# A Conceptual Design of Deployable Antenna Mechanisms
## 3 Results and Discussion  
### Dynamic Analysis of the Deployable Antenna Mechanism  
To better understand the dynamic characteristics and feasibility of the deployable antenna mechanism, a simulation study was performed using Recurdyn (Recurdyn, 2024, FunctionBay, Republic of Korea) software. Figure 3 shows the dynamic characteristics of the deployable antenna mechanism. We assumed that one of 12 bays is fixed to the boom mechanism at the satellite, with the bottom net fixed joint of the first bay set under fixed conditions. As the driving joint of the 6-bar mechanism moves linearly along the z-axis, the upper and bottom net fixed joints move, resulting in the enlargement of the areas at the top (\(\Delta Area_{top}\)) and bottom (\(\Delta Area_{bottom}\)), as denoted in Figure 3b. Note that, due the presence of the 6-bar linkage mechanism, differences between the area at the top and the bottom occur, resulting in a conical frustum morphology with a unique tapered angle. Indeed, the 12 bays, created by the 6-bar mechanism and single pantograph mechanism, exhibit the desired kinematic trajectories (See Figure 3a and Supplementary Video S1). Specifically, as plotted in Figure 3c, the area at the top continuously increases up to 173 m\({}^{2}\) for the given deployment time (6 s), yet the area at the bottom increases until 4.8 s, up to 133 m\({}^{2}\), and then does not vary till 6 s. In light of these findings, the difference between the two areas at the top and bottom is 40 m\({}^{2}\), resulting in a tapered angle of 68\({}^{\circ}\). By tracking the position of the upper net fixed part, we observed that the mechanism expands from an initial stowed configuration with a diameter of 466 mm to a maximum deployed diameter of 7430 mm, depending on the movement of the driving joint.  
Figure 3: Dynamic simulation results. (**a**) Sequential results of the deployable antenna mechanisms, with steps of 1.2 s. (**b**) A schematic of the deployable antenna mechanism, showing the variation in height (\(\Delta H\)) and the variation in areas at the top and bottom (\(\Delta Area_{top}\), \(\Delta Area_{bottom}\)), respectively. (**c**,**d**) Responses of the area and displacement (variation in height between the upper and bottom net fixed joints) with respect to the deployment time. (**e**) Deviations in the displacement variation of each node, indicating the distance between the upper and bottom net fixed joints.  
Figure 3d shows the displacement analysis of the upper net fixed part with respect to each bay that constitutes the entire deployment mechanism. The result indicates that the upper and bottom net fixed joints of each bay exhibit identical displacements, which corresponds to the variation in height of the entire structure. Specifically, the displacement increases up to 0.6 m from 0 to 3.3 s and decreases to 0.4 m at the fully deployed state (6 s). In addition to this result, Figure 3c shows the deviation of the displacement that each bay exhibits, confirming that each unit is synchronized and operates with a single degree of freedom, as controlled by the single pantograph mechanism (standard deviation of 1.25).