Book Review

Matrix Methods in the Design Analysis of Mechanisms and Multibody Systems OPEN ACCESS

J. Comput. Nonlinear Dynam 10(6), 066501 (Sep 10, 2015) (1 page) Paper No: CND-15-1244; doi: 10.1115/1.4031421 History: Received August 16, 2015; Revised August 16, 2015

This book is focused on presenting detailed formulations for the kinematic and dynamic modeling of mechanism and multibody systems (MBS). It is written by three well-known and recognized authors who made significant contributions to the development of mechanism and MBS approaches. The authors are also credited for the development of one of the earliest mechanism and MBS computer programs IMP (integrated mechanisms programs). The book is unique, particularly in the MBS literature because it provides an integrated approach for modeling mechanisms and MBS, it emphasizes the importance of accurate kinematic description in the MBS analysis, and it provides historic notes on some of the approaches that impacted the way MBS applications are currently modeled.

The book consists of 17 chapters which cover many of the important aspects of mechanism and MBS formulations and approaches. The book starts with the Song of the Screw which was published anonymously in Nature in 1877. The preface of the book also includes interesting quotations from the writings of Franz Reuleaux (1829–1905). The first chapter of the book is an introduction which is focused on concepts and definitions that are fundamental to mechanisms and MBS analysis including the definition of mechanical bodies and lower and higher pairs. The topology and kinematic architecture including incidence matrices and kinematic loops are covered in Chap. 2. Chapter 3 is focused on the transformation matrices and their important role in accurate kinematic definitions. Different forms of the transformation matrices are presented in this chapter. The use of the transformation matrices in the description of the kinematics of systems that include mechanical joints is explained in Chap. 4. Chapter 5 describes how successive transformations can be handled and introduces the well-known Denavit–Hartenberg Transformation and its use in the definition of the absolute position equations. The loop closure equations which are required in the kinematic description of closed-loop chains are presented in this chapter which also presents closed-form solution of kinematic equations of joint-variable position. Chapter 6 presents the differential kinematics and demonstrates its use in different joint formulations. Differential kinematics is particularly important when considering the numerical solution and the development of general mechanism and MBS algorithms. Chapters 7 and 8 describe, respectively, the velocity and acceleration equations and explain how these equations can be written in terms of the joint coordinates. Chapter 9 presents some of the important force elements used in modeling mechanism and MBS applications. It is appropriate to present the joint kinematics and the formulation of the forces before presenting the dynamic equations of motion in Chap. 10. The formulation of these dynamic equations requires the use of the joint kinematics and the force expressions. Chapter 11 describes how the linearized equations of motion can be obtained, while Chap. 12 discusses the equilibrium posture analysis with explanation of stable and unstable equilibrium. The system frequency and time responses are discussed in Chaps. 13 and 14, respectively. Procedures for collision detection and impact analysis are presented in Chaps. 15 and 16, respectively, while the analysis of constraint forces is presented in Chap. 17.

Each chapter of the book is followed by a list of references and a problem set which make the book suitable for use as a textbook at the senior undergraduate and first-year graduate level. The book is well written and it is a good addition to the MBS literature in particular because it emphasizes the importance of the use of accurate kinematics in the formulation of the MBS dynamic equations. The book also describes, in Chap. 6, the roots of the use of numerical techniques as the basis for identifying the independent variables in the generalized coordinate partitioning which was later generalized by Roger Wehage in his Ph.D. thesis. I find the discussion on the use of the numerical approach to iteratively solve the loop closure equations expressed in terms of the joint variables interesting. Wehage generalized this approach to the general case of absolute Cartesian coordinates and employed sparse matrix techniques to solve the kinematic equations for both open- and closed-loop systems. I highly recommend this book for readers who are interested in the MBS mechanics. The authors are to be congratulated for writing such a book which covers many topics that are not covered by other existing books on the MBS dynamics.

Copyright © 2015 by ASME
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