The theory here expounded reveals certain inescapable geometrical conditions with which all couplings must comply when they are required to reproduce at the output shaft, simultaneously and precisely, all angular input shaft displacements. Plunging-type linkage couplings, whose geometrical forms follow very simply from the theory, are fully listed for both intersecting and parallel shafts. Many, particularly those for parallel shafts, are entirely new, and it is believed that there could be useful precision-engineering applications.

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