Kinematic Inversion of Parallel Manipulators in the Presence of Incompletely Specified Tasks

[+] Author and Article Information
C. Gosselin

Départment de Génie Mécanique, Université Laval, Ste-Foy, Québec, Canada

J. Angeles

Robotic Mechanical Systems Laboratory, McGill Research Centre for Intelligent Machines, McGill University, Montréal, Québec, Canada

J. Mech. Des 112(4), 494-500 (Dec 01, 1990) (7 pages) doi:10.1115/1.2912637 History: Received January 01, 1988; Revised November 01, 1989; Online June 02, 2008


In this paper, the kinematic inversion of redundant parallel manipulators in the presence of incompletely specified tasks is formulated as an optimization problem. The performance index used is the condition number of the Jacobian matrix of the manipulator which is a measure of Jacobian invertibility. In order to optimize this index along a partially prescribed Cartesian trajectory, the concept of trajectory map is introduced. It is also shown that the optimum value of the free parameter that minimizes the condition number is not a continuous function of the prescribed Cartesian coordinates. An on-line algorithm producing continuous joint histories is then discussed. This method has been implemented and tested, as illustrated with the results presented here.

Copyright © 1990 by The American Society of Mechanical Engineers
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