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

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 meta-morphic 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 instanta-neous 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 con-ditions. 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.