## 3 Experiments
The laser interferometer and autocollimator have to place three positions to measure \(X\)-axis, \(Y\)-axis, and \(Z\)-axis, respectively. The angle square actually requires three rotated measurements for XY-plane, YZ-plane, and XZ-plane. These three measuring instruments were employed to compare the measurement outcomes with the hole plate. We have incorporated a comparison of geometric errors between our experimental results in Figure 7 of the revised manuscript. As shown in Figure 7, the largest positioning error for Eyy is \(-0.30\)\(\upmu\)m, while the largest angular error for Ebx is \(-0.78\)\". Moreover, we measured the squareness error using both a hole plate and an angle square, resulting in deviations of 89.99843\({}^{\circ}\) and 89.99717\({}^{\circ}\), respectively. The difference in squareness error deviations for the Ecox after conversion is 4.54\". The results showed that the measurement accuracy of the hole plate was high and comparable to traditional standards, with a maximum difference of \(-0.30\)\(\upmu\)m for linear error, \(-0.78\)\" for angle error and 4.54\" for squareness error. Using the above described HTM, the maximum volumetric error was 2.70 \(\upmu\)m. As shown in Figure 8, the figure presents the DCC structure for the hole plate measurement results of a CMM. The geometric position error of the measurement results was converted into XML for machine readability. The measurement results of the geometric error of the three linear axes of the CMM were obtained by measuring a hole plate. The results indicate that there are six geometric errors for every axis, with one error value for every 50 mm. The word Model presented in Figure 9 can correspond to the word <model>Model:</model> of the XML in Figure 8, and PMM-C Ultra can also correspond to the XML code of <value>PMM-C Ultra</value>. The figure illustrates the measurement results of the geometric errors for a range of distances from 0 mm to 550 mm, with measurements taken at 50 mm intervals, resulting in a total of 12 errors for each geometric parameter. In addition, there are three geometric error values for squareness. Overall, the measurement data were exported in PDF format for easy reading and use by users. These findings highlight the importance of regularly calibrating CMMs to ensure their accuracy and the production of high-quality products. Figure 6: (**a**) Experimental setup of the autocollimator (**b**) Experimental setup of the laser interferometer (**c**) Experimental setup of the angle square. Figure 8: Measurement results of (**a**) \(X\)-axis, (**b**) \(Y\)-axis, (**c**) \(Z\)-axis, and (**d**) Squareness error of CMM in XML type. Figure 7: (**a**) Measurement results for positioning error of the CMM using the hole plate and laser interferometer; (**b**) Measurement results for angular error of the CMM using the hole plate and autocollimator. The uncertainty evaluation of the hole plate measurement method is based on the ISO Guide to the Expression of Uncertainty in Measurement (GUM) [47]. Table 1 shows the uncertainty budget for the measured hole plate method. Some influence quantities are directly measured and estimated, called Type A. Other influence quantities use specification knowledge to estimate using a set of probability distributions, called Type B.