Planetary gear trains (PGTs) are used in a wide range of mechanical applications. Graphs are used to represent PGTs. PGTs are classified into single-planet and multi-planet gear trains depending on the number of vertices in the second level of the graph. In this paper, a novel method for synthesizing PGTs up to the second level is developed. The first step in the synthesis process is the enumeration of spanning trees. A combinatorial analysis is then used to obtain the link assortment arrays and categorize them into families. Based on the parent graphs and spanning trees, the geared graphs are generated for each family. For simplicity, the steps of the newly developed genetically compatible graphing method are applied to 5-link, 1-DOF planetary gear trains. The synthesis steps are programmed in MATLAB.

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