Geometric design of linkages
The book presents a mathematical study of design for articulated mechanical systems known as linkages. The focus is on sizing mechanical constraints that guide the motion of a workpiece, or end-effector, of the system. The formulated design problem is purely geometric. The text blends two approaches to this design problem in order to develop the intuition needed to go on from planar to spatial linkage design. One approach considers the geometric configuration of points and lines generated as a moving body is displaced through a finite set of positions. This is the foundation for graphical methods for planar linkage synthesis which can be generalized to spherical and spatial linkage design. The second approach focuses directly on solving nonlinear constraint equations that characterize a mechanical connection. The first chapter gives an overview of articulated systems. The generic mobility of a linkage is defined in the case of planar, spherical and spatial chains. The second chapter presents analysis of planar chains, details of their motion, and classification. Chapter 3 develops the graphical design theory for planar linkages and introduces geometric principles that are used in the remainder of the book. Chapter 4 presents the theory of planar displacements, and chapter 5 derives the algebraic design theory. The properties of spherical linkages and details of the geometric theory of the spatial rotations are introduced in chapters 6 and 7. Chapter 8 describes the design theory of these linkages, which is analogous to planar theory, whereas chapter 9 introduces the analysis of spatial linkages including open chains that are closely related to robot manipulators. The complexity of spatial linkages requires the introduction of some new techniques. The geometry of spatial displacement is topic of chapter 10. Here the screw triangle and center axis theorem are formulated using rather lines than points, and dual vector algebra provides vector operations for calculations of Plücker line coordinates. Chapter 11 presents the design theory for spatial chains, and chapter 12 treats the geometry of linear combinations of lines that arise in the construction of spatial linkage system. At the end, some mathematical background is given in five appendices. The book will be useful to specialists in mathematics, engineering and computer science dealing with the mathematical modelling of robots and other articulated mechanical systems.
scientific article; zbMATH DE number 1485377