# Laser R-Test for Angular Positioning Calibration and Compensation of the Five-Axis Machine Tools
## 6 Conclusions  
The measurement system was for angular positioning calibration and compensation of the five-axis machine tools. In this study, the uncertainties of the system are confirmed by using the Laser R-test and attempting to improve the angular error of rotary axes through compensations. The estimated uncertainty predictions and the observation in the measured results are satisfactory to each other. In order to prove the feasibility of this method, the experiments are executed including measurements, compensations, and verifications. The process ends up on actual workpieces with an angular error of 0.0121 degrees for the Laser R-test. Based on the measurement method, the system could avoid concentricity problems between instruments and the rotary table. The Laser R-test could be installed one time to measure both the C-axis and A-axis instead of re-installing components, because the measurement method simultaneously measures operations of both translational axes and rotary axes during sampling. Thus, the measured results are close to actual machining conditions and more reliable, but that means the translational axis calibrations and compensations are required using other measurement systems. That makes the system dependent; in other words, there is a limitation for cases where only the angular positioning calibration is required, and then, the system is not appropriate. However, those benefits of the system could improve the qualities and efficiency of the CNC machine tools, optimizing the process, especially for a full calibration that is required on all machine tools, including five-axis machine tools, before launching it to the market.  
Conceptualization, C.-S.T., T.-H.H. and W.-Y.J.; data curation, C.-S.T. and T.-H.H.; formal analysis, C.-S.T. and W.-Y.J.; funding acquisition, T.-H.H. and W.-Y.J.; investigation, C.-S.T. and W.-Y.J.; methodology, C.-S.T., T.-H.H. and W.-Y.J.; project administration, C.-S.T., T.-H.H. and W.-Y.J.; resources, C.-S.T., T.-H.H. and W.-Y.J.; software, C.-S.T.; supervision, [PERSON]-H.H. and [PERSON]-[PERSON]; validation, C.-S.T., T.-H.H. and W.-Y.J.; visualization, C.-S.T., T.-H.H. and W.-Y.J.; writing--original draft, C.-S.T.; writing--review & editing, C.-S.T. and T.-H.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Ministry of Science and Technology (MoST), grant number MOST-110-2218-E002-039.  
Not applicable.  
This research was funded by the Ministry of Science and Technology (MoST) of the Republic of China, Taiwan, and the authors gratefully express their sincere acknowledgement to MoST.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Laser R-Test** & **XR-20** & **Deviation** \\ \hline Radius & & 200 mm & 200 mm & - \\ \hline Measurement & C-axis & 30 degrees & 30 degrees & - \\ pitch & A-axis & 10 degrees & 10 degrees & - \\ \hline Repeatability & & 4.32 arcsec & 5.5 arcsec & 1.18 arcsec \\ \hline Error on Actual & Absolute & 0.0121 degrees & 0.0143 degrees & 0.0022 degrees \\ workpieces & Relative & 0.0056 degrees & 0.0046 degrees & 0.001 degrees \\ \hline \hline \end{tabular}
\end{table}
Table 2: System specification summary.