RESEARCH PAPERS: Robotics Papers

Workspace Analysis of Mechanical Manipulators Using Polynomial Discriminants

[+] Author and Article Information
D. Kohli, J. Spanos

Dept. of Mechanical Engineering, University of Wisconsin, Milwaukee, WI 53201

J. Mech., Trans., and Automation 107(2), 209-215 (Jun 01, 1985) (7 pages) doi:10.1115/1.3258710 History: Received July 10, 1984; Online November 19, 2009


A new method, for the investigation of manipulator workspace, based on polynomial displacement equations and their discriminants is proposed in this paper. The approach followed enables one to obtain (a ) analytical expressions describing the workspace boundary surfaces in Cartesian coordinates, (b ) the distribution of the number of ways to position the hand inside the workspace, and (c ) the conditions on kinematic parameters when the motion of the hand degenerates. Joint limitations are incorporated in the method. In the present paper and a companion paper [17], the method is rigorously applied to eight types of manipulators with various combinations of revolute and prismatic pairs having the last three revolute axes intersect orthogonally at at point. A numerical example is presented for illustration.

Copyright © 1985 by ASME
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