## 4 Measurement Methods and Data Analysis
### Data Analysis
#### 4.2.2 Data Analysis of Equal Sampling Frequency at Different Measurement Distances  
Table 2 shows the dynamic performance of the laser tracker when measuring at an equal sampling frequency. Under the same measurement distance, the dynamic limit speed of the laser tracker is a fixed value, so Table 2 does not list the dynamic limit speed of the laser tracker. For the different measurement frequencies, which were respectively 10 Hz, 20 Hz, and 50 Hz, the measurement position of sampling points shown in Figure 9 was described by the projection. We can obviously see that the measured data deviate significantly when the measurement frequency is 10 Hz. The following three conclusions can be drawn from the data analysis in Table 2.  
The dynamic indication error is smallest when the measurement distance is 5 m, indicating that the fitted diameter at a distance of 5 m is closest to the diameter of the circular trajectory generator. Figure 10 shows the relationship between measurement distance and dynamic indicating value error. For instance, when the measurement distance is 3 m, and the equal sampling frequency is set to 10 Hz, 20 Hz, and 50 Hz, the dynamic indication error is \(-\)0.0110 mm, \(-\)0.0107 mm, and \(-\)0.0060 mm, respectively. When the measurement distance is 5 m, and the equal sampling frequency is set to 10 Hz, 20 Hz, and 50 Hz, the dynamic indication error is \(-\)0.0034 mm, \(-\)0.0056 mm, and 0.0029 mm, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Measure-** \\ **Spacing** \\ **Error (mm)** \\ \end{tabular} } & \multicolumn{2}{c}{**Equal Sampling Frequency (10 Hz)**} & \multicolumn{2}{c}{**Equal Sampling Frequency (20 Hz)**} & \multicolumn{2}{c}{**Equal Sampling Frequency (50 Hz)**} \\ \cline{2-10}  & \begin{tabular}{c} **Dynamic** \\ **Indication** \\ **Error (mm)** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **Indication** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Number of** \\ **Measure-** \\ **Points** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **Indication** \\ **Error (mm)** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **Indication** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **Measure-** \\ **Parable** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **Indication** \\ **Error (mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Number of** \\ **Indication** \\ **Error (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Measure-** \\ **Parable** \\ **(mm)** \\ \end{tabular} \\ \hline \(1\) m & \(-\)0.0244 & 0.00428 & 14 & \(-\)0.0266 & 0.00448 & 27 & \(-\)0.0214 & 0.00440 & 66 \\ \(2\) m & \(-\)0.0145 & 0.00436 & 10 & \(-\)0.0176 & 0.00719 & 20 & \(-\)0.0137 & 0.00477 & 49 \\ \(3\) m & \(-\)0.0110 & 0.00796 & 8 & \(-\)0.0107 & 0.00596 & 16 & \(-\)0.0060 & 0.00659 & 40 \\ \(5\) m & \(-\)0.0034 & 0.00241 & 6 & \(-\)0.0056 & 0.00930 & 12 & 0.0029 & 0.00960 & 30 \\ \(10\) m & \(-\)0.0690 & 0.02296 & 5 & \(-\)0.0753 & 0.02553 & 9 & \(-\)0.1031 & 0.01694 & 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The dynamic performance of the laser tracker when measuring at different measurement distances and equal sampling frequency. Figure 8: Measurement distance and dynamic display value variable relationship diagram— (equally spaced). The dynamic indication variable increases as the distance increases. Under the same measurement distance, when the sampling frequency changes, the dynamic indication variable changes irregularly. For instance, when the equal sampling frequency is 50 Hz and the measuring distance increases, the dynamic indication variable is 0.00440 mm, 0.00477 mm, 0.00659 mm, 0.00960 mm, and 0.01694 mm, with an increasing trend in general. When the measurement spacing is 1 m, and the sampling frequency is 10 Hz, 20 Hz, and 50 Hz, the dynamic indication variable is 0.00428 mm, 0.00448 mm, and 0.00440 mm, showing an irregular change. Figure 11 shows the relationship between measured distance and dynamic indicating value error variate.