Mechanical Engineer's Handbook

1 Statics......Page 16
1.1 Terminology and Notation......Page 17
1.5 Unit Vectors......Page 19
1.6 Vector Addition......Page 20
1.7 Resolution of Vectors and Components......Page 21
1.8 Angle between Two Vectors......Page 22
1.10 Vector ( Cross) Product of Vectors......Page 24
1.12 Vector Triple Product of......Page 26
2.1 Position Vector......Page 27
2.3 Centroid of a Set of Points......Page 28
2.4 Centroid of a Curve, Surface, or Solid......Page 30
2.6 Mass Center of a Curve, Surface, or Solid......Page 31
2.7 First Moment of an Area......Page 32
2.8 Theorems of Guldinus ± Pappus......Page 36
2.9 Second Moments and the Product of Area......Page 39
2.10 Transfer Theorems or Parallel- Axis Theorems......Page 40
2.11 Polar Moment of Area......Page 42
2.12 Principal Axes......Page 43
3.1 Moment of a Bound Vector about a Point......Page 45
3.2 Moment of a Bound Vector about a Line......Page 46
3.3 Moments of a System of Bound Vectors......Page 47
3.4 Couples......Page 49
3.5 Equivalence......Page 50
3.6 Representing Systems by Equivalent Systems......Page 51
4.1 Equilibrium Equations......Page 55
4.2 Supports......Page 57
4.3 Free-Body Diagrams......Page 59
5. Dry Friction......Page 61
5.2 Kinetic Coefficient of Friction......Page 62
5.3 Angles of Friction......Page 63
2 Dynamics......Page 65
1.2 Numbers......Page 66
1.3 Angular Units......Page 67
2.1 Position, Velocity, and Acceleration of a Point......Page 68
2.2 Angular Motion of a Line......Page 69
2.3 Rotating Unit Vector......Page 70
2.4 Straight Line Motion......Page 71
2.5 Curvilinear Motion......Page 72
2.6 Normal and Tangential Components......Page 73
2.7 Relative Motion......Page 87
3.1 Newton\'s Second Law......Page 88
3.3 Inertial Reference Frames......Page 89
3.4 Cartesian Coordinates......Page 90
3.5 Normal and Tangential Components......Page 91
3.6 Polar and Cylindrical Coordinates......Page 92
3.7 Principle of Work and Energy......Page 94
3.8 Work and Power......Page 95
3.9 Conservation of Energy......Page 98
3.10 Conservative Forces......Page 99
3.11 Principle of Impulse and Momentum......Page 101
3.12 Conservation of Linear Momentum......Page 103
3.13 Impact......Page 104
3.14 Principle of Angular Impulse and Momentum......Page 108
4.1 Types of Motion......Page 109
4.2 Rotation about a Fixed Axis......Page 110
4.3 Relative Velocity of Two Points of the Rigid Body......Page 111
4.4 Angular Velocity Vector of a Rigid Body......Page 112
4.5 Instantaneous Center......Page 114
4.6 Relative Acceleration of Two Points of the Rigid Body......Page 116
4.7 Motion of a Point That Moves Relative to a Rigid Body......Page 117
5.1 Equation of Motion for the Center of Mass......Page 125
5.2 Angular Momentum Principle for a System of Particles......Page 127
5.3 Equations of Motion for General Planar Motion......Page 129
5.4 D\'Alembert\'s Principle......Page 131
3 Mechanics of Materials......Page 133
1.2 Stress Components......Page 134
1.3 Mohr\'s Circle......Page 135
1.4 Triaxial Stress......Page 139
1.5 Elastic Strain......Page 141
1.6 Equilibrium......Page 142
1.7 Shear and Moment......Page 145
1.8 Singularity Functions......Page 146
1.9 Normal Stress in Flexure......Page 149
1.10 Beams with Asymmetrical Sections......Page 153
1.11 Shear Stresses in Beams......Page 154
1.12 Shear Stresses in Rectangular Section Beams......Page 156
1.13 Torsion......Page 157
1.14 Contact Stresses......Page 161
2. Defection and Stiffness......Page 163
2.2 Spring Rates for Tension, Compression, and Torsion......Page 164
2.3 Deflection Analysis......Page 166
2.4 Deflections Analysis Using Singularity Functions......Page 167
