Planar Multibody Dynamics ─ Formulation, Programming and Applications

Written by Parviz Nikravesh, one of the world’s best known experts in multibody dynamics, Planar Multibody Dynamics: Formulation, Programming, and Applications enhances the quality and ease of design education with extensive use of the latest computerized design tools combined with coverage of classical design and dynamics of machinery principles. Using language that is clear, concise, and to the point, the textbook introduces fundamental theories, computational methods, and program development for analyzing simple to complex planar mechanical systems. The author chose MATLAB® as the programming language, and since students may not be skilled programmers, the examples and exercises provide a tutorial for learning MATLAB. The examples begin with basic commands before introducing students to more advanced programming techniques. The routines developed in each chapter eventually come together to form complete programs for different types of analysis. Pedagogical highlights Contains homework problems at the end of each chapter, some requiring standard pencil-and-paper solution in order to understand the concept and others requiring either programming or the use of existing programs. Electronic highlights All the programs that are listed in the book, and some additional programs, will be available for download and will be updated periodically by the author. Additional materials for instructors, such as a solutions manual and other teaching aids, will also be available on the website. The author organizes the analytical and computational subjects around practical application examples. He uses several examples repeatedly, in various chapters, providing students with a basis for comparison between different formulations. The final chapter describes more extensive modeling and simulation projects. Designed specifically for undergraduates, the book is suitable as a primary text for a course on mechanisms or a supplementary text for a course on dynamics.

Introduction Multibody Mechanical Systems Types of Analyses Methods of Formulation Computer Programming Application Examples Unit System Remarks Preliminaries Reference Axes Scalars and Vectors Matrices Vector, Array, and Matrix Differentiation Equations and Expressions Remarks Problems Fundamentals of Kinematics A Particle Kinematics of a Rigid Body Definitions Remarks Problems Fundamentals of Dynamics Newton’s Laws of Motion Dynamics of a Body Force Elements Applied Forces Reaction Force Remarks Problems Point-Coordinates: Kinematics Multipoint Representation Stationary and Primary Points Constraints Velocity and Acceleration Constraints Secondary Points Example Programs Remarks Problems Point-Coordinates: Dynamics System of Unconstrained Particles System of Constrained Particles Force and Mass Distribution Exact Mass Distribution Remarks Problems Body-Coordinates: Kinematics General Procedure Kinematic Joints Examples Velocity and Acceleration Constraints Programming Note Example Programs Other Types of Joints Remarks Problems Body-Coordinates: Dynamics System of Unconstrained Bodies System of Constrained Bodies Example Programs Remarks Problems Joint-Coordinates: Kinematics Vector-Loop Method Joint Coordinate Method Open-Chain Systems Open-Chain Example Programs Closed-Chain Systems Closed-Chain Example Programs Remarks Problems Joint-Coordinates: Dynamics Open-Chain Systems Open-Chain Example Program Closed-Chain Systems Closed-Chain Example Programs Remarks Problems Kinematic Analysis Unconstrained Formulation Constrained Formulation Solution Procedures Linear Algebraic Equations Nonlinear Algebraic Equations Body Coordinate Formulation Point Coordinate Formulation Joint Coordinate Formulation Remarks Problems Inverse Dynamic Analysis Unconstrained Formulation Constrained Formulation Different Jacobian Matrices Body Coordinate Formulation Point Coordinate Formulation Joint Coordinate Formulation Remarks Problems Forward Dynamic Analysis Unconstrained Formulation Constrained Formulation Body Coordinate Formulation Joint Coordinate Formulation Point Coordinate Formulation Constraint Violation Remarks Problems Complementary Analyses Static Analysis Static Equilibrium Initial Condition Correction Three Combined Analyses by Integration Redundant Constraints Friction Deformable Body Remarks Problems Projects Windshield Wiper Mechanism Internal Combustion Engine Sled Test and Belted Dummy Head and Neck Mountain Bike Motorcycle Elliptical Exercise Machine Swing Appendix References