The installation accuracy of angle sensors is an important factor relating to the measuring precision of an Articulated Arm Coordinate Measuring Machine (AACMM).In order to realize the dynamic calibration in real time for an AACMM, a coordinate system of the AACMM was established and a compensation expression for angle measuring errors was obtained from analyzing the effect of the off-center installed errors of circular gratings on the angle measurement. Theoretical analysis shows that a little eccentricity could cause a major error, so the angle data of circular gratings should be corrected in practical applications. A method using single-point repeatability as the objective function to identify the eccentricity parameters of the AACMM was introduced based on a simulated annealing algorithm and then it was applied to the identification and correction for the twelve eccentricity parameters of the AACMM. The result demonstrates that the repeatability of the AACMM has improved by 11.3%.