Systematic Enumeration of Epicyclic Gear Mechanisms for Automotives.

Abstract

Epicyclic gear trains used in automatic transmissions are called epicyclic gear mechanisms, which contain at least four coaxial links, no embedded structure, and no redundant links.Using the concept of admissible acyclic graphs, an efficient methodology has been developed to systematically enumerate the displacement graphs of N-link epicyclic gear mechanisms from the catalog of N-vertex admissible acyclic graphs.Using the notation of adjacency matrices, a computer program has been successfully developed for the automatic enumeration of the displacement graphs of epicyclic gear mechanisms.As a result, an atlas of the displacement graphs of epicyclic gear mechanisms with up to ten links have been automatically constructed.The result of this paper is of benefit to the development of multi-speed automatic transmissions.