Theory of Machines
S S Rattan
Professor of Mechanical Engineering
National Institute of Technology
Kurukshetra
CONTENTS
Preface xv
List of Reviewers xvii
Visual Walkthrough xviii
- Mechanisms and Machines 1
1.1 Mechanism and Machine 1
1.2 Types of Constrained Motion 2
1.3 Rigid and Resistant Bodies 3
1.4 Link 3
1.5 Kinematic Pair 3
1.6 Types of Joints 5
1.7 Degrees of Freedom 5
1.8 Classification of Kinematic Pairs 6
1.9 Kinematic Chain 6
1.10 Linkage, Mechanism and Structure 7
1.11 Mobility of Mechanisms 7
1.12 Equivalent Mechanisms 14
1.13 The Four-bar Chain 18
1.14 Mechanical Advantage 23
1.15 Transmission Angle 23
1.16 The Slider-crank Chain 27
1.17 Double Slider-crank Chain 30
1.18 Miscellaneous Mechanisms 32
Summary 34
Exercises 35 - VelocityAnalysis 38
2.1 Absolute and Relative Motions 38
2.2 Vectors 38
2.3 Addition and Subtraction of Vectors 39
2.4 Motion of a Link 40
2.5 Four-link Mechanism 41
2.6 Velocity Images 42
2.7 Angular Velocity of Links 43
2.8 Velocity of Rubbing 43
2.9 Slider-crank Mechanism 44
2.10 Crank- and Slotted-lever Mechanism 54
2.11 Algebraic Methods 62
2.12 Instantaneous Centre (I-Centre) 64
2.13 Kennedy’s Theorem 65viii Contents
2.14 Locating I-Centres 66
2.15 Angular-velocity-ratio Theorem 68
2.16 Centrode 74
Summary 76
Exercises 76 - Acceleration Analysis 79
3.1 Acceleration 79
3.2 Four-link Mechanism 81
3.3 Acceleration of Intermediate and Offset Points 83
3.4 Slider-crank Mechanism 85
3.5 Coriolis Acceleration Component 97
3.6 Crank and Slotted-lever Mechanism 99
3.7 Algebraic Methods 110
3.8 Klein’s Construction 112
3.9 Velocity and Acceleration from Displacement-time Curve 113
3.10 Centre of Curvature 114
3.11 Hartmann Construction 115
3.12 Euler-Savary Equation 116
3.13 Bobillier Construction 118
3.14 Cubic of Stationary Curvature 120
Summary 121
Exercises 122 - Computer-aided Analysis of Mechanisms 124
4.1 Four-link Mechanism 124
4.2 Use of Complex Algebra 131
4.3 The Vector Method 132
4.4 Slider-crank Mechanism 136
4.5 Coupler Curves 140
Summary 142
Exercises 143 - Graphical and Computer-aided Synthesis of Mechanisms 144
Part A: Graphical Methods
5.1 Pole 144
5.2 Relative Pole 146
5.3 Function Generation by Relative Pole Method 148
5.4 Inversion Method 151
5.5 Function Generation by Inversion Method 151
5.6 Path Generation 155
5.7 Motion Generation (Rigid-body Guidance) 158
Part B: Computer-aided Synthesis of Mechanisms
5.8 Function Generation 159
5.9 Chebychev Spacing 166
5.10 Path Generation 169
Contents ix
5.11 Motion Generation (Rigid-body Guidance) 175
Summary 179
Exercises 179 - Lower Pairs 181
6.1 Pantograph 181
6.2 Straight-line Mechanisms 182
63 Engine Indicators 190
6.4 Automobile Steering Gears 194
6.5 Types of Steering Gears 195
6.6 Hooke’s Joint 198
6.7 Double Hooke’s Joint 205
Summary 206
Exercises 207 - Cams 209
7.1 Types of Cams 209
7.2 Types of Followers 212
73 Definitions 213
7.4 Follower Displacement Programming 214
7.5 Derivatives of Follower Motion 215
7.6 High-speed Cams 216
7.7 Undercutting 216
7.8 Motions of the Follower 217
7.9 Layout of Cam Profiles 223
7.10 Cams with Specified Contours 232
7.11 Analysis of a Rigid Eccentric Cam 241
7.12 Analysis of an Elastic Cam System 244
7.13 Spring Surge, Unbalance and Wind Up 246
Summary 247
Exercises 247 - Friction 250
8.1 Kinds of Friction 250
8.2 Laws of Friction 251
8.3 Coefficient of Friction 251
8.4 Inclined Plane 252
