The articulated arm coordinate measuring machine is one of the portable highprecision coordinate measuring instruments. It is hence necessary to establish accurate mathematical model for achieving the required accuracy due to the relationship between the central coordinate of the probes at the end of the measuring machine and the complexity of rotation angle of the joints. The classic DenavitHartenberg (DH) model has defects when adjacent axes are parallel and ignores static flexibility error. Thus, this paper focuses a new mathematical model based on the generalized geometric error model for improving the DH model. Additionally, the very fast simulated annealing algorithm is applied to calibrate the generalized geometric error parameters. Experiments demonstrat that the average error, after the calibration by the generalized geometric error model, is reduced by 0500 1 mm and the standard deviation is reduced by 0337 3 mm. The average error of the measurement based on the generalized geometric error model is 0045 4 mm and the standard deviation is 0032 3 mm. Both of the methods are superior to the MDH model, which verifies the effectiveness of the proposed method.