Mechanical Simulation with MATLAB® (Springer Tracts in Mechanical Engineering)

This book deals with the simulation of the mechanical behavior of engineering structures, mechanisms and components. It presents a set of strategies and tools for formulating the mathematical equations and the methods of solving them using MATLAB. For the same mechanical systems, it also shows how to obtain solutions using a different approaches. It then compares the results obtained with the two methods. By combining fundamentals of kinematics and dynamics of mechanisms with applications and different solutions in MATLAB of problems related to gears, cams, and multilink mechanisms, and by presenting the concepts in an accessible manner, this book is intended to assist advanced undergraduate and mechanical engineering graduate students in solving various kinds of dynamical problems by using methods in MATLAB. It also offers a comprehensive, practice-oriented guide to mechanical engineers dealing with kinematics and dynamics of several mechanical systems. Preface Contents 1 Introduction 1.1 Kinematic Pairs 1.2 Degrees of Freedom 1.3 Kinematic Chains 1.4 Type of Dyads 1.5 Position Analysis for Links 1.6 Velocity and Acceleration Analysis for Rigid Body 1.7 Planar Dynamics Analysis 1.8 Problems References 2 Classical Analysis of a Mechanism with One Dyad 2.1 Position Analysis 2.2 Velocity and Acceleration Analysis 2.3 Dynamic Force Analysis 2.4 Problems References 3 Contour Analysis of a Mechanism with One Dyad 3.1 Closed Contour Equations 3.2 Closed Contour Equations for R-RTR Mechanism 3.3 Force Analysis for R-RTR Mechanism 3.4 Problems References 4 Classical Analysis of a Mechanism with Two Dyads 4.1 Position Analysis 4.2 Velocity and Acceleration Analysis 4.3 Dynamic Force Analysis 4.4 Problems References 5 Contour Analysis of a Mechanism with Two Dyads 5.1 Velocity and Acceleration Analysis 5.2 Contour Dynamic Force Analysis with D'Alembert Principle 5.2.1 Reaction Force F24 5.2.2 Reaction Force F23 5.2.3 Reaction Force F12 5.2.4 Reaction Force F03 5.2.5 Reaction Force F05 5.2.6 Reaction Force F54 and Reaction Moment M54 5.2.7 Reaction Force F01 and Moment Mm 5.3 Problems References 6 Dyad Routines for Mechanisms 6.1 Driver Link 6.2 Position Analysis 6.3 Velocity Analysis 6.4 Force Analysis 6.4.1 R-RRR Mechanism 6.4.2 R-RTR Mechanism 6.4.3 R-RRT-RTR Mechanism 6.4.4 Problems References 7 Epicyclic Gear Trains 7.1 Introduction 7.2 Epicyclic Gear Train with One Planet 7.2.1 Classical Method 7.2.2 Contour Method 7.3 Mechanism with Epicyclic Gears 7.3.1 Classical Method—Velocity Analysis 7.3.2 Contour Method—Velocity Analysis 7.4 Epicyclic Gear Train with Multiple Planets 7.4.1 Classical Method—Velocity Analysis 7.4.2 Contour Method—Velocity Analysis 7.5 Problems References 8 Cam and Follower Mechanism 8.1 Kinematics Analysis 8.2 Force Analysis 8.3 Equivalent Linkages 8.4 Differential Method 8.5 Problems References 9 Direct Dynamics 9.1 Equations of Motion—Sphere on a Spring 9.2 Dynamics of a Rotating Link with an Elastic Force 9.3 Impact of a Free Link with MATLAB 9.4 Problems References Index