The determination of the mechanical efficiency of a planetary gear train has been the object of research in the past years. However, most of the research done is oriented to obtain in a systematic manner the numerical value of the efficiency. The procedure presented in this work makes it possible to deduce symbolically the efficiency. The analytical expression of the efficiency is not unique for a given planetary gear train, since it depends on the power flow structure. The number of different cases for this structure increases rapidly with the complexity of the gear train. In spite of this, it is shown that it is possible to easily derive an analytical expression thanks to the special nature of the torque and power equations satisfied by the gear train. The procedure is applied to several types of planetary gear trains. Finally, the relation between efficiency and transmission ratio is studied.
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