In this paper we present an analytical technique, based on Newtonian mechanics with screw calculus and dual-number matrices, to derive the dynamic equations of a multi-rigid-body open-chain system. Next, we outline a systematic procedure to derive closed-form expressions for the joint forces and torques and the reaction forces and moments exerted on each member in the system. Finally, we illustrate the procedure with two examples of robot manipulators. It is hoped that the analytical technique presented here will provide a meaningful alternative, or serve as a complement to existing methods, in our common effort to advance the design of robot manipulators.

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