# 3D-Printed Bio-Inspired Mechanisms for Bird-like Morphing Drones
## 3 Results  
### Finite Element Analyses  
The two critical components in the proposed designs were optimized in SOLIDWORKS Simulation for the intended use and to guide the selection of servomotors that would actuate them. The first component is the outer wing PCTPE corrugated structure (Figure 2), and the second is the TPU flexible tail feather expansion structure (Figure 5b). The material properties used in the simulations are listed in Table 1. Due to the large deformations experienced, geometric nonlinearity was considered in solving both models to account for the change in stiffness as the structure is deformed. A convergence study was performed on each component before selecting a suitable mesh; ultimately, a biased mesh refined around smaller features was used. Due to symmetry, only half the tail structure was modeled, and appropriate symmetry boundary conditions were applied. The structure was fixed at the surface where it contacts the mounting bracket (Figure 5). The converged mesh included 35,194 3D solid elements, corresponding to 58,810 nodes. By applying a 10 mm prescribed displacement to the base of the central shaft, the outer crests extended their spread angle (defined here as the angle between the leftmost and rightmost feathers) from their normal 80\({}^{\circ}\) to 126\({}^{\circ}\), a 46\({}^{\circ}\) \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Young’s Modulus, \(E\) [MPa]** & **Poisson’s Ratio, \(\upsilon\)** & **Yield Strength, \(\sigma_{y}\) [MPa]** \\ \hline PCTPE & 73 & 0.392 & 73 \\ \hline TPU & 40 & 0.394 & 79.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of the used materials. Figure 5: (**a**) Tail morphing mechanism, (**b**) TPU compliant mechanism. increase (Figure 6a). Figure 6b shows the factor of safety (FOS) distribution under these conditions. The minimum FOS was 27.24 at one of the corrugations, indicating a safe design during feather expansion actuation. To reduce the feather spread angle by 45\({}^{\circ}\), multiple studies with various downward prescribed displacement values were performed. Only 6.6 mm of downward central shaft displacement was needed to reduce the feather spread angle from 80\({}^{\circ}\) to 35\({}^{\circ}\) (Figure 6c). In this case, the minimum FOS was 35.16 (Figure 6d), bringing the total tail feather spread actuation range from fully expanded to fully retracted to approximately 91\({}^{\circ}\) (126\({}^{\circ}-35^{\circ}\) = 91\({}^{\circ}\)). The reacting force on the base of the central shaft was 3 N in the feather expansion and 2.2 N in the feather retraction simulations. However, these forces apply to the half model and should be doubled for the full model. Hence, any servomotor providing an output force greater than 6 N is suitable for this mechanism if the stroke is \(\geq\)10 mm. Higher forces would ensure that any losses or applied loads would not alter the deformed shape of the structure. The selected micro servomotor could provide a torque of up to 4.8 kg.cm. A 1 cm servo horn was used to convert the rotational to linear motion, enabling a 10 mm stroke in both directions. The maximum force would then become \(F_{max}=T_{max}/r=4.8\times 9.81/1=47.1\) N. The minimum torque reported for this servomotor was 4 kg.cm, leading to a minimum force of \(F_{min}=T_{min}/r=4\times 9.81/1=39.2\) N. This relatively large actuation force, which was considerably higher than the required force for morphing (6 N), along with the 10 mm stroke corresponding to the maximum stroke needed for the desired deformed shape, justified the selection of the servomotor, which is also lightweight (8.5 g). Notably, the  
Figure 6: Resultant displacement (URES) and factor of safety (FOS) for the flexible tail feather expansion structure: **(a,b)** feather expansion, **(c,d)** feather retraction. The undeformed shapes appear in gray. aerodynamic transverse loads applied on the feather vanes would be transferred through the feather shafts to this structure.