All planar parallel manipulators with cylindrical singularity surface

Abstract

In this article we give the complete list of all non-architecturally singular parallel manipulators of Stewart Gough type with planar base and platform, whose singularity set for any orientation of the platform is a cylindrical surface with rulings parallel to a given fixed direction p in the space of translations. The presented list has only two entries containing the necessary and sufficient geometric conditions of the corresponding manipulator designs possessing such a singularity surface. These manipulators have the advantage that their singularity set can easily be visualized as curve by choosing p as projection direction. Moreover the computation of singularity free zones reduces to a 5-dimensional task. We close the paper by formulating a conjecture for the non-planar case.