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أخوانى فى الله أحضرت لكم كتاب Machine Analysis With Computer Applications for Mechanical Engineers James Doane Frontier-Kemper Constructors, Indiana, USA
![كتاب Machine Analysis With Computer Applications for Mechanical Engineers M_a_w_10](https://i.servimg.com/u/f61/15/36/74/14/m_a_w_10.jpg) و المحتوى كما يلي :
Contents Preface xv Acknowledgments xvii About the companion website xix 1 Introductory Concepts 1 1.1 Introduction to Machines 1 1.1.1 Brief History of Machines 1 1.1.2 Why Study Machine Analysis? 5 1.1.3 Differences between Machine Analysis and Machine Design 6 1.2 Units 6 1.2.1 Importance of Units 6 1.2.2 Unit Systems 6 1.2.3 Units of Angular Motion 8 1.2.4 Force and Mass 8 1.3 Machines and Mechanisms 10 1.3.1 Machine versus Mechanism 10 1.3.2 Simple Machines 10 1.3.3 Static Machine Analysis 11 1.3.4 Other Types of Machines 14 1.4 Linkage Mechanisms 14 1.4.1 Introduction to Linkage Mechanisms 14 1.4.2 Types of Links 14 1.4.3 Types of Joints 15 1.5 Common Types of Linkage Mechanisms 16 1.5.1 Crank–Rocker Mechanisms 17 1.5.2 Slider–Crank Mechanisms 17 1.5.3 Toggle Mechanisms 18 1.5.4 Quick Return Mechanisms 19 1.5.5 Straight Line Mechanisms 19 1.5.6 Scotch Yoke Mechanism 20 1.6 Gears 21 1.6.1 Introduction to Gears 21 1.6.2 Spur Gears 22 1.6.3 Helical Gears 231.6.4 Bevel Gears 24 1.6.5 Worm Gears 26 1.7 Cams 27 1.7.1 Introduction to Cams 27 1.7.2 Disk Cams 27 1.7.3 Cylindrical Cams 28 1.8 Solution Methods 28 1.8.1 Graphical Techniques 29 1.8.2 Analytical Methods 29 1.8.3 Computer Solutions 29 1.9 Methods of Problem Solving 30 1.9.1 Step 1: Carefully Read the Problem Statement 30 1.9.2 Step 2: Plan Your Solution 30 1.9.3 Step 3: Solve the Problem 30 1.9.4 Step 4: Read the Problem Statement Again 30 1.10 Review and Summary 31 Problems 31 Further Reading 33 2 Essential Kinematics Concepts 34 2.1 Introdction 34 2.2 Basic Concepts of Velocity and Acceleration 35 2.3 Translational Motion 35 2.4 Rotation about a Fixed Axis 36 2.4.1 Velocity 36 2.4.2 Acceleration 38 2.5 General Plane Motion 41 2.5.1 Introduction 41 2.5.2 Velocity Difference and Relative Velocity 41 2.5.3 Relative Acceleration 47 2.5.4 Instant Center of Rotation 51 2.6 Computer Methods 53 2.6.1 Numerical Differentiation 53 2.6.2 Illustrative Example 54 2.7 Review and Summary 58 Problems 58 Further Reading 65 3 Linkage Position Analysis 66 3.1 Introduction 66 3.2 Mobility 67 3.2.1 Rigid Body Degrees of Freedom 67 3.2.2 Joint Mobility 67 3.2.3 Determining Mobility of a Planar Linkage Mechanism 69 3.3 Inversion 72 3.4 Grashof’s Criterion 72 3.4.1 Introduction 72 vi Contents3.4.2 Grashof Linkage 73 3.4.3 Non-Grashof Linkage 73 3.4.4 Special Case Grashof Linkage 73 3.5 Coupler Curves 74 3.5.1 Basic Concepts of Coupler Curves 74 3.5.2 Double Points 74 3.5.3 Hrones and Nelson Atlas 75 3.6 Cognate Linkages 76 3.6.1 The Roberts–Chebyshev Theorem 76 3.6.2 Steps for Determining Cognates 76 3.6.3 Cognates for Binary Link 78 3.6.4 Cognates for Slider–Crank Mechanism 79 3.7 Transmission Angle 79 3.8 Geometrical Method of Position Analysis 80 3.8.1 Essential Mathematics 80 3.8.2 Common Approaches for Four-Bar Mechanisms 80 3.9 Analytical Position Analysis 92 3.9.1 Loop Closure Equation 92 3.9.2 Complex Number Notation 98 3.10 Toggle Positions 100 3.11 Computer Methods for Position Analysis 100 3.11.1 Position Analysis Using Spreadsheets 100 3.11.2 Distance Formula to Solve for Output Angle 101 3.11.3 