8.5 Screw Threads 256
8.6 Screw Jack 262
8.7 Wedge 265
8.8 Pivots and Collars 268
8.9 Friction Clutches 274
8.10 Rolling Friction 285
8.11 Anti-friction Bearings 285
8.12 Greasy Friction 286
8.13 Greasy Friction at a Journal 286X Contents
8.14 Friction Axis of a Link 287
8.15 Film Friction 290
8.16 Mitchell Thrust Bearing 291
Summary 292
Exercises 293 - Belts, Ropes and Chains 296
9.1 Belt and Rope Drives 296
9.2 Open- and Crossed-belt Drives 298
9.3 Action of Belts on Pulleys 298
9.4 Velocity Ratio 299
9.5 Slip 299
9.6 Material for Belts and Ropes 301
9.7 Crowing of Pulleys 301
9.8 Types of Pulleys 302
9.9 Law of Belting 304
9.10 Length of Belt 304
9.11 One (Stepped) Pulleys 307
9.12 Ratio of Friction Tensions 310
9.13 Power Transmitted 312
9.14 Centrifugal Effect on Belts 315
9.15 Maximum Power Transmitted by a Belt 316
9.16 Initial Tension 320
9.17 Creep 324
9.18 Chains 325
9.19 Chain Length 326
9.20 Angular Speed Ratio 327
9.21 Classification of Chains 328
Summary 329
Exercises 330 - Gears 332
10.1 Classification of Gears 333
10.2 Gear Terminology 337
10.3 Law of Gearing 342
10.4 Velocity of Sliding 343
10.5 Forms of Teeth 343
10.6 Cycloidal Profile Teeth 343
10.7 Involute Profile Teeth 345
10.8 Interchangeable Gears 348
10.9 Non-standard Gears 348
10.10 Path of Contact 349
10.11 Arc of Contact 350
10.12 Number of Pairs of Teeth in Contact (Contact Ratio) 351
10.13 Interference in Involute Gears 354
10.14 Minimum Number of Teeth 355Contents xi
10.15 Interference Between Rack and Pinion 360
10.16 Undercutting 361
10.17 Comparison of Cycloidal and Involute Tooth Forms 362
10.18 Helical and Spiral Gears 362
10.19 Terminology of Helical Gears 364
10.20 Velocity Ratio and Centre Distance of Helical Gears 364
10.21 Helical Gear Forces and Efficiency 365
10.22 Worm and Worm Gear 369
10.23 Terminology of Worm Gears 370
10.24 Velocity Ratio and Centre Distance of Worm Gears 370
10.25 Efficiency of Worm Gears 371
10.26 Bevel Gears 372
Summary 374
Exercises 375 - Gear Trains 378
11.1 Simple Gear Train 378
11.2 Compound Gear Train 379
11.3 Reverted Gear Train 380
11.4 Planetary or Epicyclic Gear Train 381
11.5 Analysis of Epicyclic Gear Train 382
11.6 Torques in Epicyclic Trains 390
11.7 Sun and Planet Gear 394
11.8 Bevel Epicyclic Gear 397
11.9 Compound Epicyclic Gear 399
11.10 Automotive Transmission Gear Trains 400
11.11 Differentials 405
Summary 407
Exercises 407 - Static Force Analysis 410
12.1 Constraint and Applied Forces 410
12.2 Static Equilibrium 410
12.3 Equilibrium of Two- and Three-force Members 411
12.4 Member With Two Forces and a Torque 412
12.5 Equilibrium of Four-force Members 412
12.6 Force Convention 413
12.7 Free-body Diagrams 413
12.8 Superposition 414
12.9 Principle of Virtual Work 426
12.10 Friction in Mechanisms 428
Summary 431
Exercises 432 - Dynamic Force Analysis 434
13.1 D’alembert’s Principle 434xii Contents
13.2 Equivalent Offset Inertia Force 435
13.3 Dynamic Analysis of Four-link Mechanisms 435
13.4 Dynamic Analysis of Slider-crank Mechanisms 437
13.5 Velocity and Acceleration of a Piston 437
13.6 Angular Velocity and Angular Acceleration of Connecting Rod 439
13.7 Engine Force Analysis 440
13.7 Turning Moment on Crankshaft 441
13.8 Dynamically Equivalent System 445
13.9 Inertia of the Connecting Rod 446
13.10 Inertia Force in Reciprocating Engines (Graphical Method) 449
13.11 Turning-moment Diagrams 458
