Research on the orientation-singularity and orientation-workspace of a class of Stewart—Gough parallel manipulators

Abstract

This article addresses the orientation-singularity analysis and orientation-workspace computation of a class of Stewart—Gough manipulators in which the moving and base platforms are two similar semisymmetrical hexagons. Based on the half-angle transformation, a polynomial expression of 13 degrees that represents the orientation-singularity locus of this class of Stewart—Gough manipulators at a fixed position is derived, and graphical representations of the orientation-singularity locus of this class of Stewart—Gough manipulators are illustrated with examples to demonstrate the result. Using this half-angle transformation, a discretization method is proposed for computing the orientation-workspace of this class of Stewart—Gough manipulators taking limitations of active and passive joints and the link interference into consideration. In addition, this article also presents a new discretization method for the computation of the non-singular orientation-workspace of this class of Stewart—Gough manipulators, where singularities, limitations of active and passive joints, and the link interference are all taken under consideration. The non-singular orientation-workspace can not only satisfy the kinematics demand of this class of Stewart—Gough parallel manipulators, but also can guarantee that the manipulator is non-singular in the whole orientation-workspace. Examples of a 6/6-SPS Stewart—Gough manipulator of this class are given to demonstrate the results.