Determination of the Uniqueness Domains of 3-RPR Planar Parallel Manipulators With Similar Platforms

Abstract

Abstract A uniqueness domain is a part of the Cartesian workspace corresponding to the same assembly mode of the 3-RPR (planar parallel) manipulator. This paper presents an efficient method to determine the uniqueness domains of the 3-RPR manipulators with similar platforms. The method is based on the singularity and forward displacement analysis (FDA) of the 3-RPR manipulator with similar platforms. The singularity analysis and the FDA of the 3-RPR manipulator with similar platforms is first performed. It is then proved that each of the solutions distributes into different singularity-free regions of the manipulator. Each singularity-free region corresponds to one uniqueness domain of the 3-RPR manipulator with similar platforms which can thus be determined in a direct way. At last, it is proved that the four solutions in analytic expression form to the forward displacement analysis correspond to different uniqueness domains for the 3-RPR manipulator with similar aligned platforms. This simplifies further the FDA in this case as the unique solution to the FDA can be found without the need to compute all the four solutions as long as the singularity-free region in which the manipulator works is given.