2.5 Impact Analysis......Page 171
2.6 Strain Energy......Page 174
2.7 Castigliano\'s Theorem......Page 177
2.9 Long Columns with Central Loading......Page 179
2.10 Intermediate- Length Columns with Central Loading......Page 183
2.11 Columns with Eccentric Loading......Page 184
2.12 Short Compression Members......Page 185
3.1 Endurance Limit......Page 187
3.3 Constant Life Fatigue Diagram......Page 192
3.4 Fatigue Life for Randomly Varying Loads......Page 195
3.5 Criteria of Failure......Page 197
4 Theory of Mechanisms......Page 203
1.2 Mobility......Page 204
1.3 Kinematic Pairs......Page 205
1.4 Number of Degrees of Freedom......Page 213
1.5 Planar Mechanisms......Page 214
2.1 Cartesian Method......Page 216
2.2 Vector Loop Method......Page 222
3. Velocity and Acceleration Analysis......Page 225
3.2 RRR Dyad......Page 226
3.3 RRT Dyad......Page 228
3.4 RTR Dyad......Page 229
3.5 TRT Dyad......Page 230
4.1 Moment of a Force about a Point......Page 237
4.2 Inertia Force and Inertia Moment......Page 238
4.3 Free- Body Diagrams......Page 241
4.4 Reaction Forces......Page 242
4.5 Contour Method......Page 243
5 Machine Components......Page 257
1.1 Screw Thread......Page 258
1.2 Power Screws......Page 261
2.2 Geometry and Nomenclature......Page 267
2.3 Interference and Contact Ratio......Page 272
2.4 Ordinary Gear Trains......Page 275
2.5 Epicyclic Gear Trains......Page 276
2.6 Differential......Page 281
2.7 Gear Force Analysis......Page 284
2.8 Strength of Gear Teeth......Page 289
3.2 Materials for Springs......Page 297
3.4 Helical Compression Springs......Page 298
3.5 Torsion Springs......Page 304
3.6 Torsion Bar Springs......Page 306
3.7 Multileaf Springs......Page 307
3.8 Belleville Springs......Page 310
4.1 Generalities......Page 311
4.3 Geometry......Page 312
4.4 Static Loading......Page 317
4.5 Standard Dimensions......Page 318
4.6 Bearing Selection......Page 322
5.1 Viscosity......Page 332
5.2 Petroff\'s Equation......Page 337
5.3 Hydrodynamic Lubrication Theory......Page 340
5.4 Design Charts......Page 342
6 Theory of Vibration......Page 352
1 Introduction......Page 353
2. Linear Systems with One Degree of Freedom......Page 354
2.1 Equation of Motion......Page 355
2.2 Free Undamped Vibrations......Page 356
2.3 Free Damped Vibrations......Page 358
2.4 Forced Undamped Vibrations......Page 365
2.5 Forced Damped Vibrations......Page 372
2.6 Mechanical Impedance......Page 382
2.7 Vibration Isolation: Transmissibility......Page 383
2.8 Energetic Aspect of Vibration with One DOF......Page 387
2.9 Critical Speed of Rotating Shafts......Page 393
3. Linear Systems with Finite Numbers of Degrees of Freedom......Page 398
3.1 Mechanical Models......Page 399
3.2 Mathematical Models......Page 405
3.3 System Model......Page 417
3.4 Analysis of System Model......Page 418
3.5 Approximative Methods for Natural Frequencies......Page 420
4.1 The Machine Tool as a System......Page 429
4.2 Actuator Subsystems......Page 431
4.3 The Elastic Subsystem of a Machine Tool......Page 432
4.4 Elastic System of Machine- Tool Structure......Page 448
4.5 Subsystem of the Friction Process......Page 450
4.6 Subsystem of Cutting Process......Page 453
7 Principles of Heat Transfer......Page 458
1. Heat Transfer Thermodynamics......Page 459
1.1 Physical Mechanisms of Heat Transfer: Conduction,......Page 464
1.2 Technical Problems of Heat Transfer......Page 468
2. Conduction Heat Transfer......Page 469
2.1 The Heat Diffusion Equation......Page 470
2.2 Thermal Conductivity......Page 472
2.3 Initial, Boundary, and Interface Conditions......Page 474
2.4 Thermal Resistance......Page 476
2.5 Steady Conduction Heat Transfer......Page 477
