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

Based on unit quaternion to represent the platform's orientation, the orientation singularity and orientation capability of the Stewart parallel mechanism are researched, and the singularities caused by Euler angles to represent are avoided. The expression and locus of orientation singularity of the mechanism are expressed. It can be shown that there is a singular free void in the initial-orientation around the origin. It is denoted that the minimum inscribed sphere of the orientation singularity locus can be searched inside the free void, and the sphere's radius is used to evaluate the orientation capability. Effects of geometric configuration of the mechanism and the position of the moving platform on the orientation capability are addressed.