# Research on Three-Dimensional Scanning Path Planning of Casing Parts Based on Industrial Robot
## 3 Scan Path Planning
### Repeat the Scan Area Compensation Method  
Substitute the measured casing height \(H\) = 60 cm into Equation (11) to obtain the number of scans, not the number of full turns. In the scanning process, the number of scans should also be rounded to achieve complete scanning reconstruction. In this paper, each circle's scanning height was adjusted to decrease the scanning area, and the repeated scanning area was divided into each ring. The corresponding scanning radius \(R_{i}\) will change, and the average coefficient \(v\) compensation method was used to compensate for the repeated scanning area. Taking the scanning casing as an example, there are:  
\[v=\frac{3-2.198}{3}=0.267 \tag{16}\]  
\[H_{iv}=H-H\times v \tag{17}\]  
According to Equations (3), (16) and (17), the distance between the scanner and the casing before and after scanning was obtained by adjusting the scanning height, as shown in Table 2.  
According to the data in Table 2, the corresponding position relationship diagram before and after scanning height adjustment is shown in Figure 9. It can be seen from Figure 9 that the adjusted \(H_{iv}\) is lower than the corresponding height H of the original scan, and the corresponding \(R_{iv}\) of the scan is lower than the original scan radius \(R\) as a whole.  
Using the above established circular scanning path-planning method, the relevant data of the scanning path before and after the scanning height adjustment were calculated as shown in Tables 3 and 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \(m_{i}\) & \(H_{i}\) & \(R_{i}\) & \(H_{iv}\) & \(R_{iv}\) \\ \hline \(i=1\) & 13.64 & 44.21 & 9.99 & 43.75 \\ \(i=2\) & 40.92 & 47.62 & 29.99 & 46.25 \\ \(i=3\) & 68.20 & 51.03 & 49.99 & 48.75 \\ \hline \end{tabular}
\end{table}
Table 2: The distance relationship between the scanner and the corresponding position of the casing before and after adjusting the scanning height (unit cm).  
\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 & 5.8\({}^{\circ}\) & 63 & 472.5 & 0 & 472.5 \\
2 & 6.2\({}^{\circ}\) & 59 & 487.74 & 27.49 & 487.74 \\
3 & 6.7\({}^{\circ}\) & 54 & 510.447 & 27.49 & 510.447 \\ Total & – & 176 & 1470.687 & 54.98 & 1525.67 \\ \hline \end{tabular}
\end{table}
Table 3: The relevant data of the casing scanning path before adjustment (in cm).  
If the scanning speed is \(v\) = 0.04 m/s and the posture adjustment time is \(t\) = 0.5 s/n, the total time to complete the casing scanning before and after the adjustment is as follows:  
\[\begin{cases}T_{\text{before}}=\dfrac{Q}{v}+Nt=381.4175+88=469.417\text{ s}\\ T_{\text{after}}=\dfrac{Q}{v}+Nt=373.375+91=464.375\text{ s}\end{cases} \tag{18}\]  
Through the analysis of the relevant data of the scanning path before and after the above scanning height adjustment it can be seen that the scanning range distribution can be changed by adjusting the scanning height, the complete scanning of the workpiece can be realized and the scanning quality is better than before the adjustment.