Dynamics of the manipulator with closed chains

The concept of dynamic equilibrium is used to derive a relation with which the actuator forces of a manipulator with a closed kinematic chain can be calculated in the same way as those of a manipulator with an open chain. Although the result is equivalent to that of J.Y.S. Luh and Y.F. Zheng (1985) the method provides physical insight into the dynamics of manipulators with closed kinematic chains. This relation also leads to the dynamic equations of motion with a minimal dimension for a closed kinematic chain. The semi-direct-drive robot is taken as an illustrative example. The numerical results verify the theory. The computational complexity of the inverse dynamics of this robot is also discussed