حل كتاب Kinematics, Dynamics, and Design of Machinery Solution Manual

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Kinematics, Dynamics, and Design of Machinery Solution Manual
K. J. Waldron, G. L. Kinzel
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Theory of Machines Problems Solution Manual

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CONTENTS
CHAPTER 1 INTRODUCTION 1 CHAPTER* LINKAGES WITH ROLLING AND SLIDING
CONTACTS AND JOINTS ON MOVING SLIDERS %
Historic Perspective 1
Kinematics 2
Design: Analysis and Synthesis 2
Mechanisms 3
Planar Linkages 7
Visualization 9
C'onstraint Analysis 11
Constraint Analysis of Spatial Linkages 18
Idle Degrees of Freedom 23
1.10 Overconstrained Linkages 25
1..11 Uses of the Mobility Criterion 29
1.12 Inversion 30
1.13 Reference Frames
1.14 Motion Limits
1.15 Actuation 32
1.16 Coupler-Driven Linkages 37
1.17 Motion Limits for Slider-Crank Mechanism 38
!.IS Interference 40
1.19 Practical Design Considerations 44
1.19.1 Revolute Joints 44
1.19.2 Prismatic Joints 46
1.19.3 Higher Pairs 47
1.19.4 Cams vs. Linkages 47
1.19.5 Actuation 48
Problems 54
1.1
1.2 . 3.1 Introduction 96
Reference Frames 96
General Velocity and Acceleration Equations 98
Velocity Equations 98
Acceleration Equations 101
Chain Rule for Positions
, Velocities, and
Accelerations 101
1.3 3.-2
1.4 3.3
1.5 3.3.1
1.6 3.3 2
1 7 3.3.3
1
1.9 3.4 Special Cases for the Velocity and Acceleration
Equations 104
3.4.1 Points?and حFixed to ة104
?and حAre Coincident 105
p and (9 Are Coincident and in Rolling
Contact 105
3.4.2
3.4.3
3.5 linkages with Rotating Sliding Joints 106
Rolling Contact 111
3.6.1 Basic Kinematic Relationships for Rolling
Contact 112
3.6.2 Modeling Rolling Contact Using a Virtual
Linkage 118
Cam Contact 121
3.7.1 Direct Approach to the Analysis of Cam
Contact 121
3.7.2 Analysis of Cam Contact Using Equivalent
linkages 124
General Coincident Points 128
3.8.1 Velocity Analyses Involving General Coincident
Points 130
3.8.2 Acceleration Analyses Involving General
Coincident Points 130
3.6
3.7
3
CHAPTER * GRAPHICAL POSITION, VELOCITY, AND
ACCELERATION ANALYSIS FOR MECHANISMS WITH
REVOLUTE JOINTS OR FIXED SLIDES 60 Problems 136
2.1 .Introduction 60
Graphical Position Analysis 61
2.3 Planar Velocity Polygons 62
2.4 Graphical Acceleration Analysis 65
2.5 Graphical Analysis ofa Four-Bar Mechanism 67
2.6 Graphical Analysis of a Slider-Crank
Mechanism 74
The Velocity Image Theorem 76
2.8 The Acceleration Image Theorem 79
2.9 Solution by Inversion 84
Problems 89
2 .2
CHAPTER 4 INSTANT CENTERS OF VELOCITY 145
Introduct.ion 145
Definition 145
Existence Proof 146
Tocation of an Instant Center from the Directions of
Two Velocities 147
Instant Center at a Rcvolutc Joint 148
Instant Center of a Curved Slider 148
4.1
4.2
4.3
2 7 4.4
4.5
4.6
؛؛VV ؛؛؛CONTENTS
Analytical Equations for tlie Slider-Crank
Inversion 200
5.6.1
Instant Center of a Prismatic Joint 148 5.6
Instant Center ofa Rolling Contact Pair 149
Instant Center of a General Cam-Pair
Contact 149
Centrodes 150
4.11 The Kcnnedy-Aronholdt Theorem 153
4.12 Circle Diagram as a Strategy for Finding Instant
Centers 155
4.13 Using Instant Centers: Tlie Rotating-Radius
Method 156
4.14 Finding Instant Centers Using Drafting
Programs 164
Problems 165
4.7
4.
