To date, most of the multi-DOF (degree-of-freedom) epicyclic gear trains have been used as a series of one-DOF devices. Comparatively little is known with regard to the existence and synthesis of nonfractionated, epicyclic gear trains. This paper presents a systematic methodology for the identification and enumeration of the kinematic structure of nonfractionated, two-DOF epicyclic gear trains. It has been shown that there exists no such gear trains with five or less links. It has also been shown that there exist two nonisomorphic rotation graphs of six vertices and twenty nonisomorphic rotation graphs of seven vertices. An atlas of nonisomorphic displacement graphs which can be used to construct nonfractionated, two-DOF epicyclic gear trains with six and seven links has been developed. It is hoped that this atlas will lead to more optimum and efficient designs of machines with multiple actuating requirements such as robotic wrists, grippers, and walking machines.

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