In this article, a special kind of axial flux permanent magnet machine has proved to be suitable for high torque and low speed applications. An innovative design of the machine has been proposed in order to make the machine suitable for traction applications by means of field-weakening. The aim of this paper is to analyze, in general terms, the basic equations that describe the operating conditions of such machines. Optimal sizes for design can be obtained by calculating the power density and the air-gap flux density, etc.