Computer Solutions Using MATLAB? and MathCAD 102 3.12 Review and Summary 103 Problems 103 Further Reading 107 4 Linkage Velocity and Acceleration Analysis 108 4.1 Introduction 108 4.2 Finite Displacement: Approximate Velocity Analysis 109 4.3 Instantaneous Centers of Rotation 111 4.3.1 Number of Instant Centers 111 4.3.2 Primary Instant Centers 112 4.3.3 Kennedy–Aronhold Theorem 112 4.3.4 Locating Instant Centers for Typical Four-Bar Mechanisms 112 4.3.5 Locating Instant Centers for Slider–Crank Mechanisms 114 4.3.6 Locating Instant Centers for Other Mechanisms 114 4.3.7 Velocity Analysis Using Instant Centers 115 4.4 Graphical Velocity Analysis 119 4.4.1 Basic Concepts 119 4.4.2 Component Method 122 4.4.3 Parameter Studies 124 4.5 Analytical Velocity Analysis Methods 125 4.5.1 Introduction 125 4.5.2 Vector Method 126 4.5.3 Loop-Closure Method 127 4.5.4 Differentiation of Position Coordinate Equation 129 Contents vii4.6 Graphical Acceleration Analysis Methods 130 4.7 Analytical Acceleration Analysis Methods 134 4.8 Kinematic Analysis of Linkage Mechanisms with Moving Slides 135 4.8.1 Sliding Motion 135 4.8.2 Motion Relative to Rotating Axes 138 4.8.3 Coriolis Component 141 4.8.4 Geneva Mechanisms 144 4.9 Review and Summary 147 Problems 147 Further Reading 153 5 Linkage Synthesis 154 5.1 Introduction 154 5.1.1 Synthesis Classifications 154 5.1.2 Essential Engineering Geometry and Drafting 155 5.2 Synthesis 155 5.2.1 Type Synthesis 155 5.2.2 Number Synthesis 156 5.2.3 Dimensional Synthesis 156 5.3 Two-Position Graphical Dimensional Synthesis 156 5.3.1 Introduction 156 5.3.2 Using Rocker Motion from a Double Rocker Mechanism 157 5.3.3 Using Rocker Motion from a Crank–Rocker Mechanism 158 5.3.4 Using Coupler Motion 160 5.3.5 Adding a Driver Dyad 161 5.4 Three-Position Graphical Dimensional Synthesis 162 5.4.1 Using Coupler Motion 162 5.4.2 Fixed Pivot Point Locations Defined 163 5.5 Approximate Dwell Linkage Mechanisms 167 5.6 Quick Return Mechanisms 169 5.6.1 Time Ratio 169 5.6.2 Quick Return Crank–Rocker Mechanism 170 5.6.3 Whitworth Mechanism 172 5.6.4 Offset Slider–Crank Mechanism 174 5.7 Function Generation 176 5.7.1 Introduction 176 5.7.2 Accuracy Points 176 5.7.3 Chebyshev Spacing 177 5.7.4 Freudenstein’s Equation: Four-Bar Linkage 178 5.7.5 Error Analysis for Function Generation 182 5.8 Review and Summary 182 Problems 182 Further Reading 189 6 Computational Methods for Linkage Mechanism Kinematics 190 6.1 Introduction 190 6.2 Matrix Review 190 6.2.1 Introduction 190 viii Contents6.2.2 Matrix Notation 191 6.2.3 Matrix Operations 191 6.2.4 Representing Simultaneous Equations in Matrix Form 193 6.3 Position Equations 196 6.3.1 Introduction 196 6.3.2 Iterative Solution Method 196 6.3.3 MATLAB? Program Module for Calculating ?3 and ?4 201 6.3.4 Position Analysis Using MathCAD 202 6.3.5 Linkage Center of Mass Locations 205 6.4 Velocity Analysis 206 6.4.1 Numerical Differentiation 206 6.4.2 Derivatives of Data Containing Errors or Noise 206 6.4.3 Velocity Analysis in MathCAD 207 6.5 Acceleration Equations 209 6.5.1 Numerical Differentiation 209 6.5.2 Acceleration Analysis in MathCAD 209 6.6 Dynamic Simulation Using Autodesk Inventor 210 6.6.1 Basic Concepts 210 6.6.2 Kinematic Constraints 211 6.6.3 Kinematic Analysis Example 211 6.7 Review and Summary 211 Problems 212 Further Reading 214 7 Gear Analysis 215 7.1 Introduction 215 7.2 Involute Curves 216 7.2.1 Conjugate Profiles 216 7.2.2 Properties of Involute