Singularity kinematics principle and singularity analysis of 6–3 Stewart manipulators for special orientations

This paper presents a new principle and method of kinematics to analyze the singularity of Stewart-Gough parallel manipulators and addresses the property identification of the position-singularity loci of 6-3 Stewart-Gough manipulators for some special orientations. Based on the kinematics relationship of a rigid body, a necessary and sufficient condition that three velocities of three non-collinear points in a moving rigid body can determine a screw motion is addressed in this paper. With the above-mentioned condition, a symbolic analytical polynomial expression of three degree in the moving platform position parameters is derived, which represents the position-singularity locus of the 6-3 Stewart-Gough parallel manipulators for some special orientations, and property identification of the position-singularity loci of the 6-3 Stewart-Gough parallel manipulator for these special orientations are studied in detail as well. It is shown that position-singularity loci of the 6-3 Stewart-Gough parallel manipulator for these special orientations will be a plane and hyperholic paraboloid, even three intersecting planes.