根据微分几何中的曲线理论,利用曲线的法向量得出了基于包络模型的非圆锥齿轮齿廓的简便算法。应用该算法,对二种常用的包络方法(齿条刀具包络,齿轮刀具包络)进行了计算机图形学仿真,并且利用数值算法得到非圆锥齿轮的三维模型。实例计算结果验证了该算法的正确性、简洁性、通用性与创新性。 According to the curve theory in differential geometry, a simple algorithm of tooth profile of non - bevel gear based on envelope model is derived by using the normal vector of the curve. The algorithm is applied to computer graphics simulation of two commonly used envelope methods (rack tool envelope and gear tool envelope). The three-dimensional model of non-bevel gear is obtained by using numerical algorithm. The result of example calculation verifies the correctness, conciseness, universality and innovation of this algorithm.