## 4 Measurement Methods and Data Analysis
### Data Analysis
#### 4.2.3 Data Analysis at the Same Measurement Distance and Different Rotational Velocities  
When the measurement spacing is 3 m, we set different rotational velocities to calculate the dynamic indication error. Tables 3 and 4 shows the dynamic performance of the laser tracker at different rotational velocities, equal sampling frequency, and equal spacing when the measurement distance is 3 m. The dynamic indication error here is not the measurement result of the laser tracker at the dynamic limit rotational velocity of R\({}_{\text{L}}\). The following three conclusions can be drawn from the data analysis in Tables 3 and 4. Figure 11: Measurement distance and dynamic display value variable relationship diagram—(equal sampling frequency). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Equal Sampling Frequency**} & \multicolumn{2}{c}{**Equal Sampling Frequency**} & \multicolumn{2}{c}{**Equal Sampling Frequency**} \\ \multicolumn{2}{c}{**Rotational**} & \multicolumn{2}{c}{**(10 Hz)**} & \multicolumn{2}{c}{**(20 Hz)**} & \multicolumn{2}{c}{**(50 Hz)**} \\ \cline{2-7}
**Velocity (r/s)** & \multicolumn{1}{c}{**Dynamic**} & \multicolumn{1}{c}{**Number of**} & \multicolumn{1}{c}{**Dynamic**} & \multicolumn{1}{c}{**Number of**} & \multicolumn{1}{c}{**Dynamic**} & \multicolumn{1}{c}{**Number of**} \\
**Indication** & **Inference** & **Measurement** & **Indication** & **Inference(mm)** & **Points** & **Inference(mm)** & **Points** \\ \hline
0.2 & \(-\)0.0118 & 48 & \(-\)0.0097 & 96 & \(-\)0.0109 & 240 \\
0.6 & \(-\)0.0085 & 17 & \(-\)0.0079 & 33 & \(-\)0.0047 & 83 \\
1.0 & \(-\)0.0047 & 10 & \(-\)0.0117 & 20 & 0.0058 & 50 \\
1.4 & \(-\)0.0080 & 8 & \(-\)0.0148 & 15 & \(-\)0.0017 & 36 \\
1.8 & \(-\)0.0335 & 6 & \(-\)0.0121 & 12 & \(-\)0.0403 & 28 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dynamic performance of laser tracker at equal sampling frequency and different speeds (D = 3 m). (1) At low speed, the measurement spacing of sampling points is fixed proportionally to the number of measurement points. However, at high speed, the measurement spacing of sampling points is not proportional to the number of measurement points. Figure 12 shows the relationship between the rotation speed of the circular trajectory generator and the number of measuring points. With the increase in the rotational velocity of the circular trajectory generator, the gap between the actual value of the measurement spacing of the laser tracker and the theoretical value of the measurement spacing shows an increase. For example, if the rotational velocity of the circular trajectory generator is 0.2 r/s when the equal spacing is 5 mm, the number of measurement points of the laser tracker is 600, and when the equal spacing is 10 mm, the number of measurement points is 300. If the rotational velocity is 0.06 r/s when the equal spacing is 5 mm, the number of measurement points is 549, and when the equal spacing is 10 mm, the number of measurement points is 274. When the rotational velocity of the circular trajectory generator is set to 1.0 r/s, the measurement spacing of sampling points is still fixed proportionally to the number of measurement points. But this rule does not hold anymore when the rotational velocity is set to 1.4 r/s and 1.8 r/s. When the rotational velocity is 0.2 r/s, the distance between the actual measurement points is 5.21 mm and 10.47 mm if the equal spacing of the laser tracker is set to 5 mm and 10 mm. When the rotational velocity is 1.8 r/s, the distance between the actual measurement points is 11.33 mm and 11.39 mm if the equal spacing of the laser tracker is set to 5 mm and 10 mm.