Dynamic modeling of a parallel manipulator with two translational degrees of freedom

The dynamics of a parallel manipulator with two translational degrees of freedom was investigated using the Lagrange multiplier approach. Since the algorithm does not use a coordinate transformation between the joint space and Cartesian space, it increases the calculational efficiency so that real-time control can be realized. The algorithm was applied to a modular parallel mechanism with high rigidity and high flexibility to predict the position, velocity, acceleration and Jacobian matrix of the manipulator. A closed form dynamic model was presented based on the generalized system coordinates. The dynamic simulation shows the relation between the joint actuating force and the process parameters such as the platform trajectory and the manipulator mass and acceleration.