The model simplification of open-loop arms and its application to closed-loop arms

The author discusses the general form of transmission and introduces the definition of time-invariant transmission. The use of this general time-invariant transmission to decouple the inertia matrix of two-link manipulator arms and to find its actual form is then considered. The general time-invariant transmission and the particular conclusion on two-link arms are exploited to design the structure of n-link arms and to obtain the necessary and sufficient conditions on the decoupling of the inertia matrix. The final solution unifies and completes all existing theories on the design rules which generate the model with decoupled inertia matrix. The design rules for open-loop arms extended to cover closed-loop arms