POSITION-SINGULARITY ANALYSIS OF 6-3 STEWART-GOUGH PARALLEL MANIPULATORS FOR SPECIAL ORIENTATIONS

This paper mainly addresses the property identification of the position-singularity loci of 6-3 Stewart-Gough manipulators for special orientations. Considering three non-collinear points in a moving rigid body, a necessary and sufficient condition of the direct kinematic singularity is proposed. In terms of whether or not the intersecting line between the plane where the moving platform lies in and the base platform is parallel to any side of the triangle where the base platform lies in, there are two different types of orientations, special orientations and general orientations. Using three standard Euler angles to represent the orientation of the moving platform of the 6-3 Stewart-Gough manipulators, a symbolic analytical polynomial expression representing the position -singularity of the parallel manipulator for special orientations, is derived, and the structure and property of the position-singularity loci of the parallel manipulator for special orientations is addressed. It is shown that the position-singularity loci of the 6-3 Stewart-Gough manipulator can be resolved into two parts: one is a plane and another one is a hyperbolic paraboloid, especially, in some special cases, the hyperbolic paraboloid can degenerate into two intersecting planes.