Solution to Position Equations When 02 Is
Input 202
Solution to Position Equations When 6 ] Is
Input 204
Solution to Position Equations Wlicn f ) Is
Input 204
Velocity Equations for tlie Slider-Crank
Inversion 205
Acceleration Equations for the Slider-Crank
Inversion 207
Analytical Equations for an R PR p
Mechanism 211
Solution of Closui'e Equations When 02 Is
Known 212
Solution ofClosure Equations When rA Is
Known 213
Solution of Closure Equations When 12 Is
Known 215
Velocity and Acceleration Equations for an
RPRP Mechanism 216
4.9
4.1 5.6.2
5 6 3
5.6.4
5.6.5
5 7
5 7 1
CHAPTER 5 ANALYTICAL LINKAGE ANALYSIS 171 5 7 2
5.1 Introduction 171
5.2 Position, Velocity, and Acceleration
Representations 172
5.2.1 Position Representation 172
5.2.2 Velocity Representation 172
5.2.3 Acceleration Representation 174
5.2.4 Special Cases 175
5.2.5 Mechanisms to Be Considered 175
5.7.3
5.7.4
Analytical Equations for an RRPP
Mechanism 218
5.8.1
5.8.2
5.8.3
5.8
Solution When 02 Is Known 219
Solution Vv'hcn /0! Is Known 220
Solution When 12 Is Known 221
Analytical Equations for Elliptic Trammel 223
5.9. 1 Analysis When 0] Is Known 224
5.9.2 Analysis When 2| Is Known 225
5.1(.) Analytical Equations for tlie Oldham
Mecltanism 228
5.10. 1 Analysis When 02 Is Known 229
5.10.2 Analysis When 22 Is Known 230
5.11 Closure or Loop-Equation Approach for Compound
Mechanisms 233
5.11. 1 Handling Points Not on the Vector
Loops 236
5.11.2 Solving the Position Equations 237
5.12 Closure Equations for Mechanisms with Higher
Pairs 243
5.13 Notational Differences: Vectors and Complex
Numbers 248
Problems 251
Analytical Closure Equations for Four-Bar
Linkages 175
5.3. 1
5.3
Solution of Closure Equations for 5 9
Four-Bar Linkages V7hen Link 2 Is tlie
Driver 176
5.3.2 Analysis When the Coupler (Link 3) Is the
Driving Link 179
5.3.3 Velocity Equations for Four-Bar
Linkages 179
5.3.4 Acceleration Equations for Four-Bar
Linkages 181
5.4 Analytical Equations for a Rigid Body after
the Kinematic Properties of Two Points Arc
Known 184
5.5 Analytical Equations for Slider-Crank
Mechanisms 187
Solution to Position Equations When 02 Is
Input 190
Solution to Position Equations When 2| Is
Input 192
5.5.3 Solutioji to Position Equations When 0} Is
Input 193
5.5.4 Velocity Equations for Slider-Crank
Mechanism 194
5.5.5 Acceleration Equations for Slider-Crank
Mechanism 195
5.5
5.5 2
PLANAR LINKAGE DESIGN الا?ة
6.1 Introduction 257
Two-Position Double-Rocker Design 260
6.2. 1
6.2
Graphical Soltition Procedure 260
6 ,2 ,2 Analytical Solution Procedure 261CONTENTS I X
6.3 Motion Generation 263
6.3.1
7.1.3 Exact Straight-Line Mechanisms 332
7.1.4 Pantographs 333
Spherical Linkages 340
2.1 Introduction 340
,2 Gimbals 343
3 Universal Joints 343
Constant-Velocity Couplings 347
3.1 Geometric Requirements of ConstantVelocity Couplings 347
Practical Constant-Velocity
Couplings 347
Automotive Steering and Suspension
Mechanisms 349
7.4. 1 Introduction 349
7.4.2 Steering Mechanisms 349
7.4.3 Suspension Mechanisms 353
Indexing Mechanisms 354
Geneva Mechanisms 354
Introduction 263
