In this paper, a new graphical approach for automatic enumeration of epicyclic gear mechanisms is presented using the concept of acyclic graph to enumerate displacement graphs. A new graphical code method has been introduced for automatic evaluation of displacement graphs. This graphical code has been applied as a detection tool for open graph, redundant links and isomorphic graphs. A computer program "GRSY-EGM" has been developed for automatic enumeration of the displacement graphs as will as automatic detection of isomorphic graphs and open graphs and graphs with a redundant link using the concept of graphical code without using the concept of adjacency matrices. This simplified methodology has been successfully applied for the enumeration of epicyclic gear mechanisms with 7 and 8-links having at least 4 coaxial links, two level vertices, at most tree planet gears.
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