Geometric Optimization of the MSSM Gough–Stewart Platform

Abstract

This work focuses on analyzing the effects of the geometric parameters on the singularity-free workspace in order to determine the optimal architecture for the minimal simplified symmetric manipulator Gough–Stewart platform. To this end, the reference orientation is taken as the considered orientation because it is an impartial orientation. In this orientation, the singularity surface becomes a plane coinciding with the base plane. Accordingly, an analytic algorithm is developed to determine the singularity-free workspace. The analysis shows that: (1) for similar isosceles triangle base and platform, the optimal architecture is one for which both the base and the platform are equilateral triangles, and the size ratio between the platform and the base is 12; and (2) if the base and the platform are not similar triangles, the global optimal architecture is difficult to determine. Only an approximate optimal architecture is available.