Singularity analysis is a basic problem of parallel mechanism, and this problem cannot be avoided in both workspace and motion planning. How to express the singularity locus in an analytical form is the research emphasis for many researchers for a long time. This paper presents a new method for the singularity analysis of the 6-SPS parallel mechanism. The rotation matrix is described by quaternion, and both the rotation matrix and the coordinate vectors have been expanded to four-dimensional forms. Through analyzing the coupling relationship between the position variables and the orientation variables, utilizing properties of the quaternion, eight equivalent equations can be obtained. A new kind of Jacobian matrix is derived from those equations, and the analytical expression of the singularity locus is obtained by calculating the determinant of the new Jacobian matrix. The singularity analysis of parallel mechanisms, whose moving platform actuated by 6 links and the vertices of both the base and the moving platforms has been placed on a circle respectively, can be solved by this analytical expression.
