Shaft couplings with an odd number of joints are modeled with rotation matrices such that the transmission plane in which the axis of the central joint moves can be arbitrarily specified. It is shown that when the transmission plane coincides with the homokinetic plane, the mechanism functions as a constant velocity coupling, otherwise it does not. The cyclic variation in output speed, which occurs when the constant-velocity criteria is not met, is quantified and the results enable the design engineer to predict performance of constant-velocity couplings when deviation from ideal geometry occurs because of manufacturing and installation tolerances or wear.

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