Use of coordinate measuring machines and digital optical machines for the geometric characterization of circumference arcs using the minimum zone method

Abstract

This paper presents an optimised method for the characterization of circular features of any amplitude, which includes the capture of geometric data, by means of the use of three-coordinate measuring machine or digital optical machines with a CCD camera, and its subsequent mathematical processing. The proposed model determines the radius and the circularity error, based on the minimum zone method, and to this end it uses linear programming techniques, the Simplex programming principles and the limaçon approximation. An experimental study on ring gauges and reference disks is provided, including a comparative analysis using the Chauvenet and Grubbs filtering procedures. Last of all, an uncertainty estimation method is proposed by means of the Monte Carlo simulation. The experimental analysis carried out on ring gauges and reference disks accredit that the algorithm developed, implemented in a Matlab® environment, gives reliable results for any circumference arc considered, regardless of its amplitude.