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A transverse flux permanent magnet machine (TFPM) is ideally suited to high torque and lower speed applications such us the generation of electricity by wind-energy and the electric propulsion of naval ships. This paper introduces the basic principles and construction of the transverse flux permanent magnet machine, and illustrates the flux paths of two typical TFPM topologies. The analytical approach to dimensioning an application-specific 20 kW two-phase TFPM with C-form stator cores is provided. The equivalent circuit is given and the important features of TFPM are outlined with the help of solving the equivalent circuit. The instantaneous torque equation, flux linkage equation and voltage equation are also proposed, so that the mathematical model is established.