteristics of engines, 603
Units, 428–429,713 Statics, definition, 4 TORSEN differential, 326
for Gears, 254 Stationary curvature, 188 Torsional system, 592-593
Simple-closedchain, 7 Steady precession, 701-704 Trace point, 203
Simple gear train,311-312 Steady-state vibration, 542, 574 Train value, 312
Simple-harmonicmotion, 202, 215-216 Step-input function, 551-553 Transfer formula, 476
Derivativesof, 213, 216 Stevensen, E. N., Jr., 365n, 661, 644n Transformation matrix, 373, 389-391
Simpson’s ruleintegration, 68~81 Stevensen’s rule, 646 Transient disturbances, 559-562
Single cylinderengine, 613-616 Stiction,450–451 Transient vibration, 542, 576
Single planebalancers, 624 Stoddart, D. A., 215 Translation, 72-73
Six-bar linkage, 17, 19,22-23 Straight-line mechanism, 24-25 Curvilinear, 73
Skew curve,35 Straight-tooth bevel gears, 297-302 Definition of, 72-73
Slider-crankmechanism Forces on, 457–460 Rectilinear, 73
Analysisof, 48-50, 51-53,100, Structural error, 341 Transmissibility, 581-582
108-110 Structure Transmission, automotive, 313
Inversionsof, 26 Definition, 5 Transmission angle, 30, 55, 132
Limitpositions, 78 Statically indeterminate, 12 Definition, 30
Offset, 17, 19,78,108-110 Strutt, J. w., 584n Extremes of, 30,132
Synthesis of, 333-334 Stub tooth, 258 Optimum, 335-338
Slidingfriction, 446–447,670 Suh, C. H., 365n Transmitted force, 452
Slidingjoint, 8, 9 Sun gear, 315 Tredgold’s approximation, 300
Slug, derived fps unit of mass, 428 Superposition, principle of, 485–489 Turning pair, 8, 9
Snap-action mechanism, 14-15 Synthesis Two-force member, 435–443
Soni,A. H., 365n, 372, 372n Coupler-curve, 344-348 Two-stroke engine cycle, 599
Spatial Definition, 4 Type synthesis, 332
Four-link mechanism, 371-372 Dimensional, 332
Graphical analysis, 375-384 of Linkages, 332-365 Uicker, J. J., Jr, 235-239, 373n,
Mechanism, 368-369 Number, 332 398, 398n
Motion, 35 Type, 332 Unbalance
Seven-link, 369 Analysis of, 627-635
Speed fluctuation, coefficient of, 681 Tabular analysis of epicyclic gear Dynamic, 626-627
Speed ratio, 312 trains, 319-323 Forcing caused by, 579
Spherical Tangent cam, 211, 212 Static, 621-622
Coordinates, 34 Tangential component of acceleration, Units of, 635
Joint, 8, 9 143, 146-155, 158-163, 168 Undercutting, 265-268
Linkage, 370 Tao, D. c., 189n, 365n in Cam systems, 225-226, 233-234
Mechanism, 368 Tesar, D., 212n Elimination of, 226-227, 234-239,
Spin axis, 700-702 Thearle, E. L., 641, 641n 267-268
Spiral angle, 303-304 Three cylinder engine, 599 in Gear systems, 267-268734 INDEX
Uniform motion, 201 Unit,37 Free, 542
Unit vector, 37 Velocity, 80 Phase-plane representation, 555-571
Units Velocity difference, 84 Virtual displacement, 461
Basic, 428 Velocity Virtual rotor method of balancing,
Conversion Absolute, 80 644-651
SI to U.S. customary, 713 Analysis, 79-134 Virtual work, 461-463
U.S. customary to SI, 713 of Four-bar linkage, 105-108 Viscous damping, 448
Derived, 428 Graphical, 85-91 Coefficient of, 544, 623
Systems of, 428-429 by Line of centers, 123-126 Free vibration with, 563-565
Universal joint, 22, 370, 388-389 of Offset slider-crank V-type engine, 599–600
linkage, 108-110
Vector of Spatial mechanisms, 378-383, Waldron, K. 1., 365n
Addition, 45 392-396 Wanzer needle-bar mechanism, 19
Angular momentum, 701, 703-704 Angular, 82, 97, 126 Watt, unit of power, 452
Approach to rotor Apparent, 93 WATT Mechanism Design Tool, 399
balancing, 629-632 Equation, 93 Watt’s linkage, 24
Cases, 46-49, 64-68, 374 Average, 79 Wedge cam, 198, 199
Graphical operations, 45 Condition for rolling contact, 98-99 Weight, meaning, 426
Subtraction,45 Difference, 84 Weight/mass controversy, 426
Tetrahedron equation, 373 Equation, 84 Wheel, 26, 252
Type of Vector, 84 Whitworth mechanism, 18-19
Absolute acceleration, 142 Extremes, 129-130 Whole depth, 255
Absolute displacement, 75 Image, 87-88, 91 Willis, A. B., 4n
Absolute position, 39-40 Size of, 91 Willis, A. H., 178n
Absolute velocity, 80 Instantaneous, 79 Windup, 676
Acceleration, 141 Instant centers, 117-119 Wobble-plate mechanism, 370
Acceleration difference, 144-151 Locating, 120-123 Wolford, J. c., 212n
Apparent acceleration, 155-163 Using, 123-126 Worm, 306-309
Apparent displacement, 74-75 Poles, 117 Worm gear, 306-309
Apparent position, 38-39 Polygons, 85-91 Word gear differential, 326
Apparent velocity, 93-94 Ratio, 126 Working stroke, 18-20
Displacement, 70-71 Angular, 126 Worm wheel, 306-309
Displacement difference, 71-72 Relations of slider-crank Wrapping pair, 9
Force, 430 mechanism, 108-110 Wrist-pin force, 614-616
Free, 432 Vector method, 116-117
Moment, 430-431 Vibration, 542-597 Yang, A. T., 373n
Position, 36-37 Definition, 542
Position difference, 37-38 Forced, 542 Zerol bevel gear, 303-304

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