Su, Hai-JunMcCarthy, J. MichaelWatson, Layne T.2013-06-192013-06-192003http://hdl.handle.net/10919/20102In 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.application/pdfenIn CopyrightParallel computationTechnical reportTR-03-24http://eprints.cs.vt.edu/archive/00000669/01/Homotopy7.pdf