A new method of calibration of coordinate measuring machines (CMMs) and multi-axis machine tools using a 2-D ball array is proposed in this paper. Combined with the use of a 3-D capacitive probe or a magnetic socket, this method can improve the efficiency of calibration greatly. A new kind of artifact called a 2-D ball array is proposed. The 2-D ball array combines the advantages of ball plate and 1-D ball array. Using the 2-D ball array, it is convenient to perform calibration and it is cost effective. Two methods are put forward for using a 2-D ball array in the calibration of the machines. The general method needs the 2-D ball array to be measured at only 4 different positions in the machine working zone, and the 21 parametric errors of the machine can be obtained. The second method is based on the error separation theory. By this method, information of the artifact can be fully utilized without the need to accurately a priori calibrate the artifact. These proposed methods can be used in the calibration and error compensation of CMMs and machine tools.

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