Obtaining the Maximal Singularity-Free Workspace of 6-UPS Parallel Mechanisms via Convex Optimization

Abstract

This paper explores the maximal volume inscribed ellipsoid in the singularity free constant-orientation workspace of two classes of 6-UPS parallel mechanisms, namely, quadratic and quasi-quadratic Gough-Stewart platforms. It is of paramount importance to obtain the optimum singularity-free ellipsoid by taking into account the stroke of actuators. Convex optimization is applied as the fundamental optimization tool of this paper. For this purpose, a matrix modeling for the kinematic properties of Gough-Stewart platform is proposed. The main contribution of this paper consists in improving an existing method in a such a way that it leads to a global optimum rather than a suboptimal solution. The proposed algorithm could be regarded as one of the most reliable, in terms of obtaining the global extremum, and propitious approaches, in terms of computational time in comparison with other approaches proposed in the literature for obtaining the singularity-free workspace which make it suitable for real-time applications.