## 5 Case Study
### Assemblability Optimization  
The proposed method in Section 4 is taken to find the accuracy compensation schemes. The results are shown in Figure 13.  
Figure 13 shows the accuracy compensation schemes. The first point on the X axis is the KAC quantity to be compensated. The second point is the volume of the coordination zone of the scheme. The latter ones are the number of KACs. The Y axis is the scheme number. The Z axis is the value of the X axis. Seven connectors need to be adjusted to complete assembly in scheme 1. Finally, scheme 18, which needs nine connectors to be compensated, is taken by considering the assembly quality. The coordination space of the scheme is 56d. d is the volume of the maximum pose space divided by random times. In this case, d is \(2.46\times 10^{-14}\) mm\({}^{3}\)rad\({}^{3}\). The KAC number to be compensated is 5, 6, 8, 10, 12, 14, 18, 19, and 20. The center SDT of the coordination zone in scheme 18 is \(\left(-0.0363\text{ mm},0.0210\text{ mm},0.0098\text{ mm},2.52\times 10^{-6}\text{ rad},1.64\times 10^{-6}\text{ rad},-2.35\times 10^{-6}\text{ rad}\right)\).  
The deviation is calculated under the center SDT listed in Table 3.  
After simulation accuracy compensation for the above nine connectors, which is in bold and italics in Table 3 (the proposed method), the coordination space is 101d, which is greater than 0. The average coaxiality is 0.068 mm and the average clearance is 0.014 mm. The assemblability is good and the assembly can be executed directly.  
After simulation accuracy compensation for the above 10 connectors, which is in bold and italics in Table 2 (the least square method), the coordination space is 9d. The average coaxiality is 0.084 mm and  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **dr/mm** & **dc/mm** & **No.** & **dr/mm** & **dc/mm** \\ \hline
1 & 0.145 & 0.034 & 11 & 0.150 & \(-0.036\) \\
2 & 0.188 & \(-0.031\) & 12 & 0.351 & \(-0.013\) \\
3 & 0.169 & 0.064 & 13 & 0.142 & \(-0.022\) \\
4 & 0.151 & 0.031 & 14 & 0.391 & \(-0.286\) \\
5 & 0.230 & 0.004 & 15 & 0.133 & \(0.016\) \\
6 & 0.249 & 0.070 & 16 & 0.031 & \(-0.039\) \\
7 & 0.025 & 0.037 & 17 & 0.056 & \(0.032\) \\
8 & 0.222 & \(-0.034\) & 18 & 0.204 & \(-0.145\) \\
9 & 0.162 & \(-0.021\) & 19 & 0.204 & \(0.179\) \\
10 & 0.255 & \(-0.029\) & 20 & 0.233 & \(-0.027\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The deviations of the connectors.  
Figure 13: The accuracy compensation schemes.  
the average clearance is 0.014 mm. The assemblability is good but the assembly quality on coaxiality is worse.  
The result shows that the proposed method will generate a better accuracy compensation scheme with less workload and better assembly quality, which improves the assemblability.  
The measurement and connector adjustment process took about 8 h during the assembly. The pose adjustment process took about 2 h. Therefore, it took about 10 h in total based on the proposed method. The original assembly process took more than 20 h because the first trial assembly and accuracy compensation process cannot realize the re-trial assembly smoothly. Three or four times the assembly are needed to guarantee the assembly quality.