Revelation of metamorphic phenomenon through the equivalent mechanisms and development of the novel metamorphic epicyclic gear trains

Abstract Epicyclic gear train, a typical higher pair mechanism with one-wheel axis that revolves around another fixed axis, has been widely used in mechanism design. However, applying the metamorphic mechanisms to the epicyclic gear trains remains a challenge. This paper analyses the metamorphic phenomenon of epicyclic gear trains using the equivalent mechanism approach and presents for the first time a set of novel metamorphic epicyclic gear trains with variable motion branches and changed configurations. Three 5-bar equivalent mechanisms of typical epicyclic gear trains and their equivalent geometrical relationships are introduced based on the instantaneous screw axes of the gear pairs. First- and second-order kinematic models of the equivalent mechanisms are established to obtain motion branches and their corresponding constraint conditions. With the equivalent geometrical relationship, the configurations and the motion branches of the epicyclic gear train are identified, and the constraint conditions are obtained. A set of novel metamorphic epicyclic gear trains are therefore designed by implementing the metamorphosis technique that can realize the configuration transformation of an epicyclic gear train under constraint conditions. A metamorphic epicyclic bevel gear clamping mechanism is further designed as an example to demonstrate the application of the metamorphic epicyclic gear mechanisms.