Type Synthesis of Two Degrees of Freedom 3 4R Parallel Mechanisms With Both Spherical Translation Mode and Sphere on Sphere Rolling Mode

Abstract

Parallel manipulators (PMs) with multiple operation modes are novel reconfigurable PMs, which use less number of actuators and can be reconfigured without disassembly. This paper deals with the type synthesis of 2DOF (degreesoffreedom) PMs with both spherical translation mode and sphereonsphere rolling mode. A spherical translation is the 2DOF spatial translation under which the trajectory of any point on the moving link is a sphere. A sphereonsphere rolling refers to the rolling of a sphere without slipping and spinning on another sphere of the same diameter. At first, a 2DOF 34R overconstrained PM is proposed based on an existing 5DOF US equivalent PM. From this 2DOF PM, we further obtain a 34R PM for sphereonsphere rolling and a 34R PM for spherical translation. By finding the common conditions for the 2DOF 34R PM for spherical translation and 2DOF 34R PM for sphereonsphere rolling, the types of 2DOF 34R PMs with both spherical translation mode and sphereonsphere rolling mode are then obtained. The 2DOF 34R PMs with both spherical translation mode and sphereonsphere rolling mode fall into two classes. In one class of PMs with both spherical translation mode and sphereonsphere rolling mode, the moving platform has four instantaneous DOF in a transition configuration. In another class of PMs with both spherical translation mode and sphereonsphere rolling mode, the moving platform has at most three instantaneous DOF in a transition configuration. This work enriches the types of PMs with multiple operation modes and overconstrained mechanisms.