An efficient O(mN) algorithm for the dynamic simulation of simple closed-chain robotic mechanisms is presented in this paper, where m is the number of chains, and N is the number of links for each chain. A wide range of contact conditions between each of the chains and the support surface or common body, load, or object may be simulated so that the algorithm is applicable to multilegged vehicles, multiple manipulators, and dexterous hands. The algorithm is based on the computation of the operational space inertia matrix (6 × 6) for each chain as seen by the common body, load, or object. Computation of the open-chain dynamics for each chain is also required, and the most efficient algorithm known is used for this purpose. The total computation required is tabulated in terms of the number of scalar operations needed. Efficient spatial transformations form the basis for these computations. Parallel implementation of the dynamics calculations for each chain and the common body results in an O(N) + O(log2m) algorithm.

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