Two Positions 263
Three Positions with Selected Moving
Pivots 266
Synthesis of a Crank with Chosen Fixed
Pivots 266
Design of Slider-Cranks and Elliptic
Trammels 268
Grder Problem and Change of
Brandi 270
Analytical Approach to Rigid-Body
Guidance 276
6.3 2 7 2
6.3.3 7
7 ,2
6.3.4 7 ,2
7 3
6 3.5 7
6.3.6 7 3 ,2
611 7.4
6.4 Function Generation 283
6.4.1 Function Generation Using a Four-Bar
Linkage 285
Design Procedure Wheny0= >Y-V Is to Be
Generated 287
Selection of Design Positions 288
Summary of Solution Procedure for
Four-Bar Linkage and Three Precision
Points 289
Graphical Approach to Function
Generation 293
6.4.2 7 5
7.5 1
6.4.3 References 359
6.4.4 Problems 360
6.4.5
CHAPTER ةPRGFILE CAM DESIGN 362
Synthesis of Crank-Rocker Linkages for specified
Rocker Amplitude 294
Extreme Rocker Positions and Simple
Analytical Solution 294
Tlie Rocker Amplitude Problem:
Graphical Approach 295
Transmission Angle 300
Alternative Graphical Design Procedure Based
on Specification of 06-04 301
Analytical Design Procedure Based on
Specification of 02-04 304
Use of Analytical Design Pi'ocedurc. for
Optimization 307
6.5 8.1 Introduction 362
Cam-Follower Systems 363
Syntliesis of Motion Programs 364
Analysis of Different Types of Follower
Displacement Functions 366
Uniform Motion 367
Parabolic Motion 368
Flarmonic Follower-Displacement
Programs 373
Cycloidal Follower-Displacement
Programs 375
General Polynomial Follower-Displacement
Programs 376
8.1() Determining the Cam Profile 381
8.10.1 Graphical Cam Profile Layout 381
8.10.2 Analytical Determination of Cam
Profile 391
8.2
6 5.1 3
8.4
6.5.2
8.5
6.5.3 8.6
6.5.4 7
6.5.5 8.8
8.9
Path Synthesis 308
6.6.1
6
Design of Six-Bar Linkages Using
Coupler Curves 309
Motion Generation for Parallel Motion Using
Coupler Curves 315
Four-Bar Cognate Linkages 318
6.61
References
6.6.3 Problems 417
References 320
Problems 321
CHAPTER 9 SPATIAL LINKAGE ANALYSIS 421
Spatial Mechanisms 421
9.1. 1 Introduction 421
1.2 Velocity and Acceleration
Relationships 422
Robotic Mechanisms 428
9.1
CHAPTER 1 SPECIAL MECHANISMS ?لا2?لا
1 Special Planar Mechanisms 329
1.1 Introduction 329
1.2 Approximate Straight-Line Mechanisms 329
7 9
77
ت 9X CONTENTS
9.3 Direct Position Kinematics of Serial
Chains 429
9.3. 1 Introduction 429
9.3.2 Concatenation of Transformations 431
9.3.3 Homogeneous Transformations 435
9.4 Inverse Position Kinematics 438
9.5 Direct and Inverse Velocity Problems 438
9.5.1 Introduction 438
Direct Rate Kinematics 439
14 .ا.اHelical Gears with Parallel Shafts 503
11.1.5 Crossed Helical Gears 509
11.2 Worm Gears 513
11.2.1 Worm Gear Nomenclature 514
11.3 Involut-C Bevel Gears 517
11.3.1 TredgoldS Approximation for Bevel
Gears 519
11.3.2 Additional Nomenclature for Bevel
Gears 520
11.3.3 Crown Bevel Gears and Face Gears 521
11.3.4 Miter Gears 523
11.3.5 Angular Bevel Gears 524
11.3.6 Zerol Bevel Gears 524
9.5 2
9.5.3 Inverse Velocity Problem 444
Closed-Toop Linkages 445
Lower Pair Joints 448
9.6
9.7
Motion Platforms 452
Mechanisms Actuated in Parallel 452
The Stewart Platform 452
The 3-2-1 Platform 454
9.
