## 6 Conclusions  
In this paper, a method to identify geometric deviations which exist in multi-tasking machine tools on the basis of the trajectories of simultaneous three-axis control motions is investigated. The proposed method is applied to a multi-tasking machine tool with a swivel tool spindle head in horizontal position and the identification of the deviations is carried out. From the numerical experiments, the validity of the proposed identification method is clarified. Conclusions are summarized as following. 1. The identification method for 12 geometric deviations, in which two squareness deviations of translational axes \(\alpha_{\text{YZ}}\) and \(\beta_{\text{YZ}}\) are included, is proposed. 2. From the simulation results, it is confirmed that in order to eliminate the influence of the mounting errors of the W-side ball on the eccentricities of the circular trajectories, measurements for the B axis should be performed in Cartesian coordinate system and those for the C axis should be performed in cylindrical coordinate system. 3. Considering the squareness of translational axes, six measurements by means of the ball bar are necessary to identify twelve geometric deviations. 4. The results of numerical experiments agree well with the given intentional deviations. Therefore, the influence of the analysis accuracy of the formulae on the identification could be considered to be negligible. It can be concluded that the proposed identification method and the measurement procedure can be sufficiently utilized to identify geometric deviations for multi-tasking machine tools, in which the squareness of translational axes is taken into consideration. At the next stage, the validity of the proposed method will be verified by an actual measurement of a multi-tasking machine tool. According to the proposed identification method, six measurements by using a ball bar will be conducted firstly and the eccentricities in each translational axis are obtained. Then, 12 geometric deviations of the considered machine tool will be calculated based on the formulae proposed in this paper. Finally, the measurements by a ball bar will be conducted again with compensation of deviations. If the eccentricities would disappear after the compensation, it can be \begin{table}
\begin{tabular}{c c c c c c} \hline
**Direction** & \multicolumn{3}{c}{**B Axis (\(\mu\)m)**} & \multicolumn{3}{c}{**C Axis (\(\mu\)m)**} \\ \hline  & \(\mathbf{X^{a}}\) & \(\mathbf{Y^{a}}\) & \(\mathbf{Axial^{a}}\) & \(\mathbf{Radial^{a}}\) & \(\mathbf{Radial^{b}}\) & \(\mathbf{Radial^{c}}\) \\ \hline \(ex\) & 16.63 & \(-\)11.24 & 0.29 & 25.73 & 26.89 & 28.97 \\ \(ey\) & - & - & 0.05 & \(-\)19.59 & \(-\)20 & \(-\)23.26 \\ \(ez\) & \(-\)4.02 & 10.05 & - & - & - & - \\ \hline \end{tabular}  
* \({}^{\text{a}}\)\({}^{\text{R}}_{\text{B}}\) = 360 mm; \(Z_{\text{C}}\) = 300 mm; \({}^{\text{b}}\)\(Z_{\text{C}}^{\text{r}}\) = 340 mm; \({}^{\text{c}}\)\({}^{\text{R}}_{\text{B}}\) = 410 mm.  
\end{table} 
Table 6: Eccentricities of circular trajectories in numerical experiments. \begin{table}
\begin{tabular}{c c c c} \hline  & **Initial Values** & **Identified Values** & **Difference** \\ \hline \(\delta x_{\text{BT}}\) (\(\mu\)m) & 11.00 & 10.96 & \(-\)0.04 \\ \(\delta z_{\text{BT}}\) (\(\mu\)m) & 17.00 & 16.63 & \(-\)0.37 \\ \(\alpha_{\text{BT}}\) (\(\arcsec\)) & 7.63 & 7.69 & 0.06 \\ \(\alpha_{\text{XB}}\) (\(\arcsec\)) & 3.51 & 3.44 & \(-\)0.07 \\ \(\beta_{\text{XB}}\) (\(\arcsec\)) & 3.92 & 3.80 & \(-\)0.12 \\ \(\gamma_{\text{XB}}\) (\(\arcsec\)) & 6.39 & 6.44 & 0.05 \\ \(\alpha_{\text{YZ}}\) (\(\arcsec\)) & 2.27 & 2.32 & 0.05 \\ \(\beta_{\text{YZ}}\) (\(\arcsec\)) & 4.74 & 4.79 & 0.05 \\ \(\delta x_{\text{CZ}}\) (\(\mu\)m) & 13.00 & 13.01 & 0.01 \\ \(\delta y_{\text{CZ}}\) (\(\mu\)m) & 7.00 & 6.96 & \(-\)0.04 \\ \(\alpha_{\text{CZ}}\) (\(\arcsec\)) & 2.06 & 2.11 & 0.05 \\ \(\beta_{\text{CZ}}\) (\(\arcsec\)) & 5.98 & 5.98 & 0.00 \\ \hline \end{tabular}  
\end{table} 
Table 7: Difference between initial values and identified values.