A GPU homotopy path tracker and end game for mechanism synthesis

Abstract

This paper presents an implementation of a path tracking algorithm and end game for the homotopy solution of mechanism synthesis equations using a graphical processing unit, or GPU. The goal is to have the GPU execute a large number of path tracking solutions in parallel in order to identify design candidates that satisfy a set of kinematic synthesis polynomial equations. Effective use of the GPU requires that the processors execute the same instruction set. This imposes constraints on the structure of the path tracker and the end game. In this paper, we present that our implementation of GPU-based polynomial homotopy solver and end game. We demonstrate the implementation by solving the five position planar four bar synthesis problem for a given set of task positions.