9.8.1
9.8.2
9.8.3
References 454
Problems 454
11.3.7 Spiral Bevel Gears 525
11.3 Hypoid Gears 526
References 528
Problems 528
CHAPTER 12 GEAR TRAINS 530
CHAPTER 10 SPUR GEARS 458
12.1 Gear Trains 530
12.2 Direction of Rotation 530
12.3 Simple Gear Trains 531
12.3.1 Simple Reversing Mechanism 533
12.4 Compound Gear Trains 534
12.4.1 Concentric Gear Trains 537
12.5 Planetary Gear Trains 540
12.5. 1 Planetary Gear Nomenclature 542
12.5.2
-Analysis of Planetary Gear Trains Using
Equations 544
12.5.3 Analysis of Planetary Gear Trains Using the
Tabular Method 550
1 (1.1 Introduction 458
10.2 Spur Gears 459
10.3 Condition for Constant-Velocity Ratio 460
10.4 Involutes 461
10.5 Gear Terminology and Standards 464
10.5.1 Terminology 464
10.5.2 Standards 465
10.6 Contact Ratio 467
10.7 Involutometry 471
10.8 Internal Gears 474
10.9 Gear Manufacturing 475
10.10 Interference and Undercutting 479
10.11 Nonstandard Gearing 482
10.12 Cartesian Coordinates O'l'an Involute Tootli Generated
with a Rack 487
10.12.1 Coordinate Systems 487
10.12.2 Gear Equations 491
References 494
Problems 494
References 554
Problems 554
CHAPTER 13 STATIC FORCE ANALYSIS OF
MECHANISMS ?لا?لا?لا
13.1 Introduction 559
13.2 Forces, Moments, and Couples 560
13.3 Static Equilibrium 562
13.4 Free-Body Diagrams 562
13.5 Graphical Force Analysis 565
13.6 Analytical Approach to Force Analysis 573
13.6.1 Transmission Angle in a Four- 'Bar
Linkage 575
13.7 Friction Considei0ations 578
13.7. 1 Friction in Cam Contact 579
13.7.2 Friction in Slider Joints 579
13.7.3 Friction in Revolutc Joints 581
CHAPTER 1010 HELICAL , REVEL, AND WORM
GEARS ARC
I 1 I Helical Gears 496
11.1.1 Helical Gear Terminology 497
11.1.2 Hclica!. Gear Manufacturing 501
11.1.3 Minimum Tooth Number to Avoid
Undercutting 501CONTENTS X I
In-Plane and Out-of-Plane Force Systems 586
13.9 Conservation of Energy and Power 590
13.1() Virtual Work 595
13.11 Gear Loads 597
13.11.1 Spur Gears 597
13.11.2 Helical Gears 599
13.11.3 Worm Gears 601
13.11.4 Straight Bevel Gears 603
Problems 604
13. CHAPTER SHAKING FORCES AND BALANCING 620
15.1 Introduction 629
15.2 Single-Plane (Static) Balancing 630
15.3 Multiplane (Dynamic) Balancing 633
15.4 Balancing Reciprocating Masses 639
15.4.1 Expression for Lumped Mass Distribution 640
15.4.2 Analytical Approach to Balancing
a Slider-Crank Mechanism 643
15.5 Expressions for Inertial Forces 646
15.6 Balancing Multicylindcr Machines 649
15.6.1 Balancing a Three-Cylinder In-Line
Engine 653
15.6.2 Balancing an Eight-Cylinder V Engine 655
References 657
Problems 657
CHAPTER DYNAMIC FORCE ANALYSIS 60*
14.1 Introduction 608
14.2 Problems Soluble via Particle Kinetics 610
14.2. 1 Dynamic Equilibrium of Systems of
Particles 610
14.2.2 Conservation of Energy 615
14.2.3 Conservation of Momentum 615
14.3 Dynamic Equilibrium ofSystems of Rigid Bodies 618
14.4 Flywheels 624
Problems 646
INDEX 662

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