## 2 Materials and Methods
### Spatial Deformation Analysis Results  
The analysis results were divided into six parts: the main shaft located at the low, middle, and high points of the machine, and the main shaft in these points with a one-ton load of the processed objects placed onto the worktable. The first part shows the spindle located at 245 mm, that is, between the low point of the machine and worktable (no workpiece was placed on the worktable here). The analysis results are shown in Figure 8 which revealed that the values in the Z-direction were all negative. Hence, the distance between the spindle and the worktable was less than the ideal 245 mm, and that between the highest and lowest points was 0.046 mm. The second part shows the main shaft located at 245 mm, that is, between the low point of the machine and worktable (a ton of processed objects were placed on the worktable here). The analysis results shown in Figure 9. Which revealed that the values in the Z-direction were positive and negative. Thus, the distance between the spindle and worktable was greater than 245 mm in some points and lower than 245 mm in others, and the distance between the highest and lowest points was 0.137 mm. Figure 8: Schematic diagram of no load at the low point of the spindle. Figure 7: Worktable location. Compared to the results of the first part, the errors between points 1-5 in the first part were the largest, but those in the second part were the smallest. The error between the headstock and worktable was minimal. The third part shows the spindle located at 495 mm, that is, between the center of the machine and the worktable (no workpiece was placed on the worktable here). The analysis results shown in Figure 10 which revealed that the values in the Z-direction were all negative. Thus, the difference between the spindle and the worktable was less than the ideal 495 mm, and that between the highest and lowest points was 0.001 mm. The fourth part shows the main shaft located at 495 mm, that is, between the center of the machine and the worktable (a ton of processed objects were placed on the worktable). The analysis results shown in Figure 11. Which revealed that the values in the Z-direction were positive and negative. Hence, although the distance between the pointed spindle and worktable was greater than 495 mm in some points, in other points, it was lower than 495 mm. The distance between the highest and lowest points was 0.138 mm. Figure 10: Schematic diagram of no load at the midpoint of the spindle. Figure 9: Schematic diagram of the low point of the spindle with load. Compared to the results of the third part, the point errors of the third part were quite close. The errors of points 1-5 of the fourth part were the smallest, thereby reducing the error between the spindle and worktable. The fifth part shows the spindle located at 745 mm, that is, between the high point of the machine and the worktable (no workpiece was placed on the worktable here). The analysis results which shown in Figure 12 revealed that the values in the Z-direction were all negative. Consequently, the distance between the spindle and worktable was less than the ideal 745 mm, and that between the highest and lowest points was 0.008 mm. The sixth part shows the main shaft located at 745 mm, that is, between the center of the machine and the worktable (a ton of processed objects were placed on the worktable). The analysis results in Figure 13. Which revealed that some values in the Z-direction were positive, whereas others were negative. Hence, the distance between the spindle and worktable at some points was greater than 745 mm and lower than 745 mm, whereas that between the highest and lowest points was 0.138 mm. Figure 11: Schematic diagram of the load at the midpoint of the spindle. Figure 12: Schematic diagram of no load at the high point of the spindle. Comparing the results, we see that the point errors of the fifth part were quite close, but the errors for points 1-5 of the sixth part were the smallest.