## 3 Experiments  
### Verification of the Evaluation Method of the Angular Misaligments of a Small Cylinder  
Experiments were carried out to verify the feasibility of the proposed technique for evaluation of the angular misalignments of the workpiece in roundness measurement of a small cylinder by the stitching linear-scan method. In the following verification experiments, a calibrated pin gauge with a diameter of 3.000 mm was employed as the measurement specimen. At first, basic characteristics of the proposed technique for the evaluation of \(\theta_{X}\) were investigated in experiments. Figure 11 shows a schematic of the experimental setup. Experimental conditions are summarized in Table 1. The axis of a small cylinder was aligned to be parallel with the scanning direction of the surface form stylus profilometer (\(X\)-axis in the figure). A commercial autocollimator was employed as the reference angle sensor for measurement of the angular displacement of the workpiece holder. A flat mirror was employed as the target for the commercial autocollimator and was mounted on the workpiece holder. The workpiece holder surface was scanned by the surface form stylus profilometer to obtain the inclination angle \(\theta_{\text{Scan},Y}\) of the workpiece holder surface with respect to the datum surface of the surface form stylus profiler. Figure 11: Setup for the verification of the method for measurement of \(\theta_{X}\). Figure 10: Evaluation of the angular misalignment \(\theta_{Z}\) of a small cylindrical workpiece about the \(Z\)-axis: (**a**) before shifting; (**b**) after shifting. Figure 12a shows an example of the obtained surface profile of the workpiece holder. From the obtained profile data, the inclination angle \(\theta_{\text{Scan\_Y}}\) was obtained through the linear fitting by the least-squares method. Ten repetitive trials, including the demounting and remounting operations of the holder unit at each trial, were made to evaluate the reproducibility. Figure 12b shows the results. The standard deviation of \(\theta_{\text{Scan\_Y}}\) was evaluated to be 0.005\({}^{\circ}\). Following the verification of the measurement reproducibility, an attempt was made to detect the angular displacement of the workpiece holder. By using the tilt stage, the workpiece holder was rotated about the \(Y\)-axis in steps of approximately 0.005\({}^{\circ}\), and the angular displacement of the workpiece holder was evaluated by both the proposed method and the commercial autocollimator at each step. It should be noted that the scanning length of the stylus profilometer for evaluation of \(\theta_{\text{Scan\_Y}}\) was set to be 5 mm. Figure 13 shows the results. As can be seen in the figure, the maximum deviation of the detected \(\theta_{\text{Scan\_Y}}\) from the reading of the autocollimator was less than \(\pm\)0.002\({}^{\circ}\). These experimental results demonstrated the feasibility of the proposed technique of measuring \(\theta_{\text{Scan\_Y}}\). Experiments were also carried out to evaluate the basic characteristics of the proposed technique for the evaluation of \(\theta_{Z}\). Figure 14 shows a schematic of the experimental setup. The pin gauge was first attached to a round magnet and was then placed on the V-groove in the workpiece holder. The axis of the workpiece was aligned to be parallel with the \(Y\)-axis so that its arc-profiles could be measured by the stylus profilometer. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Items** & **Value** & **Unit** \\ \hline Tip angle of a stylus & 60 & degree \\ Tip radius of a stylus & 2 & \(\mu\)m \\ Probe scanning speed & 0.1 & mm/s \\ Measuring force & 1.0 & mN \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for scanning experiments. Figure 12: Evaluation of the \(\theta_{X}\) and its reproducibility: (**a**) measured profile of the workpiece holder; (**b**) reproducibility of the evaluation of \(\theta_{X}\). Figure 13: The angular displacement of the workpiece about the \(X\)-axis measured by the proposed technique.