INTRODUCTION

REVIEW OF VECTOR ALGEBRA

Equality of Vectors, Fixed and Free Vectors

Vector Addition

Vector Components

Angle Between Two Vectors

Vector Multiplication: Scalar Product

Vector Multiplication: Vector Product

Vector Multiplication: Triple Products

Use of the Index Summation Convention

Review of Matrix Procedures

Reference Frames and Unit Vector Sets

KINEMATICS OF A PARTICLE

Vector Differentiation

Position, Velocity, and Acceleration

Relative Velocity and Relative Acceleration

Differentiation of Rotating Unit Vectors

Geometric Interpretation of Acceleration

Motion on a Circle

Motion in a Plane

KINEMATICS OF A RIGID BODY

Orientation of Rigid Bodies

Configuration Graphs

Simple Angular Velocity and Simple Angular Acceleration

General Angular Velocity

Differentiation in Different Reference Frames

Addition Theorem for angular Velocity

Angular Acceleration

Relative Velocity and Relative Acceleration of Two Points on a Rigid Body

Points Moving on a Rigid Body

Rolling Bodies

The Rolling Disk and Rolling Wheel

A Conical Thrust Bearing

PLANAR MOTION OF RIGID BODIES - METHODS OF ANALYSIS

Coordinates, Constraints, Degrees of Freedom

Planar Motion of a Rigid Body

Instant Center, Points of Zero Velocity

Illustrative Example: A Four-Bar Linkage

Chains of Bodies

Instant Center, Analytical Considerations

Instant Center of Zero Acceleration

FORCES AND FORCE SYSTEMS

Forces and Moments

Systems of Forces

Zero Force Systems and Couples

Equivalent Force Systems

Wrenches

Physical Forces: Applied (Active) Forces

Mass Center

Physical Forces: Inertia (Passive) Forces

Each chapter also contains an Introduction

INERTIA, SECOND MOMENT VECTORS, MOMENTS AND PRODUCTS OF INERTIA, INERTIA DYADICS

Second Moment Vectors

Moments and Products of Inertia

Inertia Dyadics

Transformation Rules

Parallel Axis theorems

Principal Axes, Principal Moments of Inertia: Concepts, Example, and Discussion

Maximum and Minimum Moments and Products of Inertia

Inertia Ellipsoid

Application: Inertia Torques

PRINCIPLES OF DYNAMICS: NEWTON'S LAWS AND D'ALEMBERT'S PRINCIPLE

Principles of Dynamics

D'Alembert's Principle

The Simple Pendulum

A Smooth Particle Moving Inside a Vertical Rotating Tube

Inertia Forces on a Rigid Body

Projectile Motion

A Rotating Circular Disk

The Rod Pendulum

Double-Rod Pendulum

The Triple-Rod and N-Rod Pendulums

A Rotating Pinned Rod

The Rolling Circular Disk

PRINCIPLES OF IMPULSE AND MOMENTUM

Impulse

Linear Momentum

Angular Momentum

Principle of Linear Impulse and Momentum

Principle of Angular Impulse and Momentum

Conservation of Momentum Principles

Examples

Additional Examples: Conservation of Momentum

Impact: Coefficient of Restitution

Oblique Impact

Seizure of a Spinning, Diagonally Supported Square Plate

INTRODUCTION TO ENERGY METHODS

Work

Work Done by a Couple

Power

Kinetic Energy

Work-Energy Principles

]Elementary Examples: A Falling Object, The Simple Pendulum, A Mass-Spring System

