## 2 Materials and Methods
### Analysis of the Mechanism of Weeding by Burying  
To study the mechanism of pressure burying weeding in paddy field, the dynamic analysis of pressure burying weeding is carried out by establishing the deflection curve equation of weeds, as shown in Figure 4. According to the simplified model of the actual weeding and burying process, the weed is simplified as a homogeneous cantilever beam with fixed lower end and free upper end [17]. Taking the miscellaneous grass root system as the coordinate origin \(O\), the weed stem axis before bending deformation is the \(Y\)-axis, and the horizontal soil interface is the \(X\)-axis, a rectangular coordinate system \(XOY\) is established, in which the \(XOY\) plane is the longitudinal symmetry plane of the stem. Figure 4: Dynamic model of burying weeding: (I) water layer; (II) mud layer. Figure 3: Inter row weeding device: (1) motor box cover, (2) side transmission box, (3) upper sprocket, (4) planetary gear reducer, (5) brushless DC motor, (6) motor box, (7) connecting plate, (8) weeding wheel, (9) lower sprocket, (10) weeding wheel axle, (11) chain, (12) bearing pedestal, (13) weeding wheel frame. According to the principle of material mechanics, the axis of the bent weed stalk is simplified as a deflection curve, and the coordinates of any point on the curve are \((x,y)\). Then, the deflection curve equation is as follows:  
\[y=f(x) \tag{1}\]  
According to the plane assumption, the bending deformation of weeds is perpendicular to the axial cross section. Therefore, the included angle of the cross section is the angle between the \(Y\) axis and the normal direction of the deflection curve as follows:  
\[\theta_{1}=\arctan(\frac{dy}{dx}) \tag{2}\]  
In the case of pure bending, the relationship between the bending moment and curvature is as follows:  
\[\frac{1}{\rho}=\frac{M}{EI} \tag{3}\]  
where \(\rho\) is the radius of curvature, m; \(M\) is the bending moment of the cross section of the weed stem, N\(\cdot\)m; \(E\) is the elastic modulus of the weed stem, Pa; and \(I\) is the inertia moment of the cross section of the weed stem, m\({}^{4}\). Equation (2) can be converted to Equation (4). \[\frac{\mathrm{d}\theta_{1}}{\mathrm{d}s}=\frac{\mathrm{d}\theta_{1}}{\mathrm{ d}x}\frac{\mathrm{d}x}{\mathrm{d}s}=\frac{\mathrm{d}}{\mathrm{d}x}\bigg{[} \arctan\bigg{(}\frac{\mathrm{d}y}{\mathrm{d}x}\bigg{)}\bigg{]}\frac{\mathrm{d }x}{\mathrm{d}s} \tag{4}\]  
\[\mathrm{d}s=\left[1+\bigg{(}\frac{\mathrm{d}y}{\mathrm{d}x}\bigg{)}^{2} \right]^{\frac{1}{2}}\mathrm{d}x \tag{5}\]  
where ds is the focus of both ends of the normal (the center of curvature), and the radius of curvature is determined as \(\rho\). Equation (6) is obtained by combining Equations (3)-(5). \[\frac{\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}}{\left[1+\bigg{(}\frac{\mathrm{ d}y}{\mathrm{d}x}\bigg{)}^{2}\right]^{\frac{3}{2}}}=\frac{M}{EI} \tag{6}\]  
Equation (6) is the equation of the nonlinear deflection curve of the deformed weed stem. To simplify the solution process, Equation (6) is linearized. When the weed stem is embedded in the soil layer, the bending angle \(\theta_{1}\) is small and can be approximated as:  
\[\theta_{1}\approx\tan\theta_{1}=\frac{\mathrm{d}y}{\mathrm{d}x}=f^{\prime}(x) \tag{7}\]  
When the weeds are buried into the soil, the deflection curve is relatively flat, and \(\frac{\mathrm{d}y}{\mathrm{d}x}\) is small. Equation (6) is converted to Equation (8) as follows:  
Figure 4:0  
where Equation (8) is the approximate differential equation of the deflection curve of the weed stem after being pressed into the soil. On this basis, the dynamics of weeding wheels are analyzed, and the main factors affecting the burying effect are analyzed. When the weeding wheels collide with the weedsin the form of point contact (Action Point \(O\)), the weeds are buried in the soil. A certain moment is generated on any cross-section \(P\) of the weed rhizome.