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RESEARCH PAPERS

Numerical Algorithms for Mapping Boundaries of Manipulator Workspaces

[+] Author and Article Information
E. J. Haug, Chi-Mei Luh, F. A. Adkins, Jia-Yi Wang

Center for Computer Aided Design and Department of Mechanical Engineering, The University of Iowa, Iowa City, IA

J. Mech. Des 118(2), 228-234 (Jun 01, 1996) (7 pages) doi:10.1115/1.2826874 History: Received October 01, 1994; Revised September 01, 1995; Online December 11, 2007

Abstract

Numerical algorithms for mapping boundaries of manipulator workspaces are developed and illustrated. Analytical criteria for boundaries of workspaces for both manipulators having the same number of input and output coordinates and redundantly controlled manipulators with a larger number of inputs than outputs are well known, but reliable numerical methods for mapping them have not been presented. In this paper, a numerical method is first developed for finding an initial point on the boundary. From this point, a continuation method that accounts for simple and multiple bifurcation of one-dimensional solution curves is developed. Second order Taylor expansions are derived for finding tangents to solution curves at simple bifurcation points of continuation equations and for characterizing barriers to control of manipulators. A recently developed method for tangent calculation at multiple bifurcation points is employed. A planar redundantly controlled serial manipulator is analyzed, determining both the exterior boundary of the accessible output set and interior curves that represent local impediments to motion control. Using these methods, more complex planar and spatial Stewart platform manipulators are analyzed in a companion paper.

Copyright © 1996 by The American Society of Mechanical Engineers
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