This study contributes to the development of a systematic methodology for the torque and power flow analyses of two-input epicyclic gear mechanisms (EGMs) with or without reaction link, based upon the concept of fundamental circuit. The studies on power flow analysis of EGMs are mostly done in the context of efficiency formulations. In the opinion of the authors, the design process of two-input mechanism involves not only finding the configuration that provides the correct velocity ratios, but also meets other dynamic and kinematic requirements and ensures that the two inputs have a mutually constructive nature. To demonstrate the analysis, a new motor/generator integrated hybrid transmission design is used to show how the torque acting on each link of an epicyclic gear train (EGT) can be systematically solved in terms of input torque(s) and/or controlled output torque. This paper presents a unification of kinematic and torque balance approaches for the analysis of two-input epicyclic-type transmission trains. The results presented are meant to deepen the knowledge as to how and why a two-input epicyclic-type transmission should operate in a certain way under the given conditions. In the process, this paper explores the theoretical bases of operation of the Toyota Hybrid System (THS) and the root cause of some confusion in the field of EGTs.

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