The basic relationships among gear ratios, velocity succession, torque directions, power ratios, energy losses, and efficiency are derived from first principles. The techniques presented here can be applied to ordinary, planetary, or mixed gear trains. Also, these techniques provide more insight into how power is flowing through the different parts of the mechanism. Power flow relationships are a helpful tool to study power amplification and power circulation in multipath transmissions. They also provide more insight into how the gear pair entities (GPEs) or gear train entities (GTEs) affect total power losses and allow immediate derivation of the overall efficiency. A representative two-input mechanism is analyzed to demonstrate the effectiveness of improved techniques. The theoretical results are compared with experimental data of previous work. The theoretical and experimental curves exhibit identical trends with a distinct jump in friction loss. The jump is explained by a change in the way of the power flow through the mechanism. The conditions under which power circulation occurs are determined. The results have important implications for understanding how to improve the efficiency of multipath power flow systems.