Sk9idding Vehicle Speeds: Accident Reconstruction Analysis

A Wheel rolling over a Step

The Spinning Diagonally Supported Square Plate

GENERALIZED DYNAMICS: KINEMATICS AND KINETICS

Coordinates, Constraints, and Degrees of Freedom

Holonomic and Nonholonomic Constraints

Vector Function, Partial Velocity, and Partial Angular Velocity

Generalized Forces: Applied (Active) Forces

Generalized Forces: Gravity and Spring Forces

Example: Spring-Supported Particles in a Rotating Tube

Forces that do not Contribute to the Generalized Forces

Generalized Forces: Inertia (Passive) Forces

Examples

Potential Energy

Use of Kinetic Energy to obtain Generalized Inertia Forces

GENERALIZED DYNAMICS: KANE'S EQUATIONS AND LAGRANGE'S EQUATIONS

Kane's Equations

Lagrange's Equations

The Triple-Rod Pendulum

The N-Rod Pendulum

INTRODUCTION TO VIBRATIONS

Solutions of Second-Order Differential Equations

The Undamped Linear Oscillator

Forced Vibration of an Undamped Oscillator

Damped Linear Oscillator

Forced Vibration of a Damped Linear Oscillator

Systems with Several Degrees of Freedom

Analysis and Discussion of Three-Particle Movement: Modes of Vibration

Nonlinear Vibrations

The Method of Krylov and Bogoliuboff

STABILITY

Infinitesimal Stability

A Particle Moving in a Vertical Rotating Tube

A Freely Rotating Body

The Rolling/Pivoting Circular Disk

Pivoting Disk with a Concentrated Mass on the Rim

Rim Mass in the Uppermost Position

Rim Mass in the Lowermost Position

Discussion: Routh-Hurwitz Criteria

BALANCING

Static Balancing

Dynamic Balancing: A Rotating Shaft

Dynamic Balancing: the General Case

Application: Balancing of Reciprocating Machines

Lanchester Balancing Mechanism

Balancing of Multicylinder Engines

Four-Stroke Cycle Engines

Balancing of Four-Cylinder Engines

Eight-Cylinder Engines: The Straight-Eight and the V-8

MECHANICAL COMPONENTS: CAMS

A Survey of Cam Pair types

Nomenclature and Terminology or Typical Rotating Radial Cams with Translating Followers

Grpahical Constructions

Comments on Graphical Construction of Cam Profiles

Analytical Construction of Cam Profiles

Dwell and Linear Rose of the Follower

Use of Singularity Functions

Parabolic Rise Function

Sinusoidal Rise Function

Cycloidal Rise Function

Summary: Listing of Follower Rise Functions

MECHANICAL COMPONENTS: GEARS

Preliminary and Fundamental Concepts: rolling Wheels, Conjugate Action, Involute Curve Geometry

Spur Gear Nomenclature

Kinematics of Meshing Involute Spur Gear Teeth

Kinetics of Meshing Involute Spur Gear Teeth

Sliding and Rubbing between Contacting Involute Spur Gear Teeth

Involute Rack

Gear Drives and Gear Trains

Helical, Bevel, Spiral Bevel, and Worm Gears

INTRODUCTION TO MULTIBODY DYNAMICS

Connection Configuration: Lower Body Arrays

A Pair of Typical Adjoining Bodies: Transformation Matrices

Transformation Matrix Derivatives

Euler Parameters

Rotation Dyadics

Transformation Matrices, Angular Velocity Components, and Euler Parameters

Degrees of Freedom, Coordinates, and Generalized Speeds

Transformation between Absolute and Relative Coordinates

Angular Velocity

Angluar Acceleration

Joint and Mass Center Positions

Mass Center Velocities

Mass Center Accelerations

Kinetics: Applied Forces

Kinetics: Inertia Forces

Multibody Dynamics

INTRODUCTION TO ROBOT DYNAMICS

Geometry, Configuration, and Degrees of Freedom

Transformation Matrices and Configuration Graphs

Angular Velocity of Robot Links

Partial Angular Velocities

Transformation Matrix Derivatives

Angular Acceleration of the Robot Links

Joint and Mass Center Position

Mass Center Velocities, Partial Velocities, and Acceleration

End Effector Kinematics

Kinetics: Applied Forces

Kinetics: Passive Forces

Dynamics: Equations of Motion

Redundant Robots

Constraint Equations and Constraint Forces

Governing Equation Reduction and Solution: Use of Orthogonal Complement Arrays

APPLICATION WITH BIOSYSTEMS, HUMAN BODY DYNAMICS

Human Body Modeling

A Whole-Body Model: Preliminary Considerations

Kinematics: Coordinates

Kinematics: Velocities and Acceleration

Kinetics: Active Forces

Kinetics: Muscle and Joint Forces

Kinetics: Inertia Forces

Dynamics: Equations of Motion

Constrained Motion

Solutions of the Governing Equations

Discussion: Application and Future Development

APPENDICES

INDEX