Static Analysis of Translational 3-UPU Parallel Mechanism Based on Principle of Virtual Work

Abstract

Static analysis of a translational 3-UPU parallel mechanism (PM) based on the principle of virtual work is presented in this paper. The translational 3-UPU PM is constituted with a fixed base and a movable platform connected by three identical UPU type limbs, where U and P stand for universal and prismatic joint respectively. Given configuration of PM and force applied to platform, actuating forces in prismatic joints of each limb to keep the PM in static equilibrium can be obtained with formula put forward in this paper. To decide actuating forces, gravity force of platform and three limbs are taken into account and each limb is dissected into three parts: piston, cylinder and oil between the piston and the cylinder. There is difference between actuating forces decided with the method presented in this paper and the ones calculated by using Jacobian matrix. It is thought that the method presented in this paper is more accurate than that of Jacobian method. Based on formula in this paper, static simulation of 3-UPU PM used in compensating platform in deep-ocean mineral mining is worked out finally.