Journal
JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING
Volume 4, Issue 3, Pages 226-234Publisher
ASME
DOI: 10.1115/1.1760550
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In this paper we apply a homotopy algorithm to the problem of finding points in a moving body that lie on specific algebraic surfaces for a given set of spatial configurations of the body. This problem is a generalization of Burmester' s determination of points in a body that lie on a circle for five planar positions. We focus on seven surfaces that we term reachable because they correspond to serial chains with two degree-of-freedom positioning structures combined with a three degree-of-freedom spherical wrist. A homotopy algorithm based on generalized linear products is used to provide a convenient estimate of the number of solutions of these polynomial systems. A parallelized version of this algorithm was then used to numerically determine all of the solutions.
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