The machining accuracy of cycloidal tooth surface is the key factor affecting the motion performance of RV reducer,and the reverse correction of grinding parameters according to the data of tooth surface error detection is an important link in the manufacturing process of the cycloidal gear. Through the analysis of the cycloidal gear generating grinding principle,the complex motion relationship between the grinding wheel and the cycloidal gear is clarified and the model of the movement relation of the cycloidal tooth surface is established.Besides,based on the gear meshing theory and the principle of space coordinate conversion,the mathematical expression of the cycloidal gear theoretical tooth surface and the normal vector with the parameters of the grinding adjustment are deduced,which provides a theoretical basis for correcting the tooth profile error after testing.Then according to the cycloidal generating grinding model,the influence of main grinding parameters on the tooth surface error is discussed. Finally,a comparison is made with the cycloidal tooth profile obtained by generation principle,which proves that the equation and its establishment method is correct. It can not only provide the necessary theoretical data for the machining error detection of the cycloidal gear,but also have important significance for the correction of the grinding parameters and the accuracy improvement of the cycloidal tooth surface.