2.6 Heat Transfer from Extended Surfaces ( Fins)......Page 481
2.7 Unsteady Conduction Heat Transfer......Page 485
3.1 External Forced Convection......Page 501
3.2 Internal Forced Convection......Page 533
3.3 External Natural Convection......Page 548
3.4 Internal Natural Convection......Page 562
8 Fluid Dynamics......Page 571
1.3 Specific Weight......Page 572
1.4 Viscosity......Page 573
1.8 Bulk Modulus of Elasticity......Page 574
1.9 Statics......Page 575
1.10 Hydrostatic Forces on Surfaces......Page 576
1.12 Dimensional Analysis and Hydraulic Similitude......Page 577
1.13 Fundamentals of Fluid Flow......Page 580
2.1 Absolute and Gage Pressure......Page 584
2.2 Bernoulli\'s Theorem......Page 585
2.3 Hydraulic Cylinders......Page 587
2.4 Pressure Intensifiers......Page 590
2.5 Pressure Gages......Page 591
2.6 Pressure Controls......Page 592
2.7 Flow- Limiting Controls......Page 604
2.8 Hydraulic Pumps......Page 607
2.9 Hydraulic Motors......Page 610
2.10 Accumulators......Page 613
2.12 Fluid Power Transmitted......Page 615
2.13 Piston Acceleration and Deceleration......Page 616
2.14 Standard Hydraulic Symbols......Page 617
2.15 Filters......Page 618
2.16 Representative Hydraulic System......Page 619
9 Control......Page 623
1. Introduction......Page 624
1.1 A Classic Example......Page 625
2. Signals......Page 626
3.1 Transfer Functions for Standard Elements......Page 628
3.2 Transfer Functions for Classic Systems......Page 629
4. Connection of Elements......Page 630
5. Poles and Zeros......Page 632
6.1 Input Variation Steady- State Error......Page 635
6.2 Disturbance Signal Steady- State Error......Page 636
7. Time-Domain Performance......Page 640
8. Frequency-Domain Performances......Page 643
8.1 The Polar Plot Representation......Page 644
8.2 The Logarithmic Plot Representation......Page 645
8.3 Bandwidth......Page 649
9. Stability of Linear Feedback Systems......Page 651
9.1 The Routh ± Hurwitz Criterion......Page 0
9.2 The Nyquist Criterion......Page 653
9.3 Stability by Bode Diagrams......Page 660
10. Design of Closed-Loop Control Systems by Pole- Zero Methods......Page 661
10.1 Standard Controllers......Page 662
10.2 P- Controller Performance......Page 663
10.3 Effects of the Supplementary Zero......Page 668
10.4 Effects of the Supplementary Pole......Page 672
10.5 Effects of Supplementary Poles and Zeros......Page 673
10.6 Design Example: Closed- Loop Control of a Robotic Arm......Page 676
11. Design of Closed-Loop Control Systems by Frequential Methods......Page 681
12. State Variable Models......Page 684
13.1 Nonlinear Models: Examples......Page 690
13.2 Phase Plane Analysis......Page 693
13.3 Stability of Nonlinear Systems......Page 697
13.4 Liapunov\'s First Method......Page 700
13.5 Liapunov\'s Second Method......Page 701
14. Nonlinear Controllers by Feedback Linearization......Page 703
15.1 Fundamentals of Sliding Control......Page 707
15.2 Variable Structure Systems......Page 712
A. 1 Differential Equations of Mechanical Systems......Page 715
A. 3 Mapping Contours in the......Page 719
A. 4 The Signal Flow Diagram......Page 724
Differential Equations and Systems of Differential Equations......Page 727
1.1 Ordinary Differential Equations: Introduction......Page 728
1.2 Integrable Types of Equations......Page 738
1.3 On the Existence, Uniqueness, Continuous Dependence......Page 778
1.4 Linear Differential Equations......Page 786
2.1 Fundamentals......Page 828
2.2 Integrating a System of Differential Equations by the......Page 831
2.3 Finding Integrable Combinations......Page 835
2.4 Systems of Linear Differential Equations......Page 837
2.5 Systems of Linear Differential Equations with Constant......Page 847