The error of grating encoder may affect the position accuracy of Articulated Arm Coordinate Measuring Machine (AACMM) in different poses. The position accuracy distribution effected by grating encoder accuracy may be used to guide the calibration and measurement of AACMM. The paper studies the relationship between the precision of grating encoder and the position accuracy of 6joint measurement system. The position accuracy metric of grating encoder is defined. The distribution of AACMM in the workspace is depicted. The evaluation experiments and testing results are as follows. The comparisons of position accuracy effect of grating encoder's precision in different joints are carried out. Then, the distribution characteristic is compared with Monte Carlo method. Then, the different positions are utilized to measure the singlepoint test and standard ball radius. The experimental results show that the proposed method can describe the position accuracy distribution of AACMM more comprehensively and accurately. The optimized measurement region can be determined by the position accuracy distribution which can be used to guide the practical operation.