The automotive transmission maintains a proper equilibrium between the power and torque produced by the 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 the configuration that provides the correct 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 through representation of the mechanisms by graphs and their storage in the computer as vertex-to-vertex adjacency matrices. Some of the structural characteristics of the mechanisms that arise out of its functional requirements are taken into account during the enumeration process. This helps limit the number of graphs at any stage of the enumeration procedure. Graphs of mechanisms with up to nine links have been generated using this methodology.

The representation of mechanisms by graphs precipitates the need of a methodology for reverse transformation, that is, for constructing the mechanisms from graphs. To accomplish this, a mechanism is discretized into Fundamental Geared Entities. Further, these geared entities are shown to be a conglomeration of five primitives; namely, carrier, sun, ring, the single planet, and the multiple planet gears. An algorithm is formulated to create these entities from the graph representation by using the primitives. These entities are then connected together to form the mechanism.