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A new type of non-orthogonal arc tooth face-gear is designed. The arc tooth cylindrical gear is used as an imaginary tool to envelop the working tooth surface and transition surface of the face gear. The mathematical model of the face-gear is obtained in Matlab. The full tooth surface tooth surface equations of the non-orthogonal arc tooth face-gear is derived，and the realization of tooth surface visualization through Matlab programming which laid the theoretical foundation for the subsequent research on non-orthogonal arc tooth face-gears.