13.12 Fluctuation of Energy 460
13.13 Flywheels 461
13.14 Dimensions of Flywheel Rims 469
13.15 Punching Presses 471
Summary 474
Exercises 474 - Balancing 477
14.1 Static Balancing 477
14.2 Dynamic Balancing 480
14.3 Transference of a Force From One Plane to Another 480
14.4 Balancing of Several Masses in Different Planes 481
14.5 Force Balancing of Linkages 488
14.6 Balancing of Reciprocating Mass 490
14.7 Balancing of Locomotives 492
14.8 Effects of Partial Balancing in Locomotives 492
14.9 Secondary Balancing 496
14.10 Balancing of Inline Engines 497
14.11 Balancing of V-engines 509
14.12 Balancing of W, V-8 and V-12 Engines 513
14.13 Balancing of Radial Engines 575
14.14 Balancing Machines 520
14.15 Field Balancing 524
Summary 526
Exercises 527 - Brakes and Dynamometers 530
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
Types of Brakes 530
Block or Shoe Brake 530
Band Brake 536
Band and Block Brake 541
Internal Expanding Shoe Brake 544
Effect of Braking 547
Types of Dynamometers 549
Prony Brake Dynamometer 550Contents xiii
15.9 Rope Brake Dynamometer 550
15.10 Belt Transmission Dynamometer 551
15.11 Epicyclic-train Dynamometer 552
15.12 Bevis-Gibson Torsion Dynamometer 553
15.13 Automotive Propulsion 553
Summary 556
Exercises 556 - Governors 559
16.1 Types of Governors 559
16.2 Watt Governor (Simple Conical Governor) 560
16.3 Porter Governor 562
16.4 Proell Governor 566
16.5 Hartnell Governor 569
16.6 Hartung Governor 574
16.7 Wilson-Hartnell Governor (Radial-spring Governor) 575
16.8 Pickering Governor 578
16.9 Spring-controlled Gravity Governor 579
16.10 Inertia Governor 580
16.11 Sensitiveness of a Governor 582
16.12 Hunting 582
16.13 Isochronism 583
16.14 Stability 583
16.15 Effort of a Governor 583
16.16 Power of a Governor 585
16.17 Controlling Force 589
Summary 594
Exercises 594 - Gyroscope 597
17.1 Angular Velocity 597
17.2 Angular Acceleration 597
17.3 Gyroscopic Torque (Couple) 599
17.4 Gyroscopic Effect on Aeroplanes 601
17.5 Gyroscopic Effect on Naval Ships 602
17.6 Stability of an Automobile 605
17.7 Stability of a Two-wheel Vehicle 610
17.8 Rigid Disc at an Angle Fixed to a Rotating Shaft 612
Summary 613
Exercises 613 - Vibrations
18.1 Definitions 615
18.2 Types of Vibrations 616
18.3 Basic Features of Vibrating Systems 616
18.4 Degrees of Freedom 617
615xiv Contents
Section-I (Longitudinal Vibrations) 618
18.5 Free Longitudinal Vibrations 618
18.6 Displacement, Velocity and Acceleration 623
18.7 Inertia Effect of the Mass of Spring 624
18.8 Damped Vibrations 629
18.9 Logarithmic Decrement 633
18.10 Forced Vibrations 636
18.11 Forced-damped Vibrations 638
18.12 Magnification Factor 641
18.13 Vibration Isolation and Transmissibility 644
18.14 Forcing Due to Unbalance 646
18.15 Forcing Due to Support Motion 648
Section II (Transverse Vibrations) 650
18.16 Single Concentrated Load 650
18.17 Uniformly Loaded Shaft 651
18.18 Shaft Carrying Several Loads 654
18.19 Whirling of Shafts 657
Section III (Torsional Vibration) 659
18.20 Free Torsional Vibrations (Single Rotor) 659
18.21 Inertia Effect of Mass of Shaft 660
18.22 Multifilar Systems 661
18.23 Free Torsional Vibrations (Two-rotor System) 666
18.24 Free Torsional Vibrations (Three-rotor System) 667
18.25 Torsionally Equivalent Shaft 668
18.26 Free Torsional Vibrations of Geared System 671
Summary 673
Exercises 674 - Automatic Control 677
