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RESEARCH PAPERS

Solving the Forward Kinematics of a Planar Three-Legged Platform With Holonomic Higher Pairs

[+] Author and Article Information
M. J. D. Hayes

McGill University, Dept. of Mech. Eng. & Centre for Intelligent Machines, 817 r. Sherbrooke O., Montréal, Québec, Canada

M. L. Husty

Universitätsdozent für Geometrie an der Montanuniversität Leoben, Franz-Josef-Straße 18, A-8700 Leoben, Österreich and McGill University, Centre for Intelligent Machines, 817 r. Sherbrooke O., Montréal, Québec, Canada

P. J. Zsombor-Murray

McGill University, Dept. of Mech. Eng. & Centre for Intelligent Machines, 817 r. Sherbrooke O., Montréal, Québec, Canada and Institut für Geometrie, TU Graz, Kopernikusgasse 24, A-8010 Graz, Österreich

J. Mech. Des 121(2), 212-219 (Jun 01, 1999) (8 pages) doi:10.1115/1.2829446 History: Received April 01, 1997; Revised February 01, 1999; Online December 11, 2007

Abstract

A practical solution procedure for the forward kinematics problem of a fully-parallel planar three-legged platform with holonomic higher pairs is presented. Kinematic mapping is used to represent distinct planar displacements of the end-effector as discrete points in a three dimensional image space. Separate motions of each leg trace skew hyperboloids of one sheet in this space. Therefore, points of intersection of the three hyperboloids represent solutions to the forward kinematics problem. This reduces the problem to solving three simultaneous quadratics. Applications of the platform are discussed and an illustrative numerical example is given.

Copyright © 1999 by The American Society of Mechanical Engineers
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