Orientation-workspace analysis of a special class of the Stewart-Gough parallel manipulators

This paper addresses the orientation-workspace analysis of a special class of the Stewart-Gough manipulators. Based on half-angle transformation, a polynomial expression of thirteen degree representing the orientation-singularity locus of the manipulator at a fixed position is derived and examples are given to illustrate the result. Applying half-angle transformation and the inverse kinematics solution of this special class of the Stewart-Gough parallel manipulator, a discretization method is proposed for computing the orientation-workspace of the manipulator taking limitations of active and passive joints and the link interference into consideration. Based on this algorithm, this paper also presents a new discretization method for computing nonsingular orientation-workspace of the manipulator, which can guarantee the manipulator is nonsingular in the whole orientation-workspace. Examples of a 6/6-SPS Stewart-Gough manipulator are given to demonstrate these theoretical results.