# Pitch curve and transmission ratio of reducer variable speed integrated gear

The reducer variable speed integrated gear is a new type of gear mechanism, which is composed of ordinary involute cylindrical gear and non-circular gear with orthogonal rotation axis. The non-circular gear integrates the structural characteristics of non-circular gear and face gear. The tooth surface shape of all teeth is different, and the geometric shape of the left and right sides of the same tooth is also different, so its tooth surface equation is more complex. In this chapter, the meshing principle of the reducer variable speed integrated gear is expounded, the pitch curve and tooth profile model of the non-circular gear are constructed, the internal excitation form of the gear is analyzed, and the mathematical description of the internal excitation is given, which lays the foundation for the dynamic modeling.

The graph shows the pitch curve of the non-circular gear, R2 is the radial diameter of the non-circular gear, and point m is the tangent point of the pitch curve of the small cylindrical gear and the pitch curve of the non-circular face gear at the turning angle.

Let the pitch curve equation of non-circular gear be:

Where l and a are the constant value and fluctuation amplitude of pitch curve respectively.

It can be seen from the figure that the transmission ratio function of the reducer variable speed integrated gear is as follows:

Where R is the pitch radius of the small cylindrical gear meshed with the non-circular face gear. 