# Generalized Linear Product Homotopy Algorithms and the Computation of Reachable Surfaces

2003) Generalized Linear Product Homotopy Algorithms and the Computation of Reachable Surfaces. Technical Report TR-03-24, Computer Science, Virginia Tech. (

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## Abstract

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.

Item Type: | Departmental Technical Report |
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Subjects: | Computer Science > Parallel Computation |

ID Code: | 669 |

Deposited By: | Administrator, Eprints |

Deposited On: | 26 August 2005 |