The following paper applies the theory of number synthesis to the creative design of epicyclic gear trains. First, the associated linkage of an existing epicyclic gear train is derived as an initial step of analysis. Next, the requirements for an acceptable associated linkage are established. Finally, epicyclic gear trains are derived by number synthesis from acceptable associated linkages up to and including the degree of complexity of eight links.
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Johnson et al. (1967) studied this question.
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