The formula is the calculation equation of non-circular gear profile (XCK, yck), and (XG, YG) is the involute profile of gear shaper cutter; When machining the driving noncircular gear, the gear shaper tool rotates clockwise“ ±” Take “+”; When machining the driven non-circular gear, the gear shaper cutter rotates counterclockwise“ ±” Take “-“.

According to the calculation process, all the tooth profiles of non-circular gears can be solved by using MATLAB programming. The tooth root transition curve (xGd, YGd) can also be calculated according to the process, but it is necessary to change (XG, YG) to the vertex coordinates of the gear shaper cutter (XA1, ya1) or (xc1, Yc1), and recalculate the corresponding rotation angle, revolution angle and the center coordinates of the gear shaper cutter.

Connect the tooth profile and root transition curve in order to get the complete profile of non-circular gear, as shown in the figure.