Curves 217 7.3 Terminology 219 7.3.1 Pitch Circle and Pressure Angle 219 7.3.2 Base Circle 220 7.3.3 General Gear Tooth Terminology 221 7.3.4 Clearance and Backlash 227 7.4 Tooth Contact 228 7.4.1 Involute Gear Tooth 228 7.4.2 Path of Contact 229 7.4.3 Contact Ratio 231 7.4.4 Interference 233 7.5 Analysis of Spur Gears 234 7.5.1 Basic Concepts of Spur Gears 234 7.5.2 Speed Ratio of Spur Gears 235 7.5.3 Efficiency of Spur Gears 238 7.6 Analysis of Parallel Helical Gears 239 7.6.1 Parallel versus Crossed Helical Gears 239 7.6.2 Basic Concepts of Helical Gears 240 7.6.3 Terminology Specific to Helical Gears 240 Contents ix7.6.4 Efficiency of Helical Gears 241 7.7 Analysis of Crossed Helical Gears 242 7.7.1 Graphical Solution for a Shaft Angle of 90° 242 7.7.2 Graphical Solution for Other Shaft Angles 244 7.7.3 Versatility of Helical Gears for Nonparallel Shafts 245 7.8 Analysis of Bevel Gears 246 7.8.1 Basic Concepts of Bevel Gears 246 7.8.2 Terminology Specific to Bevel Gears 247 7.8.3 Speed Ratio and Direction of Rotation 247 7.8.4 Other Types of Bevel Gears 248 7.9 Analysis of Worm Gearing 249 7.9.1 Basic Concepts of Worm Gearing 249 7.9.2 Terminology Specific to Worm Gearing 249 7.9.3 Speed Ratios of Worm Gearing 251 7.9.4 Efficiency of Worm Gearing 251 7.9.5 Self-locking Condition 252 7.10 Review and Summary 252 Problems 252 Further Reading 254 8 Gear Trains 255 8.1 Introduction 255 8.2 Simple Gear Trains 256 8.3 Compound Gear Trains 258 8.3.1 Speed Ratio Calculations 258 8.3.2 Design of Compound Gear Trains 260 8.4 Reverted Compound Gear Trains 262 8.5 Gear Trains with Different Types of Gears 264 8.6 Planetary Gear Trains 266 8.6.1 Investigation of a Historical Application 266 8.6.2 Basic Planetary Gear Train 267 8.6.3 Speed Ratio of Planetary Gear Trains 268 8.7 Differentials 273 8.8 Computer Methods for Gear Train Design 274 8.9 Review and Summary 274 Problems 275 Further Reading 279 9 Cams 280 9.1 Introduction 280 9.2 Types of Cams and Followers 281 9.2.1 Common Cam Configurations 281 9.2.2 Follower Types 281 9.3 Basic Concepts of Cam Geometry and Cam Profiles 283 9.3.1 Follower Displacement 283 9.3.2 SVAJ Diagrams 283 9.3.3 General Rules of Cam Design 285 x Contents9.4 Common Cam Functions 285 9.4.1 Introduction to Cam Functions 285 9.4.2 Simple Harmonic Function 286 9.4.3 The Cycloidal Function 287 9.4.4 The 3-4-5 Polynomial Function 290 9.4.5 The 4-5-6-7 Polynomial Function 290 9.4.6 The Double Harmonic Function 291 9.4.7 Comparison of Cam Functions 292 9.5 Using Cam Functions for Specific Applications 295 9.6 Application of Cam Functions for Double-Dwell Mechanisms 299 9.7 Application of Cam Functions for Single-Dwell Mechanisms 301 9.8 Application of Cam Functions for Critical Path Motion 308 9.8.1 Basic Concept of Critical Path Motion 308 9.8.2 Cam Functions for Constant Acceleration 308 9.8.3 Cam Functions for Constant Velocity 308 9.9 Cam Geometry 310 9.9.1 Basic Concepts 310 9.9.2 Base Circle 310 9.9.3 Pressure Angle 311 9.10 Determining Cam Size 312 9.10.1 General Ideas 312 9.10.2 Maximum Pressure Angle for Simple Harmonic Functions 314 9.10.3 Maximum Pressure Angle for More Complex Cam Functions 315 9.11 Design of Cam Profiles 316 9.11.1 Graphical Methods for Plate Cams with In-Line Followers 316 9.11.2 Graphical Methods for Offset Followers 320 9.12 Computer Methods for Cam Design 322 9.13 Review and Summary 322 Problems 323 Reference 327 10 Vibration Theory 328 10.1 Introduction 328 10.2 