19.1 Open and Closed-loop Control
(Unmonitored and Monitored Control) 677
19.2 Amplification 678
19.3 Actuator (Servomotor) 678
19.4 Transducer 678
19.5 Block Diagrams 678
19.6 Lag in Response 679
19.7 Damping 680
19.8 First-order System Response 680
19.9 Second-order System Response 682
19.10 Transfer Function 682
19.11 Transfer Function Relationships 685
Summary 686
Exercises 686
Appendix I
Appendix II
Index
687
702
705INDEX
Absolute motion 38
Absorption dynamometer 549
Accelerating force
primary 490
secondary 490
Acceleration 79
centripetal 80
Coriolis component 97
image 84
of intermediate points 83
of offset points 83
of piston 437,438
radial 80
tangential 80
Ackermann steering gear 194, 196
Actuator 678
Addendum 339
Addendum circle 339
Addendum coefficient 356
Adsorbed film 286
Amplification 678
Analysis of mechanisms 1, 124
Andrew variable stroke engine 53
Angle
of action 213, 341
of ascent 213
of dwell 213
of descent 213
of friction 25
helix 364
lead 370
of obliquity 340
pressure 340
repose 252
Angular acceleration 597, 599
of connecting rod 439
of links 83
Angular velocity of links 43
Angular velocity of
precession 599
Angular velocity ratio theorem 68
Anti-friction bearings 284
Applied forces 410
Arc of approach 341
Arc of contact 341, 350
Arc of recess 341
Automatic control 677
closed-loop 677
monitored 677
open-loop 677
unmonitored 677
Automobile steering gears
Ackeramann 194, 196
Davis 194
types 194
Automotive propulsion 553
Balancing 477
dynamic 480
field 524
In different planes 481
machines 520
static 520
dynamic 521
of in-line engines 497
two-cylinder 498
four-cylinder 499
six-cylinder 500
of linkages 488
of locomotives 492
of radial engines 515
of reciprocating mass 490
ofV-engines 509
of V-8 engines 513, 514
of V-12 engines 513, 514
ofW-engines 513
secondary 496
static 477
Ball bearings 284
Ball’s point 121
Band brake 536
Band and block brake 541
Base circle
cam 212
gear 346
Bearings
anti-friction 284
ball 284
collar 267
footstep 267
Mitchell thrust 290
pivot 267
roller 285
thrust on 441
Belt
action on pulleys 298
centrifugal effect on 315
creep in 324
crossed drive 298
flat 310
initial tension in 320
law of (belting) 304
length of crossed 306
length of open 304
material 301
maximum power
transmitted 316
open drive 298
power transmitted 312
ratio of friction tensions 310
slip 299
V 311
velocity ratio 299, 324
Bevel gears 334,372
epicyclic 397
spiral 334
straight 334706 Index
zerol 334 tangent 231 frustrum of cone 270
Block diagrams 678 trace point 212 Collar bearing 267
Bobillier construction 118 types 208 Complex numbers 63, 111
Bobillier theorem 118 unbalance in 245 Compound epicyclic gear 399
Body centrode 74 undercutting 215 Computer-aided analysis of
Body guidance 175 wedge 208 four link mechanism 124
Brakes 530 wind up in 245 slider crank mechanism 136
band 536 with specified contours 231 Computer-aided synthesis 144
band and block 541 Centre of curvature 114 Constraint forces 410
block 530 Centre distance of Constrained motion
effect of (braking) 547 helical gears 364 completely 2
internal expanding shoe 544 worm gears 370 incompletely 2
self energised 531 Centrifugal governors 559 successfully 2
self locking 531 Centrifugal clutch 275 types 2
shoe 530 Centripetal acceleration 80 Cone clutch 275
types 530 Centrode Cone pulley 307
Braking effect 547 body 74 Configuration diagram 38
moving 74 Conical collar 268, 270
