Orientation-singularity and orientation capability analysis of Stewart Platform based on unit quaternion representation

This paper mainly addresses the orientation-singularity and orientation capability analyses of the Stewart Platform. Employing a unit quaternion to represent the orientation of the moving platform, an analytical symbolic expression which represents the orientation-singularity locus of the mechanism at a given position, is derived. It is shown that for the Stewart Platform, it must exist a singularity free orientation void in the orientation space around the orientation origin for each position in the position-workspace, and then a new performance index which describes the orientation capability of the mechanism at a given position is presented. Furthermore, effects of the geometric parameters and the position of the moving platform on the orientation capability of the mechanism are also presented in detail in this paper.