# Analysis of Motion Characteristics of Bionic Morphing Wing Based on Sarrus Linkages
## 2 Materials and Methods  
### A Bionic Morphing Wing Based on Sarrus Linkages  
The schematic structure of Sarrus linkages is shown in Figure 3, which is a spatial six-bar mechanism with high stiffness, high bearing capacity, simple structure, and low cost [17; 18]. It is composed of upper and lower plates (AB) and four side plates (RSTU), which is connected by two groups of six rotating pairs. Without any moving pair or screw pair in the middle, it has relatively high transmission efficiency and is easy to maintain [19; 20].  
According to the degree of freedom analysis method of spatial closed chain mechanism [21; 22], the degree of freedom of the Sarrus mechanism can be obtained, which can be calculated by the following formulas:  
\[F=\sum_{i=1}^{p}f_{i}-\lambda \tag{1}\]  
\[\lambda=\lambda_{R}+\lambda_{PP}+\lambda_{PR} \tag{2}\]  
\[F=\sum_{i=1}^{p}f_{i}-(\lambda_{R}+\lambda_{PP}+\lambda_{PR})=6-(2+0+3)=1 \tag{3}\]  
Figure 3: Sarrus linkages.  
Figure 2: Working process of aircraft: (**a**) air navigation process; (**b**) preparation process from air to underwater; (**c**) water entry process; (**d**) underwater attitude adjustment process; (**e**) underwater navigation process; (**f**) preparation process from underwater to air; (**g**) water discharge process; (**h**) aerial attitude adjustment process.  
It can be seen that the Sarrus mechanism is a mechanical structure with only one degree of freedom, which can transform the rotation motion of an input terminal into linear motion through the interaction of each member bar in its own mechanism.  
Based on the bionics principle and Sarrus mechanism principle, this paper designed the shape of a transmedia aircraft and the structure of a morphing wing. A kingfisher was selected as the bionic object, and the design size of the morphing wing was obtained by equal scale, as shown in Table 1.  
According to the design requirements of this paper, we must choose the wing type with the highest lift to drag ratio; according to the bionic principle, we observe the shape of kingfisher wings and finally choose NACA6412, which possesses a similar shape and a higher lift-to-drag ratio. The shape of NACA6412 wing ribs and their distribution on the Sarrus skeleton are shown in Figure 4.  
SolidWorks software was used for 3D modeling of the morphing wings, as shown in Figure 5. The fuselage is connected to six rods that make up the Sarrus mechanism: the platform, the inner wing, the middle wing, the outer frame, and the bottom rods 1 and 2, of which the inner wing is of equal length to the middle wing, and the rods are connected by hinges.  
According to the principle of the Sarrus mechanism, when the inner wing is driven by the steering engine, the inner wing folds to a certain angle relative to the direction of the wingspan, and the middle wing folds to the same angle along the direction of the wingspan  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Component** & **Inner Wing** & **Middle Wing** & **Outer Wing** & **Rod 1** & **Rod 2** \\ \hline Length/mm & 150 & 150 & 200 & 170 & 180 \\ \hline \end{tabular}
\end{table}
Table 1: Design dimensions of morphing wing.  
Figure 4: The shape of NACA6412 wing ribs and their distribution on the Sarrus skeleton.  
Figure 5: Morphing wing based on Sarrus linkages.  
around hinge 2. Meanwhile, the outer frame is translated in the direction of the wingspan to ensure that the outer wing always keeps level with the body, and the two connecting rods at the bottom move accordingly.  
The maximum folding angle of the morphing wings designed in this paper is \(90^{\circ}\). Figure 6 shows the expanded and folded states of the morphing wing.