Fundamentals of biomechanics

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Title:

Personal Author:

Huston, Ronald L., 1937-

Publication Information:

Boca Raton : Taylor & Francis, 2013

Physical Description:

xv, 454 p. : ill. ; 26 cm.

ISBN:

9781466510371

Subject Term:

Biomechanics

Models, Biological

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010307343	QH513 H87 2013	Open Access Book	Book	Searching... Unknown

In the last three or four decades, studies of biomechanics have expanded from simple topical applications of elementary mechanics to entire areas of study. Studies and research in biomechanics now exceed those in basic mechanics itself, underlining the continuing and increasing importance of this area of study. With an emphasis on biodynamic modeling, Fundamentals of Biomechanics provides an accessible, basic understanding of the principles of biomechanics analyses.

Following a brief introductory chapter, the book reviews gross human anatomy and basic terminology currently in use. It describes methods of analysis from elementary mathematics to elementary mechanics and goes on to fundamental concepts of the mechanics of materials. It then covers the modeling of biosystems and provides a brief overview of tissue biomechanics. The author then introduces the concepts of biodynamics and human body modeling, looking at the fundamentals of the kinematics, the kinetics, and the inertial properties of human body models. He supplies a more detailed analysis of kinematics, kinetics, and dynamics of these models and discusses the numerical procedures for solving the governing dynamical equations. The book concludes with a review of a few example applications of biodynamic models such as simple lifting, maneuvering in space, walking, swimming, and crash victim simulation.

The inclusion of extensive lists of problems of varying difficulty, references, and an extensive bibliography add breadth and depth to the coverage. Focusing on biodynamic modeling to a degree not found in other texts, this book equips readers with the expertise in biomechanics they need for advanced studies, research, and employment in biomedical engineering.

Author Notes

Ronald L. Huston is a Distinguished Research Professor in the School of Dynamic Systems, College of Engineering and Applied Science, at the University of Cincinnati, Ohio.

