A transmission quality index for a class of four-limb parallel Schönflies motion generators

This paper presents a uniform method of evaluating both transmission quality and singularity applicable for a class of parallel Schönflies-motion generators (SMGs) with four RRPRR limbs. It turns out that the determinant of the forward Jacobian matrices for this class of parallel robots can be expressed as the scalar product of two vectors, the first vector being the cross product of the four unit vectors along the parallelograms, and the second one being related to the rotation of the mobile platform (MP). The pressure angles, derived from the determinants of forward and inverse Jacobians, respectively, are used for the evaluation of the transmission quality and the detection of robot singularities. Four robots are compared based on the proposed indices as illustrative examples.