Cam fixed 74 Conjugates 115
angle of action 208 space 74 Conjugate point 115, 119
angle of ascent 213 Chain 327 Connecting rod
angle of decent 213 block 328 angular acceleration of 439
angle of dwell 213 classification 328 angular velocity of 439
barrel 210 conveyor 328 force (thrust) along 441
base circle 212 hoisting 328 inertia of 446
circular arc 233, 234 inverted tooth 329 Contact length 340
conjugate 210 length of 326 Contact ratio 341, 351
convex 233, 234 power transmission 328 Control, automatic 679
cylindrical 209 roller 328 Convex cams 233, 234
disc 209 silent 329 Coriolis acceleration
drum 210 speed ratio 327 component 97
eccentric 240 sprocket 326 Correction couple 448
elastic 243 Chebychev spacing 168 Coupler 18
flat 208 Circular-arc cams 233, 234 Coupler curves 140
globoidal 210 Circular pitch 338, 364 Cramer’s rule 160
gravity 211 Clearance 339 Crank-crank mechanism 19
high speed 215 Closed pair 4 Crank effort 441
jump 241, 245 Clutches 273 Crank effort diagrams 458
pitch curve 212 centrifugal 275 Crank-lever mechanism 20
pitch circle 213 cone 275 Crank-rocker mechanism 20
pitch point 213 disc 274 Crank and slotted lever
positive drive 211 multi plate 274 mechanism 28
pre-loaded 211 single plate 274 Critical speed 657
pressure angle 212 Coefficient of Crowning of pulleys 301
prime circle 213 fluctuation of energy 460 Cubic of stationary curvature 120
profile, layout of 222 fluctuation of speed 460 Cycloidal motion 220
radial 209 friction 250 Cycloidal profile teeth 343
rigid eccentric 240 Coincident points 62
spiral 209 Collar 267 D’Alembert’s principle 434
spherical 210 Conical 268, 270 Damped vibrations 629
spring surge in 245 flat 268, 269 Damping 680Index 707
Damping coefficient 629
Damping factor 630
Damping ratio 630
Davis steering gear 194
Dead angle 288
Dead centre position 288
Dedendum 339
Dedendum circle 339
Degree of freedom 5
Deltoid linkage 20
Differentials 405
Differential gear 406
Direct and reverse cranks 575
Double lever mechanism 20
Double Hooke’s joint 204
Double parallelogram linkage 10
Double rocker mechanism 20
Double slider crank chain 30
Drag crank mechanism 19
Dunkerley’s method 655
Dynamic balancing 480
Dynamic force analysis 434
Dynamically equivalent
system 445
Dynamics 1
Dynamometers 530, 549
absorption 549
belt transmission 557
Bevis-Gibson torsion 553
epicyclic train 552
prony brake 550
rope brake 550
transmission 549
types 549
Eccentric cam 240
Effective driving force 440
Efficiency of
helical gears 365
spiral gears 365
worm gears 371
Elastic cam system 243
Element 3
Elliptical trammel 30
Equilibrium of members with
two forces 477
two forces and a torque 472
three forces 411
four forces 472
Energy method 655
Engine indicator 189
Crosby 190
Dobbie mclnnes 192
Simplex 190
Thomson 191
Epicyclic gear 381
bevel 397
compound 399
Epicyclic train dynamometer 552
Equilibrium of
two-force member 411
three-force member 411
four-force member 472
Equilibrium method 618
Equivalent mechanism 74
Equivalent offset inertia force 435
Error detector 677
Euler-Savary equation 116
Feedback 677
Ferguson’s paradox 408
Film friction 249, 289
Field balancing 524
First order system response 680
Fluctuation of energy 460
coefficient of 460
maximum 460
Fluctuation of speed 459
coefficient 460
maximum 460
Flywheels 460
Flywheel rims 469
Follower
displacement
programming 213
flat faced 272
knife edge 277