Preface	p. xi
Acknowledgment	p. xiii
Author	p. xv
Chapter 1 Introduction	p. 1
1.1 Principal Areas of Biomechanics	p. 1
1.2 Approach in This Book	p. 1
Problem	p. 2
References	p. 2
Chapter 2 Review of Human Anatomy and Some Basic Terminology	p. 5
2.1 Gross (Whole-Body) Modeling	p. 5
2.2 Position and Direction Terminology	p. 9
2.3 Terminology for Common Movements	p. 12
2.4 Skeletal Anatomy	p. 16
2.5 Major Joints	p. 19
2.6 Major Muscle Groups	p. 20
2.7 Anthropometric Data	p. 21
Problems	p. 23
References	p. 23
Chapter 3 Methods of Analysis I: Review of Vectors, Dyadics, Matrices, and Determinants	p. 25
3.1 Vectors	p. 25
3.2 Vector Algebra: Addition and Multiplication by Scalars	p. 25
3.2.1 Vector Characteristics	p. 25
3.2.2 Equality of Vectors	p. 26
3.2.3 Special Vectors	p. 26
3.2.4 Multiplication of Vectors and Scalars	p. 26
3.2.5 Vector Addition	p. 26
3.2.6 Addition of Perpendicular Vectors	p. 28
3.2.7 Use of Index and Summation Notations	p. 31
3.3 Vector Algebra: Multiplication of Vectors	p. 32
3.3.1 Angle between Vectors	p. 32
3.3.2 Scalar Product	p. 32
3.3.3 Vector Product	p. 34
3.3.4 Dyadic Product	p. 36
3.4 Dyadics	p. 37
3.4.1 Zero Dyadic	p. 37
3.4.2 Identity Dyadic	p. 37
3.4.3 Dyadic Transpose	p. 38
3.4.4 Symmetric Dyadics	p. 38
3.4.5 Multiplication of Dyadics	p. 38
3.4.6 Inverse Dyadics	p. 39
3.4.7 Orthogonal Dyadics	p. 39
3.5 Multiple Products of Vectors	p. 39
3.5.1 Scalar Triple Product	p. 39
3.5.2 Vector Triple Product	p. 41
3.5.3 Dyadic/Vector Product	p. 41
3.5.4 Other Multiple Products	p. 42
3.6 Matrices/Arrays	p. 43
3.6.1 Zero Matrices	p. 43
3.6.2 Identity Matrices	p. 43
3.6.3 Matrix Transpose	p. 43
3.6.4 Equal Matrices	p. 43
3.6.5 Symmetric Matrices	p. 44
3.6.6 Skew-Symmetric Matrices	p. 44
3.6.7 Diagonal Matrix	p. 44
3.6.8 Matrix Measures	p. 44
3.6.9 Singular Matrices	p. 44
3.6.10 Multiplication of Matrices by Scalars	p. 44
3.6.11 Addition of Matrices	p. 44
3.6.12 Multiplication of Matrices	p. 45
3.6.13 Inverse Matrices	p. 45
3.6.14 Orthogonal Matrices	p. 46
3.6.15 Submatrices	p. 46
3.6.16 Rank	p. 46
3.6.17 Partitioning of Matrices, Block Multiplication	p. 46
3.6.18 Pseudoinverse	p. 46
3.7 Determinants	p. 47
3.8 Relationship of 3 × 3 Determinants, Permutation Symbols, and Kronecker Delta Functions	p. 49
3.9 Eigenvalues, Eigenvectors, and Principal Directions	p. 52
3.10 Maximum and Minimum Eigenvalues and the Associated Eigenvectors	p. 57
3.11 Use of MATLAB®	p. 58
3.12 Elementary MATLAB® Operations and Functions	p. 62
3.12.1 Elementary Operations	p. 62
3.12.2 Elementary Functions	p. 63
Problems	p. 64
References	p. 74
Chapter 4 Methods of Analysis II: Forces and Force Systems	p. 77
4.1 Forces: Vector Representations	p. 77
4.2 Moments of Forces	p. 77
4.3 Moments of Forces about Lines	p. 78
4.4 Systems of Forces	p. 79
4.5 Special Force Systems	p. 81
4.5.1 Zero Force Systems	p. 81
4.5.2 Couples	p. 81
4.5.3 Equivalent Force Systems	p. 82
4.5.4 Superimposed and Negative Force Systems	p. 84
4.6 Principle of Action-Reaction	p. 84
Problems	p. 85
References	p. 91
Chapter 5 Methods of Analysis III: Mechanics of Materials	p. 93
5.1 Concepts of Stress	p. 93
5.2 Concepts of Strain	p. 97
5.3 Principal Values of Stress and Strain	p. 102
5.4 Two-Dimensional Example: Mohr's Circle	p. 103
5.5 Elementary Stress-Strain Relations	p. 107
5.6 General Stress-Strain (Constitutive) Relations	p. 110
