# A New Type Bionic Foldable Wing Design for High Maneuverable Unmanned Aerial Vehicle
## 2 Preliminary Design of the Folding Wing Structure
### Multi-Link Structure Scheme  
The design objectives of the folding wing prototype are as follows: (1) The folding rate in the wingspan direction is not less than 20%; (2) the chord length is about 20 cm; (3) expansion time t \(\leq\) 2 s; (4) single degree of freedom; (5) steering gear drive; (6) impact force F \(\leq\) 50 N.  
There are a lot of morphing structures such as piezoelectric ceramics, memory alloys, inflatable structures, etc. However, the pure mechanical structure has the advantages with large morphing, simple transmission, and manufacture which is more suitable for folding wings. Therefore, for the structural design of folding wings with large morphing, it is still the most effective way to design the morphing mechanism by using a multi-body system [21; 22].  
Connecting the rod mechanism is a mechanical structure that connects components together by a rotating pair or moving pair. Connecting rod driving can produce large displacement changes, reliable transmission, and is easy to determine the degree of freedom. This folding wing requires a single degree of freedom so that the four-bar mechanism is very suitable for the single degree of freedom drive. According to the length of the rod, it can be divided into: double crank mechanism, crank rocker mechanism, double rocker mechanism, and different types of mechanisms with different characteristics. As for the four-bar structure in Figure 3, where \(l_{1}\) is the active rod and \(l_{4}\) is the frame, Equation (12) can be obtained:  
\[\left\{\begin{array}{c}\vec{l}_{1}^{\rightarrow}+\vec{l}_{2}^{\rightarrow}+ \vec{l}_{3}^{\rightarrow}+\vec{l}_{4}^{\rightarrow}=0\\ l_{1}\sin\theta_{1}+l_{2}\sin\theta_{2}=l_{3}\sin\theta_{3}\\ l_{1}\cos\theta_{1}+l_{2}\cos\theta_{2}=l_{3}\cos\theta_{3}+l_{4}\end{array}\right. \tag{12}\]  
Figure 3: Schematic diagram of the four-bar structure.  
Equations (13) and (14) can be obtained by solving the above equations, and the speed of both can be obtained by deriving the time, as shown in Equation (15):  
\[\theta_{2}=\cos^{-1}\left(\frac{l_{3}\cos\theta_{3}+l_{4}-l_{1}\cos\theta_{1}}{l _{2}}\right) \tag{13}\]  
\[\theta_{3}=\cos^{-1}\left\{\frac{\left(l_{2}{}^{2}+2l_{1}l_{4}\cos\theta_{1}-{l _{1}}^{2}+3^{2}+l_{4}^{2}\right)\pm\frac{l_{1}\sin\theta_{1}\times\sqrt{1- \left(-{l_{2}}^{2}-2l_{1}l_{4}\cos\theta_{1}+{l_{1}}^{2}-{l_{3}}^{2}-{l_{4}}^{ 2}\right)^{2}+\left[\frac{l_{1}\sin\theta_{1}}{\left(l_{4}-l_{1}\cos\theta_{1} \right)}\right]^{2}}}{\left(l_{4}-l_{1}\cos\theta_{1}\right)}}}{1+\left[\frac{l _{1}\sin\theta_{1}}{\left(l_{4}-l_{1}\cos\theta_{1}\right)}\right]^{2}}\right\} \tag{14}\]  
The angular velocity \(\omega_{2}\), \(\omega_{3}\) can be obtained by deriving the time:  
\[\left\{\begin{array}{l}\omega_{2}=-l_{1}\omega_{1}\sin\frac{\theta_{1}- \theta_{2}}{\left[l_{2}\sin\left(\theta_{2}-\theta_{2}\right)\right]}\\ \omega_{3}=-l_{1}\omega_{1}\sin\frac{\theta_{1}-\theta_{2}}{\left[l_{1}\sin \left(\theta_{3}-\theta_{2}\right)\right]}\end{array}\right. \tag{15}\]  
The four-bar mechanism and its derivative multi-bar mechanism are powerful and varied in form. After determining the length of the connecting rod, the angle and folding length of the wing are used as parameters to design the multi-link folding structure.