## 2 Materials and Methods
### Design of Driving Weeding Device with Rake Teeth
#### 2.3.1 Structural Design of Weeding Wheels with Rake Teeth
When the weeding device moves at a uniform speed, the force state of the weeding device is shown in Figure 6a, and the force balance equation is as follows:  
\[\sum F_{x}=F_{gx}-F_{t}=0 \tag{22}\]  
\[\sum F_{y}=F_{gy}+N-G_{2}=0 \tag{23}\]  
\[\sum M_{0_{3}}(F)=M_{1}-G_{2}I_{1}+Nl_{2}-F_{t}l_{3}=0 \tag{24}\]  
where \(F_{gy}\) is the vertical force acting on the fixed end of the connecting plate, N; \(F_{gx}\) is the horizontal force on the fixed end of the connecting plate, N; \(M_{1}\) is the moment action on the fixed end of the connecting plate, N\(\cdot\)m; \(G_{2}\) is the weight of a single weeding device, N, which is taken as 150 N; \(l_{1}\) is the horizontal distance from the center of gravity of the weeding device to the end face of the connecting plate, m, which is taken as 0.17 m; \(l_{2}\) is the horizontal distance from the point where the soil acts on the weeding wheel to the end face of the connecting plate, m; and \(l_{3}\) is the vertical distance from the point where the soil acts on the weeding wheel to the connecting plate, m; \(N\) is the soil support to the weeding wheel, N.  
Figure 6: Force diagram of the weeding device: (**a**) overall stress diagram of the weeding device; (**b**) force diagram of the weeding wheel; (**c**) stress diagram of the connecting plate. The stress state of a weeding wheel is shown in Figure 6b, and the balance equation is as follows:  
\[\sum M_{o}(F)=F_{t}a_{1}+Na_{2}-M_{d}=0 \tag{25}\]  
where \(F_{t}\) is the soil friction force on the weeding wheel, N; \(a_{1}\) is the plumb distance from the rotation center to the soil force point, m; \(a_{2}\) is the horizontal distance from the rotation center to the soil force point, \(m\); and \(M_{d}\) is the driving torque, N\(\cdot\)m.  
The stress state of the connecting plate of the weeding device is shown in Figure 6c, and the balance equation of the force is as follows:  
\[\sum M_{B}(F)=M_{1}+G_{3}l_{5}-F_{gy}l_{4}=0 \tag{26}\]  
where \(G_{3}\) is the gravity of the connecting plate, N, where \(G_{3}\) = 15 N; \(l_{4}\) is the horizontal distance from the pressure acting point of the motor and reducer on the connecting plate to the end face of the connecting plate, m, where \(l_{4}\) = 0.19 m; and \(l_{5}\) is the horizontal distance from the center of gravity of the connecting plate to the point where the pressure of the motor and reducer act on the connecting plate, m, where \(l_{5}\) = 0.11 m.  
\[F_{t}=f_{s}N \tag{27}\]  
where \(f_{s}\) is the rolling friction coefficient of the weeding wheel in soil. Equation (28) is obtained by simultaneously solving Equations (24)-(27). \[\beta=\arccos\frac{a+b}{R_{r}} \tag{21}\]0  
Equation (29) is obtained based on the substitution of relevant parameters. \[\beta=\arccos\frac{a+b}{R_{r}} \tag{21}\]1  
where the range of \(\theta\) and \(f_{s}\) is 0\(-\frac{\pi}{2}\) and 0-1, respectively, and the maximum value of \(M_{d}\) is 10.34 N\(\cdot\)m. The rotating speed of the weeding wheel is 70-150 r/min. \[\beta=\arccos\frac{a+b}{R_{r}} \tag{21}\]2  
According to Equation (30), the motor power of the weeding device is 162.4 W. At present, most paddy field weeters are powered by small gasoline engines, which have the problems of violent vibration, loud noise and large weight. The motor has the advantages of convenient control, large starting torque, low noise and no pollution. Therefore, a 0.2 kW DC motor with a rotating speed of 3000 r/min and a reducer with a reduction ratio of 1:20 were selected. According to the rated power of the optional motor, the capacity of the required battery can be calculated by Equation (31). \[\beta=\arccos\frac{a+b}{R_{r}} \tag{21}\]3  
where \(C_{v}\) is battery capacity, AH; \(P_{v}\) is motor power, W; \(T_{v}\) is available time, h, where \(T_{v}\geq 6\) h; \(U\) is voltage, V, where \(U\) = 48 V.  
The minimum battery capacity required for a driving weeding device with rake teeth is 25 AH.