# Research on a Dynamic Calibration Method for Photogrammetry Based on Rotary Motion
## 3 Calibration System Design Error Analysis  
The calibration system proposed in this paper mainly introduces dynamic motion parameters based on fixed target points to realize the calibration of dynamic parameters. Therefore, the measurement accuracy of the control field's marker point and the rotating rod's target point as a static and fixed relative position measurement is higher than that of static photogrammetric measurement by more than 10 times, and its influence on the dynamic parameter calibration can be ignored. Therefore, the circular trajectory generator is a key standard device for providing dynamic displacement in the circumferential direction, and its uniform rotational speed error directly affects the dynamic circular position. For a uniform angular motion, the timed angle measurement method can be used to analyze the speed error, that is, to measure the angle that the turntable rotates in standard time. Alternatively, the fixed-angle timing method can be used, which measures  
Figure 1: Calibration system’s schematic diagram. the time it takes for the turntable to rotate through a certain angle. The latter generally travels the distance in one cycle and evaluates the stability of the turntable in a short time. For the former method, the turntable usually rotates for several cycles, and relevant equipment, such as a frequency meter, is used to measure the elapsed time, which represents the stable performance of the turntable in a long time. Considering the sensitivity of the photogrammetry system calibration to the position accuracy, this paper adopts the fixed-angle time measurement method to calibrate and test the rotational speed error of the device. There are space marks that are evenly distributed at the radius R = 500 mm of the disc installed on the turntable. When the photodetector passes through space, a high-level voltage signal will be generated, and the space between the marks is 10\({}^{\circ}\) (\(\pi\)/18). The turntable is set to create a constant speed circle at 25 rpm (2.6 rad/s), 50 rpm (5.2 rad/s), 100 rpm (10.5 rad/s), and 200 rpm (20.9 rad/s) at the same ratio, which is two times the speed range. For motion, the maximum rotational speed is calculated by measuring a value 1.2 times of the limit dynamic parameters of the photogrammetry system. The photodetector is used to record the rotational angle of the turntable, and the oscilloscope is used to record the waveform and time, as shown in Figures 2-5. The comparison data (the actual movement speed \(\omega\) and the relative velocity error \(\delta\)) between the different rotational speeds are shown in Table 1.  
At 25 rpm, the actual movement speed of the turntable from the time and angle interval and the relative velocity error are calculated as follows:  
\[\omega=\frac{\pi/18}{0.0667s}=24.99\ \mathrm{rpm}, \tag{1}\]  
\[\delta=\frac{\left|25-24.99\right|}{25}\times 100\%=0.04\%, \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline  & **n = 25 rpm** & **n = 50 rpm** & **n = 100 rpm** & **n = 200 rpm** \\ \hline \(\omega\) & 24.99 rpm & 49.98 rpm & 100.10 rpm & 200.80 rpm \\ \(\delta\) & 0.04\% & 0.04\% & 0.10\% & 0.40\% \\ \hline \end{tabular}
\end{table} 
Table 1: The comparison data between different rotational speeds. Figure 2: The 25 rpm oscilloscope waveform. At 50 rpm, the actual movement speed of the turntable from the time and angle interval and the relative velocity error are calculated as follows:  
\[\omega=\frac{\pi/18}{0.03335\mathrm{s}}=49.98\ \mathrm{rpm}, \tag{3}\]  
\[\delta=\frac{|50-49.98|}{50}\times 100\%=0.04\%, \tag{4}\]  
At 100 rpm, the actual movement speed of the turntable from the time and angle interval and the relative velocity error are calculated as follows:  
\[\omega=\frac{\pi/18}{0.01665\mathrm{s}}=100.10\ \mathrm{rpm}, \tag{5}\]  
\[\delta=\frac{|100-100.10|}{100}\times 100\%=0.10\%, \tag{6}\]  
Figure 4: The 100 rpm oscilloscope waveform. Figure 3: The 50 rpm oscilloscope waveform.