Abstract: For purpose of the computer-aided design and computer-aided manufacture of the transition curve of the dual-purpose vane pump cam ring,a mathematical model of the transition curve is proposed instead of the commonly-used transition contour equation in polar coordinates. The characteristics of different contours can be analyzed, compared and evaluated by means of the mathematical model. The model is advantageous to compiling a generally applicable computer program and favourable for optimum design of the transition contour.