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In order to meet the requirements of kinematic characteristics of driven gear，a design method of uniform non-circular gear is proposed. Based on the concept of uniform non-circular gear，the pitch curve equation is derived on the basis of velocity curve and acceleration curve，and the calculation model of gear section length and center distance is established. Taking type I uniform non-circular gear as an example，the design method of uniform non-circular gear transmission is proposed. The shape of angular velocity and angular acceleration curve of driven gear is simulated and analyzed by using Adams software，and the effectiveness of the design scheme is verified. The characteristics of pressure angle，undercutting and meshing coefficient are analyzed. The results show that，the proposed design method can realize the flexible control of pitch curve shape by changing the parameters of given speed curve and acceleration curve.