Abstract: The four mathematical equations as mentioned in the patent numbered ZL2004100K231X5 are regarded as the mathematical basis supporting both the patent itself and study on the rotary rolling process. The deduction process of the equations are detailed, and the positive internal relations between certain geometric parameters are explained. The said four equations are applicable to design and operation speed calculation of tools and workpieces for all kinds of rotary rolling processes and machining processes with rotating cutting tools which involve determination of the contact line between two rotary curved surfaces.