# A Geometric Error Measurement System for Linear Guideway Assembly and Calibration
## 4 System Verification
### Application of Proposed System  
The proposed system was used in several Taiwanese domestic machine tool and precision stage manufacturer. The application included straightness, perpendicularity, and parallelism measurement.  
The first case was for the straightness measurement of machine tool in fabrication site. We compared the proposed system with commercial straightness measurement equipment (ProLine, Status Pro Maschinenmessstechnik GmbH, Bochum, Germany). Total measurement range was 6000 mm, the application setup is shown in Figure 20, the proposed system installed in parallel with the ProLine on the saddle of the machine tool. The measurement results are shown in Table 5.  
The second case was for the straightness measurement of double-column machine tool. We compared the proposed system with commercial laser interferometer (5529A, Agilent Tech., Santa Clara, CA, USA). The total measurement range was 2000 mm; the application setup is shown in Figure 21. The measurement results are shown in Table 6.  
Figure 21: Case 2 straightness error measurement setup on double column machine tool, (**a**) the double column machine tool and (**b**) the setup of 5529A laser interferometer straightness module and proposed system.  
Figure 20: Case 1 straightness error measurement setup.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Straightness Error (Horizontal)**} & \multicolumn{2}{c}{**Straightness Error (Vertical)**} \\ \hline ProLine & 16 μm & 16 μm \\ Proposed system & 13.97 μm & 11.21 μm \\ \hline \hline \end{tabular}
\end{table}
Table 5: Case 1 straightness error measurement results.  
The third case was for the perpendicularity measurement of AOI equipment. In this case, the reference measurement value was provided by the third company with the inspection square (triangular) (1200 mm grade 0, OPUS, Taoyuan, Taiwan). The total measurement range was 1100 mm; the application setup is shown in Figure 22. The measurement results are shown in Table 7.  
The fourth case was for the parallel error measurement of the machine tool. In this case, the fourth company provided the reference measurement value. The total measurement range was 1600 mm; the application setup is shown in Figure 23. The measurement results are shown in Table 8.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Straightness Error (Horizontal)** & **Straightness Error (Vertical)** \\ \hline
5529A & 34 \(\upmu\)m & 24 \(\upmu\)m \\ Proposed system & 36 \(\upmu\)m & 28 \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table}
Table 6: Case 2 straightness error measurement results.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Two-Axis Perpendicularity** & **Two-Axis Perpendicularity** \\  & **Displacement Error** & **Angle Error** \\ \hline Inspection square (triangular) & 5 \(\upmu\)m/1.1 m & N/A \\ Proposed system Y1\_L\_X & 14.3 \(\upmu\)m/1.1 m & 2.68 arcsec \\ Proposed system Y2\_L\_X & 14.1 \(\upmu\)m/1.1 m & \(-\)2.66 arcsec \\ \hline \hline \end{tabular}
\end{table}
Table 7: Case 3 perpendicularity error measurement results.  
Figure 22: Case 3 perpendicular error measurement setup. (**a**) The Automated optical inspection (AOI) equipment to be measured, (**b**) the inspection square (triangular) measurement setup, (**c**) the Y1\_LX measurement setup of proposed system, and (**d**) the Y2\_LX measurement setup of proposed system.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parallelism Angle Error** & **Parallelism Displacement Error** \\ \hline Company & 3.3 arcsec & 16 \(\upmu\)m/1.6 m \\ Proposed system & 1.09 arcsec & 5.29 \(\upmu\)m/ 1.6 m \\ \hline \hline \end{tabular}
\end{table}
Table 8: The parallelism error measurement results.