Automatic detection of degenerate planetary gear trains with different degree of freedoms

Planetary gear trains (PGT) are widely used in transmissions of vehicles, pulley blocks, wrist watches, machine tool, robots, etc. The structural synthesis of PGTs is an effective way to create novel transmissions. In the synthesis process, one of the most important problems is to detect and eliminate degenerate PGTs. This paper proposes a fully automatic algorithm to resolve this key problem. Our previous graph representation of PGT is first introduced and the corresponding adjacency matrix is used as the numerical tool, based on which the fundamental circuits (f-circuit) of PGT can be easily determined. The present algorithm is executed by successively adding a single f-circuit to generate sub-graphs. The detection process has been automated by an interactive computer program. The algorithm is applicable for PGTs with any number of degree of freedoms (DOF). The algorithm has been applied to a large number of PGTs, including the counterexamples found in literature. Our results of all the tested PGTs are verified to be correct.