System Components 329 10.3 Frequency and Period 333 10.4 Undamped Systems 333 10.4.1 Equations of Motion 333 10.4.2 Graphical Representation of Initial Conditions 339 10.4.3 Energy Methods 340 10.5 Torsional Systems 344 10.6 Damped Systems 346 10.6.1 Equations of Motion 347 10.6.2 Critically Damped Systems 348 10.6.3 Overdamped Systems 348 10.6.4 Underdamped Systems 350 10.7 Logarithmic Decrement 353 10.8 Forced Vibration: Harmonic Forcing Functions 356 Contents xi10.8.1 Harmonic versus Periodic Functions 357 10.8.2 Equations of Motion for Harmonic Excitation 357 10.8.3 Resonance 359 10.8.4 Damped Response to Harmonic Excitation 362 10.8.5 Harmonic Support Motion with Viscous Damping 369 10.9 Response of Undamped Systems to General Loading 372 10.9.1 Constant Force 372 10.9.2 Ramp Load 375 10.9.3 Exponentially Decaying Motion 377 10.9.4 Combination of the Basic Forcing Functions 378 10.10 Review and Summary 381 Problems 381 Further Reading 386 11 Dynamic Force Analysis 387 11.1 Introduction 387 11.2 Superposition Method of Force Analysis 388 11.2.1 Introduction 388 11.2.2 Equivalent Offset Inertia Force 391 11.2.3 Superposition Method for Dynamic Force Analysis of a Four-Bar Mechanism 394 11.3 Matrix Method Force Analysis 399 11.3.1 General Concepts 399 11.3.2 Four-Bar Linkage 399 11.4 Sliding Joint Forces 405 11.5 Energy Methods of Force Analysis: Method of Virtual Work 410 11.6 Force Analysis for Slider–Crank Mechanisms Using Lumped Mass 412 11.6.1 Lumped Mass Assumption 412 11.6.2 Acceleration of the Slider 413 11.7 Gear Forces 416 11.7.1 Introduction 416 11.7.2 Spur Gears 416 11.7.3 Other Gear Types 418 11.8 Computer Methods 418 11.9 Review and Summary 418 Problems 419 Further Reading 421 12 Balancing of Machinery 422 12.1 Introduction 422 12.2 Static Balancing 423 12.2.1 Basic Concepts 423 12.2.2 Graphical Method for Rotor Balancing 424 12.2.3 Analytical Method for Rotor Balancing 426 12.3 Dynamic Balancing 431 12.4 Vibration from Rotating Unbalance 437 12.5 Balancing Slider–Crank Linkage Mechanisms 439 xii Contents12.5.1 Introduction 439 12.5.2 Inertial Forces 439 12.5.3 Balancing Primary Forces 441 12.5.4 Illustrative Example of Slider–Crank Balancing 442 12.5.5 Lanchester Balancer 445 12.6 Balancing Linkage Mechanisms 447 12.6.1 Introduction 447 12.6.2 Global Center 447 12.6.3 Shaking Forces 448 12.7 Flywheels 448 12.7.1 Introduction 448 12.7.2 Speed Fluctuation 449 12.7.3 Flywheel Energy 450 12.7.4 Fluctuation of Energy 451 12.7.5 Flywheel Design 452 12.7.6 Flywheel Analysis for a Punching Press 454 12.8 Measurement Devices 455 12.9 Computer Methods 458 12.9.1 Balancing 458 12.9.2 Flywheels 459 12.10 Review and Summary 459 Problems 459 References 464 Further Reading 464 13 Applications of Machine Dynamics 465 13.1 Introduction 465 13.2 Cam Response for Simple Harmonic Functions 465 13.2.1 Background 465 13.2.2 General Equation of Motion 466 13.2.3 Response for Simple Harmonic Cam Function 467 13.3 General Response Using Laplace Transform Method 469 13.3.1 Introduction 469 13.3.2 Basic Concepts of Laplace Transform 470 13.3.3 Step Functions 471 13.3.4 Transforms of Derivatives 473 13.3.5 Inverse Transforms 473 13.3.6 Vibration Analysis with Laplace Transforms 477 13.4 System Response Using Numerical Methods 479 13.5 Advanced Cam Functions 482 13.5.1 Introduction 482 13.5.2 Combination of Basic Cam Functions 483 13.5.3 Higher Order Polynomial Functions 492 13.6 Forces Acting on the Follower 492 