From the application characteristics of the stepless speed regulating mechanism, it can be seen that the non-circular gear stepless speed regulating mechanism needs to be in the range of 0 ~ 360 ° According to figure 1 (b), a single pair of non-circular gear pair will inevitably have a transition section which can not meet the requirements of transmission and speed ratio integration. Therefore, it is necessary to adopt the form of multi group non-circular gear combination, and realize the constant speed ratio transformation through the alternative selection of output branches, so it is necessary to design the branch mechanism of non-circular gear.

According to figure 1 (a), the simplified model of time-varying integration part is established, as shown in Figure 2.

Combined with the speed ratio equivalent simplified model of differential gear train shown in Figure 2, the relationship between the final output speed ratio of non-circular gear stepless speed regulation mechanism and the output speed ratio of non-circular gear pair 1 and 2 can be obtained as follows:

Among them, I2（ θ 2) And I1（ θ 1) It is the output speed ratio of non-circular gear pair 1 and 2; I1 and I2 are two-stage speed ratios of integrated differential gear pair; A is the tooth ratio of sun gear and outer ring gear of integrated differential gear pair. It can be seen from the formula that the final output speed ratio function of the non-circular gear speed regulating mechanism is related to the speed ratio function of each gear pair.

According to the basic parameters of the working section of the non-circular gear pair, the whole period speed ratio curves of single pair of non-circular gear pairs with different paired branches can be obtained, as shown in Figure 3.

Figure 3 shows the speed ratio curves of non-circular gears with different number of paired branches. It can be seen that the whole cycle speed ratio of a single pair of non-circular gears consists of two parts: the speed ratio of working section and the speed ratio of transition section. Because the speed ratio characteristics of a given working section must be satisfied, the overshoot of the transition section speed ratio function is inevitable, but it will change with the number of pairs and the speed ratio function of the working section.