1.Noncircular gear ratio
The non-circular gear transmission ratio is a periodic function with the driving wheel angle as the independent variable, which represents the speed change relationship of the driving and driven gears. Taking external meshing gear pair as an example, set the given transmission ratio as i12（ φ 1 ) = f( φ 1) it can be deduced from the motion law:
Where, ω 1 is the angular speed of driving wheel; ω 2 is the angular velocity of driven wheel. Driven wheel position function φ 2 ( φ 1) yes φ 1. When the driving wheel rotates for one cycle, the driven wheel is a closed non-circular gear, which must comply with φ 2 ( 2π) = 2π × N or φ 2 (2 π) = 2 π / N, where n is an integer.
The calculation formula of driven wheel position function is:
2.Nodal curve equation
Set the center distance as a and the rotation angle of the driving wheel as φ 1. Transmission ratio expression i12 = f（ φ 1), then the calculation formula of driving gear pitch curve:
Driven gear pitch curve R2（ φ 1) and corner φ 2. The calculation formula is:
3.Center distance of noncircular gear
Because the driving and driven wheels can rotate all round, the motion process can be regarded as pure rolling of the pitch curve of the driving and driven wheels. If the number of teeth of the driving wheel is Z and the modulus is m, the arc length is:
Assuming R1a = R1 / A, the calculation formula of the installation center distance a of the driving and driven wheels can be obtained according to the formula as follows:
