This paper proposed a method of representing the geometry of an imaginary disc cutter in parameter form. The undercutting condition of the imaginary disc cutter is studied, and the mathematical model of the generated gears is developed by the undercutting condition of the cutter. Through a mathematical model of the generation process, the vector equations of generated gears are established. According to the proposed method, a planetary gear mechanism and a pair of gear pump with smaller numbers

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... of teeth are illustrated. A cutting simulation process is presented for machining the proposed gear pairs. Stress analysis for the proposed gear mechanism is performed. Finally, the proposed method is applied to determine singular points of the proposed disc cutter.