Reconfiguration Analysis of a Two Degrees of Freedom 3 4R Parallel Manipulator With Planar Base and Platform1

Abstract

This paper deals with a 2DOF (degreesoffreedom) 34R parallel manipulator (PM) with planar base and platform—a novel PM with multiple operation modes (or disassembly free reconfigurable PM) that can use the minimum number of actuated joints. At first, a set of constraint equations of the 34R PM are derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler–Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 34R PM has six 2DOF operation modes, including the two expected spherical translation mode and sphereonsphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspacebased approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2DOF 34R PM with both 2DOF spherical translation mode and 2DOF sphereonsphere rolling mode.