Dynamic Balancing with Respect to a Given Trajectory

Abstract

To control the parallel link robots with better performance in terms of high rigidity, high degree of accuracy, high speed or acceleration, high load-carrying capacity, static balancing, and dynamic balancing are important factors. Generally, static balancing can be obtained by using counterweights or springs, and no computer control is involved. On the other hand, dynamic balancing utilizes control system to coordinate the motions of balancing elements. In this chapter, we persist on dynamic balancing with respect to a given trajectory for the parallel link robots by modeling control system. This chapter is organized in the following manner. In section “Modeling of Kinematics,” geometric feature of Stewart Platform is introduced and modeling process of kinematics and Jacobian matrices is introduced. In section “Jacobian Analysis,” modeling process of Jacobian matrix is presented. In section “Dynamics,” modeling process of dynamics equations of a six DOF Stewart Platform is presented. In section “The Operational Space Formulation,” the Operational Space Formulation is presented to control task dynamics at the end-effector. In section “Trajectory Generation,” modeling method of smooth trajectory is presented. In section “Trajectory Tracking Control,” control method to realize stable trajectory tracking motion is presented. Finally, control method to realize dynamic balancing with respect to a given trajectory is presented in section “Dynamic Balancing with Respect to a Given Trajectory.”