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RESEARCH PAPERS: Mechanisms Papers

Mappings of Spatial Kinematics

[+] Author and Article Information
B. Ravani

Department of Mechanical Engineering, University of Wisconsin, Madison, WI 53706

B. Roth

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305

J. Mech., Trans., and Automation 106(3), 341-347 (Sep 01, 1984) (7 pages) doi:10.1115/1.3267417 History: Received April 27, 1984; Online November 19, 2009

Abstract

This paper studies mappings of spatial kinematics and the geometry for which a spatial displacement is an element. Study’s soma is reviewed and it is shown that Euclidean geometry in three-space with spatial displacements as elements corresponds to elliptic geometry of points in a projective dual three-space. Study’s eight parameters are used to define the mapping of spatial kinematics into points of this projective dual three-space. The basic geometric properties of this dual three-space representation of Study’s soma is developed and it is applied to the study of spatial motions and mechanisms.

Copyright © 1984 by ASME
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