# Analysis of Motion Characteristics of Bionic Morphing Wing Based on Sarrus Linkages
## 3 Results  
### Simulation Motion Analysis and Optimization Design of Morphing Wing  
In the process of motion simulation, it can be seen that the morphing wing designed in this paper can smoothly complete folding and unfolding motion. Due to the motion characteristics of the steering engine, the morphing wing can complete folding (unfolding) motion in 0.33 s. The displacement, velocity and acceleration changes of each wing are shown in Figure 11. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Size** & **Weight** & **Velocity** & **Torque** \\ \hline
40.4 \(\times\) 19.8 \(\times\) 36.0 & 48 g & 0.22 s/60\({}^{\circ}\) (4.8 V) & 3.9 kg/cm (4.8 V) \\  & & 0.18 s/60\({}^{\circ}\) (6.0 V) & 5.2 kg/cm (6.0 V) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Basic parameters of Futaba S9001. Figure 10: Morphing wing experimental prototype: (**a**) prototype unfolded state; (**b**) prototype folded 45\({}^{\circ}\) state; (**c**) prototype folded 90\({}^{\circ}\) state; (**d**) skinned wings. The skeleton of the morphing wing designed in this paper is a spatial six-bar mechanism based on a Sarrus mechanism. The main bearing point and the most vulnerable part of the structure are the connecting hinges between the links. The measured forces and torques of the six revolute pairs in the model are shown in Figure 12, which can provide help for the strength design of the hinge. The hinges are made of PLA 3D printing material, and it can be seen from Figure 12 that all six hinges are subjected to a force of no more than 8 N. In this case, considering the mechanical properties of PLA, all the hinges meet the strength design requirements. As can be seen from Figure 12, the maximum torque value at hinge 1 is less than 0.3 N-m, which translates into a torque of about 3 kg/cm. According to the maximum torque 3.9 kg/cm of  
Figure 11: Variation of displacement, velocity and acceleration of each wing: (**a**) displacement diagram; (**b**) velocity diagram; (**c**) acceleration diagram. Figure 12: Measurement of forces and torques on 6 revolute pairs: (**a**) force on the revolute pairs; (**b**) torque on the revolute pairs. the selected steering engine Futaba S9001, this type of steering engine can provide enough power to make the morphing wing complete its folding action. Additionally, as can be seen from the solid green line in Figure 12, due to the action of gravity, hinge 5--the hinge between the bottom two links--receives the maximum torque value during the movement of all the hinges. In the design of a transmedia aircraft morphing wing, the strength of hinges is a key aspect that affects the structural strength of the whole wing. On one hand, we can produce high-performance hinges from high-strength materials. On the other hand, we can start from the rod size, because reasonable relative size can make the hinge bear relatively small torque. ADAMS provides powerful parametric modeling and optimization design functions for users to seek the optimal size within the target. Since ADAMS does not support parametric modeling and optimization design of imported models directly, an optimization model must be created in ADAMS first, as shown in Figure 13.  
As shown in the figure above, the parts that do not affect the motion form were removed, and the remaining parts were simplified. Similarly, the same driving function as above was applied to the inner wing connecting rod to make it have the same motion state as the above simulation model. The torque between the bottom two connecting rods (_JOINT_6_MEA_) was measured, and its value is shown in Figure 14.  
The hinge between the two links at the bottom is the revolute pair subject to the maximum torque, which will then be used as the objective function. The design objective is to minimize the maximum torque value in the process of motion. The body wing designed in this paper was designed in proportion, and the inner wing's connecting rod is equal to the middle wing's connecting rod.