Geometric design of linkages
type: Item
instance of: scholarly article
title: Geometric design of linkages
zbMATH Open document ID: 0955.70001
author: J. Michael McCarthy
published in: Interdisciplinary Applied Mathematics
publication date: 2000-08-07T00:00:00Z
review text: 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…
Mathematics Subject Classification ID: 70-02
Mathematics Subject Classification ID: 53-02
Mathematics Subject Classification ID: 52C25
Mathematics Subject Classification ID: 53A17
Mathematics Subject Classification ID: 70B15
Mathematics Subject Classification ID: 70E55
zbMATH DE Number: 1485377
zbMATH Keywords: spherical linkage design
zbMATH Keywords: spatial linkage design
zbMATH Keywords: graphical methods
zbMATH Keywords: planar linkage synthesis
zbMATH Keywords: articulated systems
zbMATH Keywords: planar chains
zbMATH Keywords: geometric principles
zbMATH Keywords: theory of planar displacements
zbMATH Keywords: algebraic design theory
zbMATH Keywords: screw triangle
zbMATH Keywords: center axis theorem
zbMATH Keywords: dual vector algebra
zbMATH Keywords: Plücker line coordinates
reviewed by: Bozhidar Cheshankov
MaRDI profile type: Publication
full work available at URL: b98861
OpenAlex ID: W2136938510
DOI: 10.1007/B98861
Recommended article: Geometric design of linkages.
Recommended article: Geometric design of interference-free planar linkages
Recommended article: Geometry and dynamics of planar linkages
Recommended article: Geometric structures as design approach
Recommended article: Complex geometry of polygonal linkages
Recommended article: Polyhedral Linkages
Recommended article: ON THE NUMBER OF TRIANGULATION SIMPLEXES
Recommended article: Q3004057
Recommended article: Configuration spaces of mechanical linkages
description: scientific article; zbMATH DE number 1485377