Topological analysis of single-degree-of-freedom planetary gear trains

D. G. Olson, A. G. Erdman, D. R. Riley

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


Graph theory has been demonstrated by many researchers to be useful during the conceptual phase of mechanism design. For the particular class of mechanisms known as planetary gear trains, the graph representation has been used primarily for “topological synthesis,” the enumeration of kinematic chains satisfying the requirements for planetary gear trains. The subsequent “topological analysis” steps resulting in the specification of ground, input, and output links, have received very little attention in the literature, perhaps because the conventional graph representation is not well suited to these steps. This paper addresses the inadequacies of the conventional graph representation for topological analysis, and utilizes a new graph representation which enables these steps to be performed in a straightforward manner. It is shown that among the thirteen distinct displacement graphs representing planetary geared kinematic chains with five links and one degree-of-freedom, only four distinct planetary gear trains result after assigning the ground, input, and output links subject to meaningful topological requirements.

Original languageEnglish (US)
Pages (from-to)10-16
Number of pages7
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number1
StatePublished - Mar 1991


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