## 2 Materials and Methods
### Design of Driving Weeding Device with Rake Teeth
#### 2.3.1 Structural Design of Weeding Wheels with Rake Teeth  
The designed weeding wheels with rake teeth could bury the weeds in the soil through rake teeth penetration and excavation, which disturbs and compacts the soil to achieve weeding and soil plowing. The diagram of the structure of the weeding wheels is shown in Figure 5.  
The turning radius of the weeding wheels \(R_{r}\) is:  
\[R_{r}=a+b+c \tag{13}\]  
where \(a\) is the distance from the center of the weeding wheel to the bottom of the transmission box, m, which is taken as 0.06 m; \(b\) is the distance between the bottom of the transmission box and the mud surface, m, which is taken as 0.002 m; and \(c\) is the weeding depth, m, according to the root length of the weeds, which is taken as 0.07 m.  
In triangle \(OCA\):  
\[OA=a+b \tag{14}\]  
\[AC=\sqrt{{R_{r}}^{2}-OA^{2}} \tag{15}\]  
\[BC=CA-AB \tag{16}\]  
The rake teeth and the weeding disc are connected by bolts. To facilitate the installation, \(AB\) is taken as 0.1 m, and the installation position of the rake teeth can be determined by substituting the relevant parameters into Equations (14)-(16). When the weeder is working, the path of the weeding rake teeth is a cycloid, and the weeding operation can be performed such that Equation (17) should be satisfied. \[\frac{R_{r}\omega}{V_{m}}>1 \tag{17}\]  
where \(V_{m}\) is the forward speed of &#13; the weeder, m/s, which is taken as 1 m/s; \(\omega\) is the angle speed of the&#13; weeding wheels, rad/s, where \(\omega=\frac{\pi n}{30}\) and \(n\) is the rotating speed of the weeding wheels, r/min. The calculated &#13; rotational speed of the weeding wheels should be greater than 63 r/min and is&#13; determined to be 70-150 r/min. To ensure that leakage does not occur during working conditions, the sum of the action length of all the rake teeth on the weeding wheels should be greater than the forward distance when the weeding wheels rotate for one circle. \[Zx\geq V_{m}\frac{60}{n} \tag{18}\]  
where \(Z\) is the number of all rake teeth on the weeding wheels and \(x\) is the action distance of a single rake tooth when the weeding wheels rotate for one cycle, m.  
Equation (19) is obtained according to the geometric relationship of Figure 5.  
\[ \begin{array}{ll}x&=l_{1}-V_{m}t\\ &=2R_{r}\sin\beta-V_{m}t\end{array}  \tag{19}\]  
\[t=\frac{2\beta\pi}{180\omega} \tag{20}\]  
\[\beta=\arccos\frac{a+b}{R_{r}} \tag{21}\]  
where \(l_{1}\) is the forward distance of the weeder, m; \(\beta\) is the angle between the line from the tip of the rake tooth to the rotation center of the weeding wheels and the plumb line, (\({}^{\circ}\)); and Equations (17)-(21) give \(Z\geq 5.36\), where \(Z\) is rounded to 6, and the tooth width is 170 mm. Figure 5: Diagram of the structure of a weeding wheel with rake teeth when working. 2.3.2. Power Analysis of the Driving Weeding Device with Rake Teeth  
The driving weeding wheels with rake teeth adopt the driving rotary burying plowing mode during operation, and the matching driving motor forms the driving rake teeth weeding device, which can effectively ensure the working quality. In the selection of a driving motor, the working torque of the weeding device should be considered to prevent excessive power consumption.