# Research on Three-Dimensional Scanning Path Planning of Casing Parts Based on Industrial Robot
## 3 Scan Path Planning
### Analysis of the Scan Path Parameters  
The casing geometry is shown in Figure 7, where the casing cone angle \(\beta\) is 7.125\({}^{\circ}\). According to the corresponding data after adjusting the scanning height in Table 4, the ring scanning radius \(R_{1}\) of the scanner in the first circle is 43.75 cm. In the process of annular scanning in the limited scanning area, the changes in related parameters such as \(\gamma\), \(A_{1}W_{1}\), \(A_{1}B_{1}\), \(A_{1}C_{1}\) and \(L\) in the scanning path are shown in Table 5. The relationship between the deflection angle and the scanning distance was plotted, as shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Order** & **Angle of** & **The Number** & **Surround** & **Rising Path** & **Total Path** \\
**Number** & **Deflection** & **of Postures** & **Path Length** & **Length** & **Length** \\ \hline
1 & 5.5\({}^{\circ}\) & 66 & 462 & 0 & 462 \\
2 & 6\({}^{\circ}\) & 60 & 487.2 & 20.15 & 507.35 \\
3 & 6.5\({}^{\circ}\) & 56 & 504 & 20.15 & 5245.1 \\ Total & & 182 & 1453.2 & 40.3 & 1493.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The relevant data of the casing scanning path after adjustment (in cm).  
Figure 9: Scanning height adjustment before and after scanning the corresponding position diagram.  
It can be seen from Table 5 that the deflection angle \(\gamma\) at 0-5\({}^{\circ}\) is an effective scanning range in the first circular scanning. When \(\gamma\) = 0\({}^{\circ}\), the scanner is in the standard position, and the distance between \(A_{1}C_{1}\) and \(A_{1}B_{1}\) and the scanner is equal. The laser beam at the boundary of the scanner is an isosceles triangle. It can be seen from Figure 10 that \(A_{1}W_{1}\) and \(A_{1}C_{1}\) increase with the increase in \(\gamma\). When the deflection angle \(\gamma\) is between 0-4\({}^{\circ}\), \(A_{1}B_{1}\) decreases with the increase in \(\gamma\). When the deflection angle \(\gamma\) is 4-5\({}^{\circ}\), \(A_{1}B_{1}\) increases with the increase in \(\gamma\).  
During the second and third rounds of scanning, the radius of the casing gradually increases, and the corresponding scanning radius and deflection angle increase to varying degrees. The data of the relationship between the deflection angle of the second and third turns and the scanning distance are shown in Tables 6 and 7, respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & \(\gamma\) & \(A_{1}B_{1}\) & \(A_{1}C_{1}\) & \(A_{1}W_{1}\) & \(L\) \\ \hline
1 & 0\({}^{\circ}\) & 34.56 & 34.56 & 30 & 0 \\
2 & 1\({}^{\circ}\) & 34.10 & 35.08 & 30.01 & 1.33 \\
3 & 2\({}^{\circ}\) & 33.72 & 35.70 & 30.06 & 2.66 \\
4 & 3\({}^{\circ}\) & 33.45 & 36.45 & 30.16 & 4.01 \\ \hline
5 & 4\({}^{\circ}\) & 33.29 & 37.38 & 30.35 & 5.35 \\
6 & 5\({}^{\circ}\) & 33.27 & 38.55 & 30.64 & 6.72 \\
7 & 6\({}^{\circ}\) & 33.42 & 40.04 & 31.06 & 8.12 \\
8 & 7\({}^{\circ}\) & 33.76 & 41.94 & 31.64 & 9.56 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Deflection angle and scan distance relationship data (second circle) (in cm).  
Figure 10: Curve diagram of the relationship between deflection angle and scanning distance.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & \(\gamma\) & \(A_{1}B_{1}\) & \(A_{1}C_{1}\) & \(A_{1}W_{1}\) & \(L\) \\ \hline
1 & 0\({}^{\circ}\) & 34.70 & 34.70 & 30 & 0 \\
2 & 1\({}^{\circ}\) & 34.23 & 35.25 & 30.01 & 1.29 \\
3 & 2\({}^{\circ}\) & 3 Figure 11 shows the relationship between the deflection angle, scanning radius and scanning distance in the second circular scanning. It can be seen from Figure 11 that when the scanner rises for scanning, the deflection angle \(\gamma\) increases with the increase in the corresponding scanning radius and the corresponding scanning path also increases.