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RESEARCH PAPERS

A Derivation of a Minimal Set of Multilinear Loop Equations for Spatial Mechanisms

[+] Author and Article Information
P. D. Potts

Mathematics Department, Liverpool Polytechnic, Liverpool, England

J. Eng. Ind 98(4), 1301-1305 (Nov 01, 1976) (5 pages) doi:10.1115/1.3439104 History: Received June 21, 1976; Online July 15, 2010

Abstract

The relationship between skew-symmetric and rotation matrices due to Cayley is associated with the quaternion representation of finite rotations. Novel rotation parameters yield three real (dual) equations of simple form for spherical (spatial) polygons which are multilinear in half-tangents. This new form of the equations implies that all mechanisms (with the exception of geared linkages) are multilinear systems. Solution strategies for these equations are discussed for simple spatial structures.

Copyright © 1976 by ASME
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