Design Optimization of a Cartesian Parallel Manipulator

Abstract

This paper introduces a 3-DOF translational parallel manipulator called Cartesian Parallel Manipulator (CPM). The manipulator consists of a moving platform that is connected to a fixed base by three limbs. Each limb is made up of one prismatic and three revolute joints and all joint axes are parallel to one another. In this way, each limb provides two rotational constraints to the moving platform and the combined effects of the three limbs lead to an over-constrained mechanism with three translational degrees of freedom. The manipulator behaves like a conventional X-Y-Z Cartesian machine due to the orthogonal arrangement of the three limbs. Two actuation methods are analyzed. However, the rotary actuation method is discarded because of the existence of singularities within the workspace. For the linear actuation method, there exists a one-to-one correspondence between the input and output displacements of the manipulator. The effects of misalignment of linear actuators on the motion of the moving platform are discussed. Each limb structure is exposed to a bending moment induced by external forces exerted on the moving platform. In order to minimize the deflection at the joints caused by the bending moment, a method to maximize the stiffness is suggested. A numerical example of the optimal design is presented.