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Reviewer: Taghi J. Mirsepassi

Haug has written an excellent book on the matrix method of formulating the kinematics and dynamics of mechanical systems composed of parts such as the slider crank, four-bar, quick-return, gear-slider, and valve-lifter mechanisms. This approach has the following advantages over the old analytical methods: (1)once the method is mastered, the formulating process can effectively be mechanized and thereby directly applied to complex systems; (2)by using the available matrix numerical computation programs, kinematic and dynamic responses of a mechanical system can readily be obtained in the form of tables, graphs, or even animation; (3)since numerical methods for solving nonlinear matrix equations are well developed and available, system nonlinearities do not present any problem; and (4)the designer can identify system inconsistencies ahead of time by evaluating the determinant of the system constraint Jacobian matrix. This essentially mathematical book is useful for practicing engineers engaged in the design and analysis of complex mechanisms. The basis of the method plus a few examples, condensed into three lectures, could also be included in a graduate course on the kinematics and dynamics of mechanical systems. This material would provide the students with enough familiarity with the technique for future applications in case they become mechanical system designers. The prerequisites for comprehending the system modeling and subsequent mathematical discussions and derivations in this book are substantial experience with real mechanical systems and a working knowledge of matrix operations including matrix and vector differentiation. The book is well organized and, despite the complexity of the mathematical discussions, easy for those who possess the prerequisites to understand. Many solved examples throughout the book serve to clarify the application details of various processes. Readers would have greatly appreciated it if the author had included simple computer programs for numerical evaluation of the examples in the book. Chapter 1, “Elements of Computer Aided Kinematics and Dynamics,” provides examples of complex systems, discusses methods of solution, and presents the objectives of the book. Chapter 2, “Planar Vectors, Matrices, and Differential Calculus,” is a review of vectors, matrices, transformations, and matrix differentiation as used in the formulation of planar systems. Finally, the author provides methods of obtaining the velocity and acceleration of a point fixed in a moving frame. Chapter 3, “Planar Cartesian Kinematics,” introduces Cartesian general coordinates and derives matrix formulations of various kinematic elements of mechanical systems. These elements include absolute constraints, relative constraints, joints, gears, cams, and driving constraints. The chapter ends with velocity and acceleration analyses. Chapter 4, “Numerical Methods in Kinematics,” covers numerical solutions. The topics presented include the evaluation of constraint equations and Jacobians, Gaussian methods, matrix factorization, and the Newton-Raphson method. The author also discusses the detection and elimination of redundant constraints. Chapter 5, “Planar Kinematic Modeling and Analysis,” presents the steps in developing a model and carrying out the subsequent analyses for the slider crank mechanism, four-bar mechanism, quick-return mechanism, gear-slider mechanism, and valve-lifter mechanism. Chapter 6, “Dynamics of Planar Systems,” covers variational equations of dynamic motion, the Lagrange multiplier theorem, mixed differential-algebraic equations of motion, inverse dynamics of kinematically driven systems, equilibrium conditions, and constraint reaction forces. Chapter 7, “Numerical Methods in Dynamics,” presents an overview of the computational requirements for the equilibrium, inverse dynamic, and dynamic modes of a multibody system. Among the methods discussed are numerical integration of first-order initial value problems, polynomial interpolation, the Adams-Bashforth predictor, and the Adams-Moulton corrector. Chapter 8, “Planar Dynamic Modeling and Analysis,” applies the methods described in chapters 6 and 7 to the slider-crank mechanism, quick-return mechanism, coil spring, and valve-lifter mechanism. Chapter 9, “Spatial Cartesian Kinematics,” extends the analysis of chapter 3 to three-dimensional space. After a review of operations on vectors in space and vector differentiation, the author derives the equations governing the spatial kinematics of rigid bodies. The applications are then clarified by means of several examples. Chapters 10, 11, and 12 are extensions of chapters 5, 6, and 8, respectively, into spatial systems. A list of 48 references and a table of symbols complete the book.