An articulated arm coordinate measuring machine (AACMM) is a type of nonorthogonal coordinate measuring system

whose probe coordinate values are transformed from joint angle values which are measured by angle sensors

such as circular gratings. As a result

the installation accuracy of angle sensors is an important factor relating to the measuring precision of an AACMM. The coordinate system of an AACMM was established and a compensation expression for angle measuring error was obtained from analyzing off-center installed error of circular gratings of an AACMM. Theoretical analysis showed that a little eccentricity could cause major error

so that angle data of circular gratings should be corrected in practical applications. A method of using single-point repeatability as the objective function to identify eccentricity parameters of an AACMM based on a simulated annealing algorithm was introduced and applied to identify the twelve eccentricity parameters of an AACMM. The result demonstrated that the repeatability of an AACMM was improved about 11.3%.