Geometric design of linkages. (Q608140)

Analysis and synthesis of mechanisms and linkages are two sides of the same coin. Both need a profound understanding of theoretical kinematics. The book under review is the most extensive source of the synthesis side, containing all the theoretical basics needed for the design of planar, spherical and spatial linkages. The material is published now in a second, extended edition of a book with the same title, written by the first author in 2000 (for the review see Zbl 0955.70001). It starts with a short introduction to mobility questions of different types of planar, spherical and spatial linkages. Some examples demonstrate the basic tasks of linkage design: motion generation, function generation and point-path generation. Chapter two is devoted to the analysis of planar linkages, dealing with position and velocity analysis of the building blocks of planar mechanisms. Chapter three focuses on classical, graphical synthesis methods for the design of planar linkages for precision point synthesis. In the chapter on planar kinematics the Euclidean coordinate transformations are introduced, the positions of relative poles of displacements are computed and the classical theorem of Aronhold-Kennedy is proven. Then the two main chapters on planar synthesis follow. The first one is devoted to the algebraic formulation of multi-position theory. Chapter six is new in the second edition and shows recent results in the design of multi-loop planar linkages, such as six-bar and eight-bar linkages, including very nice real-life examples. Chapters seven to ten are devoted to spherical linkage analysis and synthesis, and have a similar structure to those dealing with the planar case. Chapter ten is especially worth mentioning: it shows recent results in the theory of multi-loop spherical linkages including the practical design of examples. The remainder of the book addresses the synthesis of spatial linkages. Due to the advances in symbolic and numeric computing during the recent years, this area of kinematics has undergone the most rapid development. Therefore one can find in this part the major difference to the first edition. New are the chapters on synthesis of spatial chains, the synthesis of spatial chains which reach predefined surfaces, and the chapter on synthesis of spatial linkages using the Clifford algebra associated to the spatial Euclidean transformations. The book closes with a chapter on platform manipulators, which have found particular attention in the community within the last years. In conclusion one can note that this book is a real guide from the very beginnings of synthesis of simple mechanisms to the latest, theoretically involved results in the synthesis of multi-loop planar, spherical and spatial linkages.