For a simple epicyclic train, the controlling element is almost invariably fixed, i.e., prevented from rotating by being connected, in some way, to the frame. Such trains are easy to synthesize because there are a limited number of variations of the three basic elements and, normally, six equations will define all possible velocity ratios. For a compound epicyclic train, the number of equations is considerably increased. A method of synthesizing compound epicyclic trains is developed using the concept of a velocity ratio spectrum. To facilitate the application of this concept, only one train in a compound epicyclic train is regarded as basic; all others are considered as merely serving the purpose of modifying the motion of the controlling element in the basic train.

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