## 4 Deployment Test
### Torque Margin Evaluation  
From the deployment test result, for all test cases the deployment of the truss-link mechanism was successful. However, we re-validated the EFTs with torque margin analy  
Figure 14: Comparison of the deployed motion history for case 3.  
sis [30]. If the torque margin was negative, the deployment would fail due to inadequate driving torque. If the torque margin was positive, the selected driving torque would be appropriate and completely deployed. To analyze this phenomenon, the torque margin was calculated as  
\[E_{D}^{90^{\circ}}=\int_{0}^{\frac{\pi}{2}}T_{D}d\theta \tag{17}\]  
\[E_{D}^{180^{\circ}}=\int_{0}^{\pi}T_{D}d\theta \tag{18}\]  
\[E_{R}^{90^{\circ}}=\int_{0}^{\frac{\pi}{2}}T_{R}d\theta \tag{19}\]  
\[E_{R}^{180^{\circ}}=\int_{0}^{\pi}T_{R}d\theta \tag{20}\]  
\[\textit{Torque Margin}=\left(\frac{E_{D}}{E_{R}}-1\right)\times 100(\%) \tag{21}\]  
where \(T_{D}\), \(T_{R}\) are the driving torque and the resistance torque of Joint O (90\({}^{\circ}\)) and Joint I (180\({}^{\circ}\)), respectively. Moreover, \(E_{D}\), \(E_{R}\) are the driving torque energy and the resistance torque energy value of Joint O and Joint I. The torque margin calculation results for Joint O and I are summarized in Tables 10 and 11. If the torque margin value was negative, then the deployment of panels at the corresponding joints would not be achieved. For the test cases, all torque margin values were positive. As seen in Figures 12-14, all the test cases were fully deployed. Through this evaluation, it can be predicted that the worst case cannot be deployed in advance. Therefore, the EFT estimation method developed in this work was verified with excellent reliability.  
expensive. As driving mechanisms, only conventional torsion spring hinges with proper latching mechanisms were employed in this work.  
To demonstrate the performance of the deployable structure with truss-links, a deployment simulation with the MBD model was conducted with proper joint modeling and rotational spring stiffness. Furthermore, a deployment test was conducted to check the correlation between the test and analysis. The results revealed that the time history of the deployment test was slightly behind that of the deployment analysis. To compensate for this, an inverse identification technique for equivalent friction torque (EFT) was proposed based on the results of the response surface method combined with the central composite design technique. Finally, with the EFTs, the angular rotation history in the deployment analysis was much closer to that of the deployment test with a trajectory error of less than 8%. Therefore, the adequacy of the proposed design of the deployable structure with truss-links was verified. This kind of truss-links mechanism has strong potential to extend a multi-modular deployable structure for small satellites. It will be further discussed in our future works.  
Conceptualization, J.H.L.; methodology, H.-S.C., T.S.J.; software, J.-H.P., H.-S.C.; validation, H.-S.C., J.-H.P.; investigation, D.-Y.K., H.-S.C.; data curation, H.-S.C.; writing--original draft preparation, J.H.L.; writing--review and editing, T.S.J.; supervision, J.H.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2018M1A3A02065478).  
Not applicable.  
The authors declare no conflict of interest.