Terminal constraint and mobility analysis of serial-parallel manipulators formed by 3-RPS and 3-SPR PMs

Abstract

Although the serial-parallel manipulators(S-PMs) formed by the symmetric 3-RPS and 3-SPR PMs have been widely studied, the terminal constraint and mobility criterion for this class of manipulators are still open questions. This paper solves the terminal constraint and mobility problems of the (3-SPR) + (3-RPS) and the (3-RPS) + (3-SPR) S-PMs. In this paper, the terminal mobility composition principle for the two S-PMs is presented. By analyzing the rank of two types screw systems composed of six constraint forces concerned with the two S-PMs under different geometry conditions, the degree of freedom (DOF) of the two S-PMs are determined. From algebraic and geometric concepts, the approaches for solving the intersection of two sub three order screw systems in determining the terminal constraint are proposed. In addition, the terminal constraint form and mobility property for the two S-PMs under different conditions are discussed. The results show that the terminal constraint of the (3-SPR) + (3-RPS) S-PM is one finite-non-zero pitch screw and the terminal constraint of the (3-RPS) + (3-SPR) S-PM is empty in the general case. This research provides a foundation for the terminal constraint and mobility analysis for S-PMs.