Principles of Biomechanics

Introduction Principal Areas of Biomechanics Approach in This Book Review of Human Anatomy and Some Basic Terminology Gross (Whole-Body) Modeling Position and Direction Terminology Terminology for Common Movements Skeletal Anatomy Major Joints Major Muscle Groups Anthropometric Data Methods of Analysis I: Review of Vectors, Dyadics, Matrices, and Determinants Vectors Vector Algebra-Addition and Multiplication by Scalars Vector Algebra-Multiplication of Vectors Dyadics Multiple Products of Vectors Matrices/Arrays Determinants Relationship of 3 X 3 Determinants, Permutation Symbols and Kronecker Delta Functions Eigenvalues, Eigenvectors, and Principal Directions Maximum and Minimum Eigenvalues and the Associated Eigenvectors Methods of Analysis II: Forces and Force Systems Forces: Vector Representations Moments of Forces Moments of Forces About Lines Systems of Forces Special Force Systems Principle of Action-Reaction Methods of Analysis III: Mechanics of Materials Concepts of Stress Concepts of Strain Principal Values of Stress and Strain A Two-Dimensional Example-Mohr's Circle Elementary Stress-Strain Relations General Stress-Strain (Constitutive) Relations Equations of Equilibrium and Compatibility Use of Curvilinear Coordinates Review of Elementary Beam Theory Thick Beams Curved Beams Singularity Functions Elementary Illustrative Examples Listing of Selected Beam Displacement and Bending Moment Results Magnitude of Transverse Shear Stress Torsion of Bars Torsion of Members with Noncircular and Thin-Walled Cross Sections Energy Methods Methods of Analysis IV: Modeling of Biosystems Multibody (Lumped Mass) Systems Lower Body Arrays Whole Body, Head/Neck, and Hand Models Gross-Motion Modeling of Flexible Systems Tissue Biomechanics Hard and Soft Tissue Bones Bone Cells and Microstructure Physical Properties of Bone Bone Development (Wolff's law) Bone Failure (Fracture and Osteoporosis) Muscle Tissue Cartilage Ligaments/Tendons Scalp, Skull, and Brain Tissue Skin Tissue Kinematical Preliminaries: Fundamental Equations Points, Particles, and Bodies Particle, Position, and Reference Frames Particle Velocity Particle Acceleration Absolute and Relative Velocity and Acceleration Vector Differentiation, Angular Velocity Two Useful Kinematic Procedures Configuration Graphs Use of Configuration Graphs to Determine Angular Velocity Application with Biosystems Angular Acceleration Transformation Matrix Derivatives Relative Velocity and Acceleration of Two Points Fixed on a Body Singularities Occurring with Angular Velocity Components and Orientation Angles Rotation Dyadics Euler Parameters Euler Parameters and Angular Velocity Inverse Relations between Angular Velocity and Euler Parameters Numerical Integration of Governing Dynamical Equations Kinematic Preliminaries: Inertia Force Considerations Applied Forces and Inertia Forces Mass Center Equivalent Inertia Force Systems Human Body Inertia Properties Second Moment Vectors, Moments and Products of Inertia Inertia Dyadics Sets of Particles Body Segments Parallel Axis Theorem Eigenvalues of Inertia, Principal Directions Eigenvalues of Inertia: Symmetrical Bodies Application with Human Body Models Kinematics of Human Body Models Notation, Degrees of Freedom, and Coordinates Angular Velocities Generalized Coordinates Partial Angular Velocities Transformation Matrices-Recursive Formulation Generalized Speeds Angular Velocities and Generalized Speeds Angular Acceleration Mass Center Positions Mass Center Velocities Mass Center Accelerations Summary-Human Body Model Kinematics Kinetics of Human Body Models Applied (Active) and Inertia (Passive) Forces Generalized Forces Generalized Applied (Active) Forces on a Human Body Model Forces Exerted Across Articulating Joints Contribution of Gravity (Weight) Forces to the Generalized Active Forces Generalized Inertia Forces Dynamics of Human Body Models Kane's Equations Generalized Forces for a Human Body Model Dynamical Equations Formulation for Numerical Solutions Constraint Equations Constraint Forces Constrained System Dynamics Determination of Orthogonal Complement Arrays Summary Numerical Methods Governing Equations Numerical Development of the Governing Equations Outline of Numerical Procedures Algorithm Accuracy and Efficiency Simulations and Applications Review of Human Modeling for Dynamic Simulation A Human Body in Free-Space: A "Spacewalk" A Simple Weight Lift Walking Swimming Crash Victim Simulation I: Modeling Crash Victim Simulation II: Vehicle Environment Modeling Crash Victim Simulation III: Numerical Analysis Burden Bearing-Waiter/Tray Simulations Other Applications Appendix A Anthropometric Data Tables Glossary Bibliography Index