Dynamic analysis of a 3-DOF 3-PUU parallel manipulator based on the principle of virtual work

This paper presents a straightforward and systematical methodology for conducting the inverse dynamic analysis of a 3-prismatic-universal-universal (PUU) parallel kinematic manipulator (PKM) through employing the principle of virtual work. The proposed 3-PUU PKM possesses three translational degree-of-freedom (DOF). The position, velocity and acceleration of joints are solved via the inverse kinematic analysis, the link Jacobian matrices which map the velocity of the moving platform into the velocity and angular velocity of struts are derived in the fixed coordinate system. Based on the d´Alembert´s form of the principle of virtual work, the applied generalized forces of the whole mechanical system are divided into the applied forces of moving platform, struts, sliders, and motor-coupling-leadscrew, respectively. The joint actuated torques are obtained through eliminating the virtual displacement in the dynamic equations. Furthermore, the inertial term, centrifugal and Coriolis term, and gravitational term of the total joint torque are determined. Simulation for a conical spiral trajectory demonstrates that the total torque is dominated by the inertial term.