When given only part of transmission ratio function of non-circular gear in period

two methods to design entire transmission ratio in period and ensure non-circular gear can smooth transmission are proposed.The period of transmission ratio function is determined according to the requirement of rotation number.On condition that the gear smooth transmission

the transmission ratio of outside given interval in period is complemented by using Fourier series and polynomials.Finally

the example is given

design process of the two transmission ratio function are explained compared.The basis of transmission ratio design of non-circular gear of closed pitch curve is provided.