Epicyclic gear transmissions have many applications. The internal power flow of epicyclic systems is highly related to the power loss of the system. A systematic method and generic formulas based on kinematic constraints are derived to conduct the power flow analysis, by means of Lagrange multipliers and newly introduced selection matrices. The method and formulas can be readily applied to complicated epicyclic systems. The graphic representation of the power flow of two examples verifies the balance of the power flow and virtual power flow. In the example of the Dual-E powertrain for hybrid electrical vehicles, an estimation of the total efficiency is derived. The pattern of contour maps of the total efficiency indicates the operational ranges of the powertrain with relatively low power losses.

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