5.7 Equations of Equilibrium and Compatibility	p. 112
5.8 Use of Curvilinear Coordinates	p. 114
5.8.1 Cylindrical Coordinates	p. 114
5.8.2 Spherical Coordinates	p. 116
5.9 Review of Elementary Beam Theory	p. 117
5.9.1 Sign Convention	p. 118
5.9.2 Equilibrium Consideration	p. 119
5.9.3 Strain-Curvature Relations	p. 119
5.9.4 Stress-Bending Moment Relations	p. 121
5.9.5 Summary of Governing Equations	p. 122
5.10 Thick Beams	p. 123
5.11 Curved Beams	p. 125
5.12 Singularity Functions	p. 126
5.13 Elementary Illustrative Examples	p. 128
5.13.1 Cantilever Beam with a Concentrated End Load	p. 128
5.13.2 Cantilever Beam with a Concentrated End Load on the Right End	p. 130
5.13.3 Simply Supported Beam with a Concentrated Interior Span Load	p. 134
5.13.4 Simply Supported Beam with Uniform Load	p. 136
5.14 Listing of Selected Beam Displacement and Bending Moment Results	p. 139
5.15 Magnitude of Transverse Shear Stress	p. 140
5.16 Torsion of Bars	p. 140
5.17 Torsion of Members with Noncircular and Thin-Walled Cross Sections	p. 142
5.18 Energy Methods	p. 144
Problems	p. 149
References	p. 159
Chapter 6 Methods of Analysis IV: Modeling of Biosystems	p. 161
6.1 Multibody (Lumped Mass) Systems	p. 161
6.2 Lower-Body Arrays	p. 161
6.3 Whole-Body, Head/Neck, and Hand Models	p. 166
6.4 Gross-Motion Modeling of Flexible Systems	p. 169
Problems	p. 170
References	p. 172
Chapter 7 Tissue Biomechanics	p. 173
7.1 Hard and Soft Tissue	p. 173
7.2 Bones	p. 173
7.3 Bone Cells and Microstxucture	p. 174
7.4 Physical Properties of Bone	p. 175
7.5 Bone Development (Wolff's Law)	p. 175
7.6 Bone Failure (Fracture and Osteoporosis)	p. 176
7.7 Muscle Tissue	p. 176
7.8 Cartilage	p. 177
7.9 Ligaments/Tendons	p. 178
7.10 Scalp, Skull, and Brain Tissue	p. 179
7.11 Skin Tissue	p. 180
Problems	p. 180
References	p. 182
Chapter 8 Kinematical Preliminaries: Fundamental Equations	p. 183
8.1 Points, Particles, and Bodies	p. 183
8.2 Particle, Position, and Reference Frames	p. 183
8.3 Particle Velocity	p. 184
8.4 Particle Acceleration	p. 185
8.5 Absolute and Relative Velocity and Acceleration	p. 186
8.6 Vector Differentiation, Angular Velocity	p. 188
8.7 Two Useful Kinematic Procedures	p. 192
8.7.1 Differentiation in Different Reference Frames	p. 192
8.7.2 Addition Theorem for Angular Velocity	p. 194
8.8 Configuration Graphs	p. 196
8.9 Use of Configuration Graphs to Determine Angular Velocity	p. 206
8.10 Application with Biosystems	p. 208
8.11 Angular Acceleration	p. 211
8.12 Transformation Matrix Derivatives	p. 213
8.13 Relative Velocity and Acceleration of Two Points Fixed on a Body	p. 214
8.14 Singularities Occurring with Angular Velocity Components and Orientation Angles	p. 215
8.15 Rotation Dyadics	p. 217
8.16 Euler Parameters	p. 221
8.17 Euler Parameters and Angular Velocity	p. 223
8.18 Inverse Relations between Angular Velocity and Euler Parameters	p. 226
8.19 Numerical Integration of Governing Dynamical Equations	p. 228
Problems	p. 228
References	p. 240
Chapter 9 Kinematic Preliminaries: Inertia Force Considerations	p. 241
9.1 Applied Forces and Inertia Forces	p. 241
9.2 Mass Center	p. 243
9.3 Equivalent Inertia Force Systems	p. 247
Problems	p. 249
Chapter 10 Human Body Inertia Properties	p. 255
10.1 Second Moment Vectors, Moments, and Products of Inertia	p. 255
10.2 Inertia Dyadics	p. 258
10.3 Sets of Particles	p. 260
10.4 Body Segments	p. 261
