Mechanical systems are becoming increasingly sophisticated and continually require greater precision, improved reliability, and extended life. To meet the demand for advanced mechanisms and systems, present and future engineers must understand not only the fundamental mechanical components, but also the principles of vibrations, stability, and balance and the use of Newton's laws, Lagrange's equations, and Kane's methods. Dynamics of Mechanical Systems provides a vehicle for mastering all of this. Focusing on the fundamental procedures behind dynamic analyses, the authors take a vector-oriented approach and lead readers methodically from simple concepts and systems through the analysis of complex robotic and bio-systems. A careful presentation that balances theory, methods, and applications gives readers a working knowledge of configuration graphs, Euler parameters, partial velocities and partial angular velocities, generalized speeds and forces, lower body arrays, and Kane's equations.
Evolving from more than three decades of teaching upper-level engineering courses, Dynamics of Mechanical Systems enables readers to obtain and refine skills ranging from the ability to perform insightful hand analyses to developing algorithms for numerical/computer analyses. Ultimately, it prepares them to solve real-world problems and make future advances in mechanisms, manipulators, and robotics.
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