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A novel method of scheme design is proposed for power shifting transmissions of parallel hybrid electric vehicles (HEVs).First,shift sequences considering the path of power flow and shift logics are analyzed based on the graph theory model,abstracted from the degree-of-freedom (DOF)of the schemes.Second,the scheme of gear-pair and shaft,defined as the scheme that ignores the arrangement of synchronizers,is derived from the basic configuration,defined as the scheme of gear-pair and shaft that contains only one of each type of the variable connections,and the numbers of each type of the variable connections.Finally,a multi-parameter scheme,including the arrangement of synchronizers and gear ratios,is designed to optimize the results of synthesis.This method helps to gain a deeper understanding of the systematic design of other fixed gear transmission schemes,such as automated mechanical transmission,dual clutch transmission,and even some novel multi-input transmission.