A new fitting method for measurement of the curvature radius of a short arc with high precision

Abstract

The measurement of an object with a short arc is widely encountered in scientific research and industrial production. As the most classic method of arc fitting, the least squares fitting method suffers from low precision when it is used for measurement of arcs with smaller central angles and fewer sampling points. The shorter the arc, the lower is the measurement accuracy. In order to improve the measurement precision of short arcs, a parameter constrained fitting method based on a four-parameter circle equation is proposed in this paper. The generalized Lagrange function was introduced together with the optimization by gradient descent method to reduce the influence from noise. The simulation and experimental results showed that the proposed method has high precision even when the central angle drops below 4° and it has good robustness when the noise standard deviation rises to 0.4 mm. This new fitting method is suitable for the high precision measurement of short arcs with smaller central angles without any prior information.