Kinematics analysis of a novel parallel platform with passive constraint chain

Abstract

A novel 4-DOF (degree of freedom) parallel platform with the passive constraint chain is proposed in this paper, according to the topology of the mechanism 4-UPS/1-RPU (4-Universal-Prismatic-Spherical joints and 1-Revolute-Prismatic-Universal joints). The inverse kinematics is studied in detail. In the formulation of Jacobian matrix of the presented parallel mechanism, the full Jacobian matrix with 6×6 dimensional matrix that consists of actuated Jacobian matrix and the constraint Jacobian matrix is formulated by the screw theory. The positional and orientational workspace is analysed using the method of boundary mapping. The dexterity analysis is then carried out based on the full Jacobian matrix under different orientations. As an application example of the proposed parallel mechanism a 5-DOF hybrid parallel kinematic machine is developed, verifying that the proposed novel parallel mechanism has the desired 4-DOFs and the dexterity of the mechanism is good enough to use in the machining process.