Mechanical efficiency of Simpson gear trains

Simpson gear trains have the advantage of compactness, high speed reduction and capability of differential drive, so they are often used in automobile, aerospace, mill, and automation industries. The purpose of this paper is to propose a systematic methodology for the analysis of the mechanical efficiency of Simpson gear train. Based on the fundament circuits of epicyclic gear train, the kinematic structure of Simpson gear train is presented. Then, the equations of the kinematics and mechanical efficiency of the Simpson gear train have been constructed. The results of the paper provide a powerful tool for the analysis of the kinematics and mechanical efficiency of the Simpson gear trains.