mushroom 272
offset 272
oscillating 272
radial 272
reciprocating 272
roller 277
spherical faced 272
types 277
Follower motions 276
constant accel, and decel. 218
constant velocity 219
cycloidal 220
SHM 216
Footstep bearing 267
Force analysis
dynamic 434
static 410
Forced vibrations
damped 638
harmonic 637
periodic 637
step input 63
Forces
constraint 410
applied 410
Forcing due to
unbalance 646
support motion 648
Forms of teeth 343
Four-bar chain 18
Four-link mechanism 41, 81, 124,
148, 151, 435
Free-body diagrams 413
Free longitudinal vibrations 618
Free torsional vibrations 666, 667
of geared system 671
Friction
angle of 257
axis 286
boundary 249, 285
circle 286
clutches 273
coefficient of 250
dry 249
film 249, 289
greasy 249, 285
in mechanisms 428
kinds 249
laws of 250
limiting angle of 257
rolling 249, 284
skin 249
solid 249
tension 310
wheels 332
Freudenstein’s equation 159
Function generation 744, 148,
151, 159
Fundamental frequency 667
Gear ratio 338
Gear box
sliding 400
pre-selective 401
Gears
bevel 334, 372708 Index
classification 333
conjugate 343
contact ratio 341, 351
crossed helical 335, 336
differential 405
double helical 333
epicyclic 381
for intersecting shafts 334
for parallel shafts 333
for scew shafts 334
helical 333, 336, 362
Herringbone 333
Humpage 409
hypoid 337
Interchangeable 348
Interference in involute 354
law of (gearing) 342
mitre 334
non-standard 348
pairs of teeth in contact 351
pressure angle 340
spur 333
spiral 335, 362
rack and pinion 360
worm 336
zerol bevel 334
Gear teeth
bottom land 340
comparison of teeth forms 362
cycloidal 343
face 340
face width 340
flank 340
forms of 343
involute 343, 345
left-handed 362
minimum number of 355
right-handed 362
space width 339
top land 340
Gear trains
automotive transmission 400
bevel epicyclic 397
compound 379
compound epicyclic 399
epicyclic 381
planetary 381
reverted 380
simple 378
sun and planet 394
torques in 390
Geared system 671
Governor 559
Centrifugal 559
coefficient of
insensitiveness 590
controlling force 589
effort of 583
Hartnell 569
Hartung 574
height of 560
hunting 582
inertia 560, 580
isochronous 583
Pickering 578
Porter 562
Proell 566
power of 585
radial spring 575
sensitiveness of 582
spring-controlled gravity 579
stability of 583
types 559
Watt 560
Wilson-Hartnell 575
Graphical differentiation 111
Graphical methods of
synthesis 144
Grass-Hopper mechanism 185
Grashof’s law 20
Gruebler’s criterion 8
Gyroscope 597
Gyroscopic couple 599
Gyroscopic effect on
aeroplanes 601
naval ships 602
Gyroscopic torque 599
Hammer-blow 492
Hand pump 29
Harmonic forcing 637
Hartmann construction 115
Hart mechanism 183
Hartnell governor 569
Hartung governor 574
Height of governor 560
Helical gears 333, 336, 362
centre distance of 364
crossed 335, 336
double 333
efficiency of 365
forces in 365
helix angle 364
herringbone 333
spur 333
velocity ratio 364
Helical pair 5
Helix angle 364
Herringbone gear 333
Higher pair 4
High speed cam 215
Hooke’s joint 197
acceleration of driven
shaft 201
double 204
polar velocity diagram 200
velocity ratio 199
Humpage reduction gear 409
Hypoid gears 337
Inclined plane 251
Indexing mechanisms 33
Indicators, engine 189
Inertia effect 624
Inertia force 449
Inertia governor 560, 580
Inertia of connecting rod 446
Initial tension 320
Instantaneous centre 64
Interchangeable gears 348
Intermediate pulley 302
Internal expanding shoe brake 544
