Derivation and analysis of equations of motion for 6-DOE direct-drive wrist joint

Complete equations of motion for 6-DOF direct drive wrist joint´s based on the Stewart platform are derived and analyzed. Although the derived equations are highly complex, the dynamics of the wrist joint are simple if the centroid of the hand is close to the platform, and if the centroid; of the actuators are close to the base. In the case of a specific position and orientation of the platform, it is found that the dynamics of the actuators cancel each other and that the equations are simple because the actuators in the Stewart platform are placed in parallel. The equations are simple and so is the design of a controller for the wrist especially when the mechanism of the wrist joint is symmetrical and uses actuators