As shown in the figure, according to the geometric relationship, the turning angle of single tooth is cut according to the formula:

Where, φ a = 90 ° – β a, and φ B = 90 ° – β B.

Get β A and β B, and then bring them into the formula to obtain the arc length of the imaginary flat top gear turning the big end. See the formula: the arc length of the big end of the wheel blank is equal to that of the imaginary flat top gear.

Where the variable with subscript 1 represents the driving wheel variable. For the large gear engaged with it, the rolling arc length is equal to that of the small gear, and the value can be obtained by the formula.