Cycloid drives are widely used in the industries because of their excellent characteristics, namely, high gear ratio, smooth transmission, compact size, high efficiency, low noise and long service life. In this paper, a mathematical model of an epitrochoid gear for a cycloid drive with a small tooth number difference has been proposed. Computerized simulation of the generated epitrochoid gear has also been developed. In this paper, the pressure angle, which has an important role in the analysis of cycloid drives as it influences the direction and magnitude of force transmission in gears, is derived based on the theory of differential geometry. The rack cutter profile, which is the fundamental tooth profile of a hob cutter, which in turn is the main manufacturing process of epitrochoid gear, has been obtained based on the theory of gearing. It is anticipated that the results from this paper will be beneficial to the design, analysis and manufacture of cycloid drives.