Singular Manifold of the General Hexagonal Stewart Platform Manipulator

Abstract

The knowledge of the singular manifold of a manipulator is essential for its design, path-planning and control. However, due to the computational complexity, it is very difficult to obtain an analytical description of the manifold in terms of the architecture as well as configuration parameters of the manipulator. In this paper, the singularity of a general hexagonal Stewart platform manipulator (GHSPM) is studied and its singular manifold is obtained. The manifolds geometric structure is analysed by projecting it to the position and orientation subspaces, respectively. An explicit geometric characterisation is obtained in the former case, where is it found that the geometric nature of the singular surface is the same as in the case of the SRSPM. The other surface, however, defies such analysis at this point due to its high degree. The theoretical results are illustrated with numerical examples and plots.