Dynamic modeling and contouring control of parallel kinematic machines

This study concerns dynamic modeling and contouring control of parallel kinematic machines. The Orthopod, a 3 degree-of-freedom parallel manipulator designed for an engraving machine, is introduced as the control plant. Since the tracking error does not reflect truly its product quality, the contouring error is introduced in dynamic control. In this paper, the dynamic equations of the Orthopod are obtained by Lagrange-D´Alembert formulation. The contouring control is implemented by approximating the contouring error as the distance from the actual position to the tangent plane of the desired trajectory at the corresponding desired position. By attaching a moving frame to each point on a desired trajectory, the tracking error is decomposed into tangential and normal parts. For comparison purpose, the augmented PD control and the computed torque control are also carried out. Experimental results show that the contouring control has better performance in contouring accuracy.