Involute gear is a key part of mechanical equipment. In the process of gear measurement or mapping

the base circle center needs to be obtained by inverse calculation of the measuring points

and the precision of inverse calculation will directly affect the accuracy of gear measurement or mapping. In this paper

under the condition of known radius of base circle

the method of establishing the non-linear least squares equation for inverse calculation of the center of base circle was studied and solved by Newton method

and the coordinates of the center of base circle were obtained. The main factors affecting the accuracy of inverse calculation were discussed: the number of measuring points of single involute

the number and position distribution of the measured involute

the selection range of the initial value of the center of base circle. The experimental design of the influence of the above factors on the accuracy was carried out. Taking the involute cylindrical gears with modulus 3.5 and tooth number 36 as an example

the method proposed in this paper was verified and the influence of main factors on the accuracy of reverse calculation was quantitatively analyzed. It is found that at least 100 measuring points should be selected for each measured involute profile

and four involute profiles should be selected in the circumferential uniform distribution direction for the reverse calculation of the base circle center. The research in this paper has certain guiding significance and reference value for the inversion of the base circle center in the measurement and mapping of involute gears.