Curvic couplings have been widely applied to various industrial applications. Presently the Gleason No.120 special grinding machine developed by Gleason Works Co. is one of the commonly used machine tool for the curvic coupling manufacturing. On the other hand, in response to the issue of improving the domestic design and manufacturing ability, an alternative manufacturing method of curvic coupling is introduced in this study. In this study the geometrical characteristics of the novel gear profile are investigated. Firstly, applying the spatial transformation matrix theorem to the relationship between the cutting tool path and the cutting tool position, the cutting tool profile equation of curvic coupling is successfully derived. Secondly, the mathematical model of the envelope surface of the generating tool, or generally being called the gear surface, is constructed based on the trajectory equation of the generating tool motion and the tool-workpiece meshing equation. Finally, the solid model is established based on the obtained mathematical model, and the comparison works with the conventional curvic coupling are also carried out. The analysis of gear surface is graphically depicted with respect to the various machining parameters. It is believed that this thesis provides a useful tool for the following studies of curvic couplings for the different demand of application fields.