Statics of rotational 3-UPU parallel mechanisms based on principle of virtual work

Statics of rotational 3-UPU parallel mechanisms (PM) based on principle of virtual work is presented in this paper. The rotational 3-UPU PM is made up of a fixed base and a movable platform interconnected by three identical UPU type limbs, where U and P stand for universal and prismatic joint respectively, and platform can only change its orientation relative to fixed base. Given configuration of PM and force applied on 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 the actuating forces, gravity of platform and three limbs are taken into account and each limb is dissected to three parts. They are piston, cylinder and oil between the piston and the cylinder. There is difference between the actuating forces decided with the method presented in this paper and the ones calculated by using Jacobian matrix. It is thought the method presented in this paper is more accurate than that of Jacobian method. Based on formula in this paper, static simulation of the rotational 3-UPU PM used in compensating platform in deep-ocean mineral mining is worked out finally.