Abstract: According to the deficiency of tooth contact analysis analysis,an improved tooth contact analysis algorithm was proposed.Based on the spatial surface engagement theory,the Enler-Rodrigues formula and the equivalent relationship between the contacted areas' shapes,the tooth contact analysis algorithm was proved.Through the equation transformation,the dimensions of the nonlinear equations for the contact points' position were decreased.The initial value was obtained regularly by the meshing equations.Taking a pair of spiral bevel gears as an example,the algorithm was proved.The results show that the complexity of initial values is decreased,the stability of the solution for nonlinear equations is enhanced,and the complex calculation of relative curvatures of the tooth surface is avoided by using the geometrical educational relationships between the geometrical parameters.