Articulated Arm Coordinate Measuring Machines (AACMM) are usually used to measure mechanical parts of different sizes in practical applications. When the size of parts is smaller than that of the AACMM, a redundant measurement space of the measuring machine is generated, resulting in reduced measurement accuracy of the AACMM. Moreover, due to the series structure of the AACMM, the joint errors would be propagated with the increasing length of the bar, which could amplify the measurement error. Therefore, on the premise of ensuring the measurement space required by the measured parts, this work proposes a new method based on variable measurement space, i.e., locking some movable joints of the AACMM, to improve the measurement accuracy of the AACMM for small mechanical parts. The measurement accuracy of the AACMM is examined under various measurement spaces. Firstly, the Monte Carlo method is used to simulate the measurement space of the AACMM with one or more joints locked. Then, the spatial error of the AACMM and the multipoint calibration with joint locked are simulated and discussed in detail. Finally, the feasibility and effectiveness of the proposed variable-measurement-space method are verified by the standard single-point cone experiments. The results show that the measurement accuracy of the AACMM is substantially improved under three kinds of strategies, i.e., locking joint 1, joint 2, and joint 3, respectively.