RESEARCH PAPERS: Mechanisms Papers

The Elliptic Polarity of Screws

[+] Author and Article Information
H. Lipkin, J. Duffy

Center for Intelligent Machines and Robotics, University of Florida, Gainesville, FL 32611

J. Mech., Trans., and Automation 107(3), 377-386 (Sep 01, 1985) (10 pages) doi:10.1115/1.3260725 History: Received July 10, 1984; Online November 19, 2009


The nature and invariant properties of the elliptic polarity of screws in Euclidean space is established using a novel series of mappings, central to which is a quaternion representation. The role of the elliptic polarity in modeling constrained motion is detailed and illustrated by way of an example which has application in the control of robot manipulators. Ball’s planar representation of the two system of screws is generalized and is shown to be a representation on a complex plane where the elliptic polarity is a conformal mapping.

Copyright © 1985 by ASME
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