This investigation is concerned with the determination of the rotatability of the input and output cranks and the optimization of transmission characteristics of spherical two-gear drives. Algebraic solutions are shown to be feasible only in a few special cases. In general, numerical synthesis procedures, involving either optimization or parameter scanning processes, are essential and they are developed from the general theory presented in this paper. The results, including conditions that can be regarded as an extension of the Grashof’s rule to the class of spherical geared mechanisms, are useful for the rational design of mechanisms. Applications of the theory to practical mechanisms design are given in Part 2.

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