## 3 Experimental Results and Analysis  
### Measurement Experiments of 21 Geometric Errors  
In order to verify the effectiveness of the above key error identification method, the 21 geometric errors of the vertical machine tool TH5656 are measured beforehand using our developed measurement system [21], as depicted in Figure 1. This system mainly consists of the laser source, the sensor head, the 18-error sensing target and beam-steering device. In the 18-error sensing target, three mutually perpendicular six-error sensing components have been assembled; each component is sensitive to the six geometric errors for the \(X\)-, \(Y\)-, and \(Z\)-axes, respectively. The beam-steering device features a pentaprism as its primary component. By introducing the pentaprism into the optical path and rotating it 90 degrees via a translation stage and a turntable, the measuring beams can be parallel to the \(Y\)- and \(Z\)-axes, respectively. Thus, this system allows simultaneous and precise measurement of the six-degree-of-freedom geometric errors of a linear guide. By precisely controlling the measuring beam to rotate 90\({}^{\circ}\) and utilizing a specially designed target, the 18 errors of the three linear axes can be directly sensed. Consequently, all 21 geometric errors are obtained through a one-step installation and a three-step automated measurement. Before the measurement process, by adjusting the sensor head, the beam-steering device, and the 18-error sensing target, the beams along the \(X\)-, \(Y\)-, and \(Z\)-axes are all in the measuring range of the detectors. The installation and adjustment time is about 30 min. The measured distances are 400 mm, 140 mm, and 175 mm for the \(X\)-, \(Y\)-, and \(Z\)-axes of the TH5656, respectively, and the measurement intervals are 50 mm, 20 mm, and 25 mm, respectively. The measuring time for the three linear axes is about 5 min. The total time for measuring the TH5656 is about 35 min. A Renishaw XL-80 laser interferometer is used for comparison. It is noted that the roll cannot be measured by the interferometer, and an electronic level (Qianshao WLII, accuracy 0.2 arcsec) is used for roll comparison, thus the roll of the vertical axis cannot be measured by the electric level. Since the different components need to be installed for each error measurement, the interferometer needs to be readjusted. The total time for measuring 20 errors of the TH5656 is about 680 min. Compared with the laser interferometer and electronic level, the measuring time of the developed system saves nearly 11 h and greatly improves measurement efficiency. Table 2 shows the measurement results of the 21 geometric errors of the three linear axes of the TH5656 obtained by the developed system. These results refer to the difference between the maximum and minimum measurement values for each error component. Figure 2 shows the comparison results of three kinds of errors on different axes. The maximum comparison deviations are 0.43\({}^{\prime\prime}\), 0.24 \(\upmu\)m, and 0.65 \(\upmu\)m for yaw, position error, and straightness, respectively. It can be observed that the accuracy of the proposed system is equivalent to that of the interferometer. Furthermore, the laser interferometer has long measurement period, during which the measurement environment undergoes changes, leading to a decrease in comprehensive accuracy. In contrast, the proposed high-efficient measurement method not only significantly reduces the time required for machine tool measurements, but also ensures higher comprehensive measurement accuracy.