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An automotive transmission maintains a proper equilibrium between the power and torque produced by an engine and those demanded by the drive wheels. Most automatic, transmissions employ some kind of epicyclic gear mechanisms to achieve the above purpose. The first step in the design process of such a mechanism involves finding a configuration that provides a set of desired speed ratios, and meets other dynamic, and kinematic requirements. In this work, the kinematic structural characteristics of epicyclic gear mechanisms have been identified, and a methodology is formulated to systematically enumerate all possible configurations of such mechanisms. This is achieved by defining a canonical graph to represent the mechanisms. Graphs of mechanisms with up to ten links have been generated using this methodology.