10.5 Parallel Axis Theorem	p. 263
10.6 Eigenvalues of Inertia: Principal Directions	p. 265
10.7 Eigenvalues of Inertia: Symmetrical Bodies	p. 268
10.8 Application with Human Body Models	p. 270
Problems	p. 283
References	p. 285
Chapter 11 Kinematics of Human Body Models	p. 287
11.1 Notation, Degrees of Freedom, and Coordinates	p. 287
11.2 Angular Velocities	p. 290
11.3 Generalized Coordinates	p. 294
11.4 Partial Angular Velocities	p. 295
11.5 Transformation Matrices: Recursive Formulation	p. 297
11.6 Generalized Speeds	p. 300
11.7 Angular Velocities and Generalized Speeds	p. 302
11.8 Angular Acceleration	p. 304
11.9 Mass Center Positions	p. 307
11.10 Mass Center Velocities	p. 312
11.11 Mass Center Accelerations	p. 314
11.12 Summary: Human Body Model Kinematics	p. 315
Problems	p. 316
References	p. 318
Chapter 12 Kinetics of Human Body Models	p. 319
12.1 Applied (Active) and Inertia (Passive) Forces	p. 319
12.2 Generalized Forces	p. 320
12.3 Generalized Applied (Active) Forces on a Human Body Model	p. 323
12.4 Forces Exerted across Articulating Joints	p. 323
12.4.1 Contact Forces across Joints	p. 323
12.4.2 Ligament and Tendon Forces	p. 325
12.4.3 Joint Articulation Moments	p. 326
12.5 Contribution of Gravity (Weight) Forces to the Generalized Active Forces	p. 328
12.6 Generalized Inertia Forces	p. 329
Problems	p. 331
References	p. 331
Chapter 13 Dynamics of Human Body Models	p. 333
13.1 Kane's Equations	p. 333
13.2 Generalized Forces for a Human Body Model	p. 333
13.3 Dynamical Equations	p. 334
13.4 Formulation for Numerical Solutions	p. 335
13.5 Constraint Equations	p. 338
13.6 Constraint Forces	p. 339
13.7 Constrained System Dynamics	p. 342
13.8 Determination of Orthogonal Complement Arrays	p. 344
13.9 Summary	p. 344
Problems	p. 346
References	p. 348
Chapter 14 Numerical Methods	p. 349
14.1 Governing Equations	p. 349
14.2 Numerical Development of the Governing Equations	p. 350
14.3 Outline of Numerical Procedures	p. 351
14.4 Algorithm Accuracy and Efficiency	p. 352
Problems	p. 354
Reference	p. 354
Chapter 15 Simulations and Applications	p. 355
15.1 Review of Human Modeling for Dynamic Simulation	p. 355
15.2 Human Body in Free Space: A "Spacewalk"	p. 356
15.2.1 X-Axis (Yaw) Rotation	p. 357
15.2.2 Y-Axis (Pitch) Rotation	p. 358
15.2.3 Z-Axis (Roll) Rotation	p. 358
15.3 Simple Weight Lift	p. 358
15.4 Walking	p. 361
15.4.1 Terminology	p. 362
15.4.2 Modeling/Simulation	p. 362
15.4.3 Results	p. 362
15.5 Swimming	p. 362
15.5.1 Modeling the Water Forces	p. 363
15.5.2 Limb Motion Specification	p. 364
15.5.3 Kick Strokes	p. 364
15.5.4 Breaststroke	p. 365
15.5.5 Comments	p. 366
15.6 Crash-Victim Simulation I: Modeling	p. 366
15.7 Crash-Victim Simulation II: Vehicle Environment Modeling	p. 367
15.8 Crash-Victim Simulation III: Numerical Analysis	p. 368
15.9 Burden Bearing: Waiter/Tray Simulations	p. 369
15.9.1 Heavy Hanging Cable	p. 369
15.9.2 Uniform Muscle Stress Criterion	p. 371
15.9.3 Waitron/Tray Analysis	p. 372
15.10 Other Applications	p. 375
15.10.1 Load Sharing between Muscle Groups	p. 375
15.10.2 Transition Movements	p. 375
15.10.3 Gyroscopic Effects in Walking	p. 376
15.10.4 Neck Injuries in Rollover Motor Vehicle Accidents	p. 376
Problems	p. 376
References	p. 378
Appendix: Anthropometric Data Tables	p. 381
Glossary	p. 439
Bibliography	p. 447
Index	p. 449

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