Determination of the maximal singularity-free zones in the six-dimensional workspace of the general Gough–Stewart platform

This paper addresses the singularity-free workspace analysis of the general Gough–Stewart platform. Unlike in serial mechanisms, where there exist only boundary singularities, the closed-loop nature of parallel mechanisms generates complex singularities inside the workspace, which makes the workspace analysis and the trajectory planning of parallel mechanisms a very difficult problem. Therefore, it is highly desirable to develop algorithms that can locate singularity-free zones inside the workspace. The analytical expression of the six-dimensional singularity locus of the general Gough–Stewart platform was previously obtained by the authors [H.D. Li, C.M. Gosselin, M.J. Richard, B. Mayer St-Onge, Analytic form of the six-dimensional singularity locus of the general Gough–Stewart platform, in: Proceedings of the 2004 ASME International Design Engineering Technical Conference, September 28–October 2, Salt Lake City, USA, 2004]. In this paper, first, the singularity equation is briefly recalled. Then, based on the known singularity locus equation, three procedures are presented to determine singularity-free zones in the 3-D and 6-D workspace, respectively. The zones obtained are the maximal singularity-free spheres or hyper-spheres for a given centre configuration within a given workspace. The determination of these singularity-free zones does not involve any discretization of the workspace and the results obtained are guaranteed. Finally, numerical examples are given to graphically illustrate the procedures. The procedures can be applied to analyze other similar parallel mechanisms with known singularity equations.