Interference in gears 354
Inversion method of synthesis 151
Inverted slider-crank
mechanism 57
Inversions of mechanisms 27
Involute profile teeth 343, 345
Joints 5
Kempe’s mechanism 188
Kennedy’s theorem 65
Kinematics 1
Kinematics chain 6
Kinematic derivatives 214
Kinematics link 3
Kinematics pair 3
classification 6
types 3
Kinetics 1
Klein’s construction 112
Kutzback’s criterion 8Index 709
Lag in response 679
Law of
belting 304
gearing 342
Laws of friction 250
Lazy tongs 189
Lead 370
Lead angle 370
Least square technique 161
Limiting angle of friction 251
Line of action 340
Line of centres 338
Linear system 780
Link 3
Linkage 7
Logarithmic decrement 633
Longitudinal vibrations 616
damping coefficient 629
damping factor 630
energy method 622
equilibrium method 618
inertia effect of mass 624
magnification factor 641
Rayleigh’s method 623
Loose and fast pulley 303
Lower pairs 4
Machine 1
Magnification factor 641
Mechanical advantage 23
Mechanism
crank-crank 19
crank-lever 20
crank-rocker 20
double-crank 19
double-lever 20
double-rocker 20
drag-crank 19
of zero order 7
oscillating-oscillating 20
rotary-oscillating 20
rocker-rocker 20
rotary-rotary 19
Mechanisms 1, 7
classification 7
degree of freedom 8
mobility 7
Mitchell thrust bearing 290
Motion
absolute 38
of a link 40
relative 38
Motion generation 144
Multifilar systems 661
bifilar suspension 661
trifilar system 662
Multiplate clutch 274
Natural frequency 615
Non standard gears 348
Number synthesis 8
Oldham’s coupling 31
Oscillating cylinder engine 28
Oscillating-oscillating
converter 20
Pair 3
Pantograph 180
Parallel-crank four bar linkage 20
Parallel linkages 188
Parallel ruler 188
Path generation 144
Path of approach 340
Path of contact 340
Path of recess 340
Paucellier mechanism 181
Periodic forcing 637
Physical derivatives 214
Pickering governor 578
Pinion 333, 338
Piston
acceleration 437, 438
effort 440
velocity 437, 438
Pitch
axial 370
circle 213, 337
circular 338, 364
curve 212
cylinder 337
diametral 338
diameter 338
line 338
module 338
normal circular 364
point 213, 338
surface 338
Pivots 267, 271
conical 268, 272
flat 268, 272
Pivot bearing 267
Planetary gear train 381
Polar velocity diagram 200
Pole 144
Porter governor 562
Pre-selective gear box 401
Prime circle 213
Principle of virtual work 426
Pressure angle 212, 340
Primary accelerating force 490
Proell governor 566
Pulleys
cone 307
crowning of 301
guide 303
idler 302
intermediate 302
loose and fast 303
stepped 307
types 302
Quadric-cycle mechanism 41
Quick return mechanisms
crank and slotted lever 28
Whitworth quick return 27
Rack 333
Rayleigh’s method 623
Redundant chain 7
Redundant degree of freedom 10
Redundant link 10
Relative motion 38
Relative pole 146
Relative pole method 148
Relative velocity method 383
Resistance
aerodynamic 554
frictional 554
gradient 554
road 553
rolling 553
tractive 554
Resistant body 3
Resonance 641
Rigid body 3
Rigid-body guidance 175
Rigid disc at an angle 612
Robert mechanism 207
Rocker-rocker mechanism 20
Roller bearing 285
Rolling pair 5
Rolling friction 249, 284710 Index
Root circle 339
Rope drive 296, 297, 311
Rope material 301
Rotary engine 27, 28
Rotary-oscillating converter 20
Rubbing velocity 43
Scotch yoke 31
Scott-Russel mechanism 185
Screwjack 261
Screw pair 5
Screw threads 255
Secondary accelerating force 490
Secondary balancing 496
Servomotor 678
