Noncircular gear can be considered as a deformation of circular gear, that is, its rolling pitch circle has changed into noncircular, which is called pitch curve. The curvature radius of pitch curve of non-circular gear is a variable, which can realize the nonlinear relationship between the rotation angles of master and follower, namely variable speed ratio transmission. Noncircular gear is widely used in automatic machines, instruments and settlement devices With the rapid development, like other mechanical structures, only the accuracy of the non-circular gear can meet the requirements of normal transmission in production. Therefore, in addition to ensuring the machining accuracy of non-circular gear from the manufacturing method, it is necessary to have reasonable and feasible measurement devices and methods to detect whether the accuracy meets the use requirements.

The elliptic gear is a non-circular gear, which is a first-order elliptic gear. If the radial diameter R1 of a point on the ellipse is kept unchanged and its polar angle is reduced by an integer multiple N1, that is, the original polar angle φ 1 on the elliptical gear is now N1 φ 1, and the new curve evolved from this is a multi-stage elliptic gear.

Elliptical gear is the most common non-circular gear. The non-circular gear used in this paper is the first-order elliptical gear, and its three-dimensional theoretical model is shown in the figure.