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It is shown that the time lower bound of computing the inverse dynamics of an n-link robot manipulator parallelly using p processors is O(k1 [n/p] + k2 [log<2 p]), where k1 and k2 are constants. A novel parallel algorithm for computing the inverse dynamics using the Newton-Euler equations of motion was developed to be implemented on a single-instruction-stream multiple-data-stream computer with p processors to achieve the time lower bound. When p = n, the proposed parallel algorithm achieves the Minsky's time lower bound O([log2 n]), whidc is the conjecture of parallel evaluation. The proposed p-fold parallel algorithm can be best described as consisting of p-parallel blocks with pipelined elements within each parallel block The results from the computations in the p blocks form a new homogeneous linear recurrence of size p, which can be computed using the recursive doubling algorithm. A modified inverse perfect shuffle interconnection scheme was suggested to interconnect the p processors. Furthermore, the proposed parallel algorithm is susceptible to a systolic pipelined architecture, requiring three floating-point operations per complete set of joint torques.