## 3 Comprehensive Evaluation of Configuration
### Mechanism Performance Indicators
Consequently, the type and number of joints significantly influence the transmission performance of the kinematic chain. Once the original moving parts and the frame are established, the efficiency of each drive loop can be calculated separately to facilitate the preliminary selection of the mechanism configuration. The jointtransmission efficiencies can be represented in the following matrix (Equation (7)) for the mechanism configuration. \[\eta= \begin{bmatrix}\eta_{11}&\eta_{12}&\cdots&\eta_{1n}\\ \eta_{21}&\eta_{22}&\cdots&\eta_{2n}\\ \cdots&\cdots&\cdots&\cdots\\ \eta_{11}&\eta_{12}&\cdots&\eta_{1n}\end{bmatrix}  \tag{7}\]  
Each row in the matrix represents the transmission efficiency of each joint within its respective independent loop, progressing from the original moving part to the output member. In this context, \(n\) denotes the maximum number of joints for each independent loop; for loops containing fewer than \(n\) joints, the remaining components are filled with a value of 1. The transmission efficiency of each independent loop can be calculated using Equation (8). \[\eta_{1}=\eta_{11}\eta_{12}\eta_{1m} \tag{8}\]  
For the multi-loop mechanism with \(l\) outputs, the overall transmission efficiency of the mechanism can be calculated by averaging the transmission efficiencies of the independent branches. It can be computed as per Equation (9). \[\eta=\frac{\eta_{1}+\eta_{2}+\cdots+\eta_{l}}{l} \tag{9}\]  
Let the transmission efficiency of the translational joint be 0.97 and that of the revolute joint be 0.98. As illustrated in Figure 7e, the overall joint transmission efficiencies for each configuration in Figure 5 can be calculated accordingly. The obtained performance indicators for each configuration are indicated in Table 4. In summary, Figure 7a illustrates that conformations (p) and (q) are more compact, while conformations (k), (l), and (m) are less so. Figure 7b indicates that configuration (o) has higher constitutive stiffness, in contrast to configuration (m), which demonstrates lower stiffness. Figure 7c shows that configurations (c), (n), and (o) possess lower sensitivity values, correlating with superior dynamic performance, whereas the other configurations exhibit higher sensitivity values and, consequently, poorer dynamic performance. Figure 7d reveals that configuration (o) has a lower KIC value, facilitating its kinematic analysis, while configuration (h) has a higher KIC value, leading to a more complex analysis. Finally, Figure 7e indicates that configuration (o) offers greater joint transmission efficiency, while configuration (g) presents lower efficiency. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Configuration** & \(\mathbf{L}\) & \(\mathbf{K}\) & \(\mathbf{D}\) & \(\mathbf{KIC}\) & \(\mathbf{\eta}\) \\ \hline (a) & 102 & 1.673 & 2 & 16 & 0.889 \\ (b) & 100 & 1.587 & 2 & 17 & 0.883 \\ (c) & 100 & 1.845 & 1 & 14 & 0.901 \\ (d) & 104 & 2.045 & 2 & 17 & 0.883 \\ (e) & 104 & 1.962 & 2 & 13 & 0.907 \\ (f) & 104 & 1.864 & 2 & 15 & 0.895 \\ (g) & 104 & 1.812 & 2 & 17 & 0.882 \\ (h) & 106 & 1.5 & 2 & 18 & 0.877 \\ (i) & 106 & 1.758 & 2 & 14 & 0.901 \\ (j) & 106 & 1.725 & 2 & 16 & 0.889 \\ (k) & 108 & 1.812 & 2 & 15 & 0.895 \\ (l) & 108 & 1.745 & 2 & 15 & 0.895 \\ (m) & 108 & 1.323 & 2 & 17 & 0.883 \\ (n) & 102 & 1.689 & 1 & 16 & 0.895 \\ (o) & 102 & 2.4 & 1 & 12 & 0.913 \\ (p) & 96 & 1.943 & 2 & 14 & 0.901 \\ (q) & 96 & 1.589 & 2 & 16 & 0.889 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance metrics for multi-wing deployment mechanism configurations.