13.6.1 Basic Concepts 492 13.6.2 Compression Spring Design 492 13.7 Computer Applications of Cam Response 494 Contents xiii13.8 Internal Combustion Engines 494 13.8.1 Introduction 494 13.8.2 Engine Force Analysis 496 13.9 Common Arrangements of Multicylinder Engines 499 13.9.1 Introduction 499 13.9.2 In-Line Engines 501 13.9.3 Opposed Engines 502 13.9.4 V Engines 504 13.10 Flywheel Analysis for Internal Combustion Engines 504 13.11 Review and Summary 506 Problems 506 References 507 Further Reading 507 Appendix A – Center of Mass 509 Appendix B – Moments of Inertia 512 Appendix C – Fourier Series 521 Index Index A Acceleration angular 38, 130–1 cam follower (see Cams) Coriolis 141–2, 144, 408 definition of 8–9, 35, 38 numerical differentiation 53–7, 206, 209 relative 47, 131, 134 slider approximation 413–15, 440 Accelerometer 458 Accuracy points 176 Addendum 223–9, 232, 234 Amplitude ratio 359–61, 365–6 Antikythera mechanism 1–2 Arc of approach 231, 238, 241 Arc of recess 231, 238, 241 B Backlash 227–8 Balancing dynamic 422, 431–4 engine 501–2 linkages 422, 447–8 slider-crank 422, 439–43, 465, 499–500 static 422–4, 426, 431–3 Base circle cam 310–12, 317–20 gear 217–21, 223, 228, 233 Base pitch 228, 231–2 Bevel gears 24–5, 215, 246–9, 264–5, 418 speed ratio 247–8, 264–5 Binary link 14–15 Bisector 155, 158–63, 165 Blobs 7 Bottom dead center 495 C Cam 11, 27 axial (see Disk cam) barrel (see Drum cam) cylindrical (see Drum cam) disk 27, 281, 313–14, 317 drum 28, 281 followers 27–8, 281–3, 465–6 radial (see Disk cam) Cam functions 285–6 combination functions 483–91 constant acceleration 308 constant velocity 308–10 cycloidal 287–90, 483–5, 489 double harmonic 291–2 3-4-5 polynomial 290 4-5-6-7 polynomial 290–91 simple harmonic 286–7, 314, 465–9 using 295, 298 Cam geometry 310 Cam mechanism 27–8 double dwell 284, 299–300 single dwell 284, 301–3 Cam profile in-line follower 316–19 offset follower 320–21 Cam response Laplace transform 477 numerical methods 479–82 simple harmonic 465–9 Cayley diagram 76–7 Center of mass. See Centroid Center of rotation. See Instant center of rotation Central difference 53–4, 109 Machine Analysis with Computer Applications for Mechanical Engineers, First Edition. James Doane.
2015 John Wiley & Sons, Ltd. Published 2015 by John Wiley & Sons, Ltd.Centroid 447–8, 509–10 Change points 73 Chebyshev spacing 177–8 Chebyshev 76, 78–9 Cognate linkage 76–9 binary coupler 78 slider-crank 79 ternary coupler 76 Conjugate profile 216–17, 229, 233 Contact ratio 231–2, 239 Coriolis acceleration 141–2, 144, 408 Coupler curve 74–6, 78–9, 154, 167 Critical damping 348 Cusp 74–5 Cycloid 75, 215 D d’ Alembert 392, 423 Damped natural frequency 351 Damped vibration. See Vibration Damping critical damping 348 damping coefficient 347, 355 damping ratio 347, 350 fluid damping 347 Dedendum 223–5, 227–8 Degrees of freedom 16, 67–9 Determinant 192 Diametral pitch 220–24, 227, 236, 247, 263 Differential 273–4 Double point 74–5 Dwell 144, 167, 468–9 cam (see Cam mechanism) double 168, 284, 299–300 linkage mechanism 167–9 single 167–9, 284, 301–3 Dynamic balancing. See Balancing E Efficiency helical gear 241 spur gear 238 worm gear 251–2 Energy elastic 341 fluctuation of 451–2 kinetic 108, 293, 340–3, 449–52, 512–13 method 340–4, 410 potential 340–3 Epicyclic gear train. See Planetary gear train Equivalent offset inertia force 391–4 spring stiffness 329–31 F Face width 223–4, 240 Finite displacement 109 Fluctuation