## 4 Calibration and Analysis of Rotation Axis Position Error
### Analysis of Average Position Error of A and C Axes
This revealed that the position error of the C-axis was affected by the rotation angle of  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Position of A/C Axes**} & \multicolumn{2}{c}{**A = \(-\)30\({}^{o}\)**} & \multicolumn{2}{c}{**A = 0\({}^{o}\)**} & \multicolumn{2}{c}{**A = 45\({}^{o}\)**} & \multicolumn{2}{c}{**A = 90\({}^{o}\)**} & \multicolumn{2}{c}{**C = 0\({}^{o}\)**} & \multicolumn{2}{c}{**C = 180\({}^{o}\)**} & \multicolumn{2}{c}{**C = 270\({}^{o}\)**} \\ \hline \multirow{6}{*}{Precision column 1} & \multirow{3}{*}{+X direction} & X & \(-\)542.852 & \(-\)542.558 & \(-\)542.838 & \(-\)543.228 & \(-\)542.558 & \(-\)349.362 & \(-\)82.458 & \(-\)276.223 \\  & & Y & 279.061 & \(-\)248.368 & \(-\)194.373 & \(-\)151.346 & \(-\)248.368 & 14.301 & \(-\)178.918 & \(-\)445.515 \\  & & Z & \(-\)152.402 & \(-\)124.420 & \(-\)117.968 & \(-\)155.992 & \(-\)124.420 & \(-\)127.283 & \(-\)125.500 & \(-\)126.748 \\  & & X & \(-\)522.888 & \(-\)522.478 & \(-\)522.650 & \(-\)522.478 & \(-\)329.562 & \(-\)63.072 & & \\  & & Y & \(-\)297.603 & \(-\)270.640 & \(-\)212.5393 & \(-\) — & \(-\)270.640 & \(-\)4.267 & \(-\)197.653 & — \\  & & Z & \(-\)152.402 & \(-\)124.419 & \(-\)117.968 & & \(-\)124.419 & \(-\)127.283 & \(-\)125.500 & \\ \cline{2-10}  & & X & \(-\)502.606 & \(-\)502.948 & \(-\)502.627 & \(-\)502.706 & \(-\)502.948 & \(-\)308.803 & \(-\)42.241 & \(-\)235.750 \\  & & Y & \(-\)276.389 & \(-\)253.204 & \(-\)195.493 & \(-\)151.723 & \(-\)253.204 & 16.877 & \(-\)176.624 & \(-\)446.369 \\  & & Z & \(-\)152.403 & \(-\)124.419 & \(-\)117.968 & \(-\)155.992 & \(-\)124.419 & \(-\)127.283 & \(-\)125.500 & \(-\)126.748 \\ \cline{2-10}  & & \multirow{3}{*}{-Z direction} & \multirow{3}{*}{-Z} & X & \(-\)523.182 & \(-\)522.553 & \(-\)521.928 & \(-\)523.408 & \(-\)522.553 & \(-\)329.052 & \(-\)62.126 & \(-\)255.644 \\  & & & Y & \(-\)278.313 & \(-\)249.902 & \(-\)193.589 & \(-\)151.722 & \(-\)249.902 & 15.898 & \(-\)175.944 & \(-\)46.370 \\  & & Z & \(-\)135.031 & \(-\)108.214 & \(-\)101.017 & \(-\)137.995 & \(-\)108.214 & \(-\)108.300 & \(-\)108.273 & \(-\)108.225 \\ \hline \multirow{6}{*}{Precision column 2} & \multirow{3}{*}{+X direction} & X & \(-\)356.170 & \(-\)356.154 & \(-\)356.159 & — & \(-\)356.154 & \(-\)92.175 & \(-\)264.277 & \(-\)528.390 \\  & & Y & \(-\)35.644 & \(4.713\) & \(-\)42.591 & — & 4.713 & \(-\)167.813 & \(-\)430.469 & \(-\)259.742 \\  & & Z & \(-\)61.554 & \(-\)167.678 & \(-\)328.667 & & \(-\)167.678 & \(-\)166.801 & \(-\)167.099 & \(-\)168.327 \\ \cline{2-10}  & & X & \(-\)338.678 & \(-\)338.865 & \(-\)339.574 & — & \(-\)338.865 & \(-\)75.173 & \(-\)247.467 & \(-\)510.274 \\  & & Y & \(-\)53.944 & \(-\)13.060 & \(-\)62.417 & — & \(-\)133.060 & \(-\)158.877 & \(-\)449.819 & \(-\)277.854 \\  & & Z & \(-\)61.554 & \(-\)146.275 & \(-\)328.668 & — & \(-\)164.275 & \(-\)166.801 & \(-\)167.09A-axis under actual situations. The reason for this could be the manufacturing accuracy of the two rotating axis components and the assembly clearance between them. The reason for this also could be that during the long-term operation of the machine tool, the A-axis was geometrically displaced due to uncertainty factors such as the weight of machine itself and the inertia of workpiece under high-speed motions [33]. Displacements indirectly affected the position error of the C-axis.