Sewing machine mechanism 73
Shaking force 490
Shaking couple 490
Simple conical governor 560
Simple harmonic motion 216
Single plate clutch 274
Slider-crank mechanism 44, 85,
136, 151, 288, 437
Sliding gear box 400
Sliding pair 4
Slip 299
Snap action mechanisms 32
Space centrode 74
Speed ratio 327
Spherical pair 5
Spiral gears 362
Spring surge 245
Sprocket 326
Spur gears
addendum 339
addendum circle 339
addendum coefficient 356
angle of action 213, 341
angle of obliquity 340
arc of approach 341
arc of contact 341
arc of recess 341
backlash 340
base circle 346
circular pitch 338, 364
clearance 339
contact length 340
contact ratio 341, 351
cycloidal tooth profile 343
dedendum 339
dedendum circle 339
diametral pitch 338
face 340
face width 340
flank 340
forms of teeth 343
gear ratio 338
interference in 354
involute tooth profile 343, 345
line of action 340
line of centres 338
minimum number of teeth 355
module 338
path of approach 340
path of contact 340
path of recess 340
pinion 333, 338
pitch 338
pitch circle 337
pitch diameter 338
pitch line rack 338
pitch point 338
pitch surface 338
pressure angle 340
pressure line 340
rack 338
rack and pinion 333, 360
top land 340
tooth thickness 340
velocity of sliding 343
undercutting 361
Square threads 256
Stability of automobile 605
Stability of two-wheel vehicle 610
Static balancing 477
Static equilibrium 410
Static force analysis 410
Statics 1
Steering gears
Ackermann 194, 196
Davis 194
Straight line mechanisms 181
Structure 7
Sun and planet gear 394
Superposition of loads 414
Superstructure 7
Swaying couple 493
Synthesis of mechanisms 144
Tangential acceleration 80
Tchebicheff mechanism 187
Thrust
along connecting rod 441
on bearings 441
on sides of cylinder 441
Torsional system 681
Torsionally equivalent shaft 668
Torsional vibrations 659
geared system of 671
inertia effect of mass 660
three-rotor system 667
two-rotor system 666
Trace point 212
Tractive force 492
Tractive resistance 554
Transducer 678
Transfer function 682
open loop 685
closed loop 685
Transmission angle 23
Transmissibility 644
Transverse vibrations 650
Dunkerley’s method 655
energy method 655
shaft carrying several
loads 654
single concentrated load 650
uniformly-loaded shaft 651
Turn buckle 260
Turning pair 4
Turning-moment diagrams 458
Turning moment on
crankshaft 441
Unbalance 245
Unclosed pair 4
Undercutting
cam 215
gear 361
Uniform pressure theory 268
Uniform wear theory 268
Universal drafting machine 189
Universal joint 197
V-belt 311
Vector approach 62, 111
Velocity
Angular 43
from displacement curve 111
image 42
of piston 437,438
of rubbing 43
of sliding 343Index 711
ratio 339, 364 of three-rotor system 667 Whipping speed 657
Vibrations 615 of two-rotor system 666 Whirling of shaft 657
cycle 615 period of 615 Whirling speed 657
damped 615, 229 resonance in 615 Whitworth quick return
degree of freedom 617 torsional 616 mechanism 27
free 615 transmissibility of 644 Wilson-Hartnell governor 575
frequency of 615 transverse 616 Wind up 245
forced 615 types 616 Worm gears
forced damped 638 Virtual work 426 axial pitch of 372
isolation 644 V-threads 259 centre distance 372
logarithmic decrement 633 efficiency of 373
longitudinal 616 Watt governor 560 lead 372
magnification factor 641 Watt mechanism 186 lead angle 372
natural 615 Wedge 264 velocity ratio 372
كلمة سر فك الضغط : books-world.net
The Unzip Password : books-world.net