Spatial engaging theory was used to deduce mathematical equation of gear surface. Mathematical equation of arc tooth line of cylindrical gear surface shaped by origin face of rotary cutter,which could be used for both theoretical analysis and computer simulation,was built by dividing arc tooth line of cylindrical tooth surface into three main component surface,establishing dynamic and static coordinate system in machining process,constructing working surface mathematical equations based on theory of conjugate surface,deriving tooth bottom surface equation and tooth root surface equation from coordinate transformation and establishing equations of gear surface on this basis.Point cloud data of the tooth surface was calculated and output,tooth surface was tailored on the relationship between gear surfaces,and 3D model entities of arc tooth line of cylindrical gear was obtained.The arc tooth line cylindrical gear 3D model obtained by this method was consistent with the model generated by the method of simulating machining means.