coefficient 453 Flywheel 448, 496 design 452–3 energy 450–2 engine 504–6 moment of inertia 453 Forced vibration. See Vibration Fourier series 521–8 Frequency 333, 441, 521–2 damped natural 350 forcing 356, 358–9, 364 natural 333–4, 343, 346, 350, 358 ratio 360, 365, 457–8, 468 Freudenstein 5, 94, 178 Full joint 67–9 Function generation synthesis 176–82 G Gear helical (see Helical gears) interference 233–4, 257 spur (see Spur gears) worm (see Worm gearing) Geneva mechanism 144–5 Global center of mass 205–6, 447–8 Grashof’s criterion 72–4 Ground link 14, 69 H Half joint 68–9 Helical gears 23–4, 215, 262, 264 crossed 24, 239, 242–6 efficiency 241 helix angle 240 lead 240 parallel 23–4, 239 Herringbone gear 23–4, 240 I Instant center of rotation 51–3, 75, 111–15 Involute curve 4, 21, 215–20, 225, 228 J Jerk 284 530 IndexK Kennedy-Aronhold theorem 112–13 Kutzbach 69, 156 L Lanchester balancer 445–7, 499 Laplace transform 469–70 derivatives 473 inverse transform 473–4. (see also Partial fractions) Linkage inversion 72–3, 163 Linkage joint types 15–16 Logarithmic decrement 353–5 Loop closure 92–3, 98, 127 Low pass filter 207 Lumped mass approximation 412–13, 440–3, 445, 448, 492, 504 M MathCAD acceleration analysis 209–10 Laplace transform 477 position analysis 201 solve blocks 201–2 velocity analysis 207–9 Matrix method for linkage forces 399–403 Matrix notation 191 Matrix operations addition 191–2 determinate 192 inverse 192 multiplication 192 Mobility 67–9. See also Degrees of freedom Moment of inertia 449–50, 452–3, 512–20 Motion generation synthesis 154–5 Multiple joint 68 N Natural frequency 333–4, 343, 346, 350, 358 Neutral axis. See Centroid Newton-Raphson 197 Number synthesis 156 O Output angle 80–2, 94–7, 101–3 P Parallel axis theorem 515–16 Partial fractions 474–6 Path generation synthesis 154 Perpendicular bisector. See Bisector Pitch diameter 221, 223, 230–31, 237, 241–6, 263 Pitch point 217, 219–20, 229, 231 Polar moment of inertia 517–18 Planetary gear train 255, 266–71 Precision point. See Accuracy point Pressure angle 219–23, 229, 233–4, 311–12, 483 Primary forces 441–2, 444–7, 500–502 Primary instant center 112 Q Quick return 169 crank-rocker 170–2 offset slider 174–6 Whitworth 172–3 R Radius of gyration 515 Resonance 359–60, 367 Roberts–Chebyshev theorem 76, 78–9 Roberts diagram 77–8 S Secondary forces 441, 444–7, 500 Simultaneous equations MathCAD 201 matrix representation 193 Spring 283 design for cam system 492–4 equivalent stiffness 329–33 force 329 strain energy 341 Spur gears 22–3, 234–9, 264, 418 efficiency 238 speed ratio 235–6 Static balancing. See Balancing Step function 471–3 Straight line mechanism 3, 19–20 Superposition 388–92, 394 SVAJ diagram 283–4 T Time ratio 169–70 Toggle mechanism 18–19 Toggle position 100, 159, 161, 169–70, 174–6 Top dead center 495 Transmission angle 79–82 Turning moment diagram 451, 453, 504–5 Type synthesis 155–6 Index 531U Undamped vibration. See Vibration V Velocity angular 35, 119 finite difference 109–111 instant center 51–3, 75, 115–17 numerical differentiation 53–4, 109, 206 relative 41–2, 119–22 rotation about fixed axis 36–7 Vibration 465–6, 470–71 damped 346–53 forced 356–9, 362–7, 372–9, 527–8 Laplace transform 477 rotating unbalance 437–9 support motion 369–70 undamped 333–9 W Whitworth mechanism 172–3 Worm gearing 11, 26, 249–52, 264 efficiency 251–2 self-locking 252 speed ratio 251 532 Index
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