Identifying Singularity-Free Spheres in the Position Workspace of Semi-regular Stewart Platform Manipulators

摘要

This paper presents a method to compute the largest sphere inside the position-workspace of a semi-regular Stewart platform manipulator, that is free of gain-type singularities. The sphere is specific to a given orientation of the moving platform, and is centred at a designated point of interest. The computation is performed in two parts; in the first part, a Computer Algebra System (CAS) is used to derive a set of exact symbolic expressions, which are then used further in a purely numerical manner for faster computation. The method thus affords high computation speed, while retaining the exactness and generic nature of the results. The numerical results are validated against those obtained from an established numerical algebraic geometry tool, namely, Bertini, and are illustrated via an example.