# A Conceptual Design of Deployable Antenna Mechanisms
## 3 Results and Discussion
### Static Analysis of the Deployable Antenna Mechanism  
The mesh antenna is integrated with the net fixed part of the deployable antenna mechanism. To ensure the antenna exhibits the desired mechanical behaviors, the flatness of the mechanism must remain consistent. To validate the robustness of the proposed mechanism, the structural deformation is analyzed by applying the external loads generated by the tension from the mesh antenna. This analysis aims to identify how the mechanism can maintain its flatness under the given conditions, (e.g., under the influence of the tension forces), ensuring that the antenna can achieve its desired performance. Specifically, in a 6 m class double pantograph, the average tension in the nylon cable is 10 N, resulting in a reaction force of approximately 10.4 N acting on each bay of the upper and lower sections of the double pantograph [21]. Similarly, a tension of 10 N was applied to each point of the conical frustum-shaped deployable antenna mechanism. Moreover, similar to the given conditions imposed in the dynamic analysis, the simulation was performed under the assumption that one of 12 bays is fixed to the boom mechanism at the satellite.  
With these in mind, we assumed that the linkages of the deployable antenna mechanism were made of T-300 CFRP and that the joints were made of aluminum (AL6061). The material properties used in this simulation study are detailed in Table 1. This setup allows for an accurate analysis of how the mechanism responds to the tension from the mesh antenna, ensuring that it maintains the required structural integrity and performance.  
As a result of the static analysis, it is identified that the entire structure weight is 8.6 kg and that the stress distribution induced by the tension results in a maximum stress of 10.5 MPa, as depicted in Figure 4a. Specifically, in terms of deformation, each frame in the structure undergoes deformations along both the x- and y-axes, respectively. The maximum displacement in the x-axis direction is 0.8 mm, occurring at the upper part of the 6-bar linkage. The maximum displacement in the y-axis direction is 5.8 mm, observed at the V-folding bar. These results imply that the structure is likely to withstand the applied load of 10 N while maintaining its performance.  
Consequently, we can tentatively conclude, by comparing the static analysis results with dynamic analysis results, that the deployable antenna mechanism can exhibit a high area-to-mass ratio of 5.003 m\({}^{2}\)/kg without significant deformations. Notably, the areas of maximum stress likely occur at the linkages and joints, yet the structure can achieve a high safety factor of 323.8 (safety factor = tensile stress/maximum stress), ensuring its structural integrity under operational conditions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Materials** & **Density [g/cm\({}^{3}\)]** & **Elastic Modulus [GPa]** & **Poisson’s Ratio** & **Shear Strength** [MPa]** & **Tensile Strength** [MPa]** \\ \hline CFRP T-300 & 1.6 & 240 & 0.25 & 40 & 3400 \\ AL6061 & 2.7 & 68.9 & 0.33 & 207 & 276 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties employed at static simulation setup.