## 2 Materials and Methods  
### Double-Cutterbar Configuration Methods  
#### 2.1.1 Upper Cutterbar Configuration Method Based on Rice Crop Deformation  
As shown in Figure 1(a), the panicle should be cut off before the reel bar, leaving the connection joint of panicle and stalk (point \(A_{2}\)) to support the cutting process of stalks by the upper cutterbar [19]. Moreover, to ensure all panicles are harvested with less stalks, the cutterbar should be set under the lowest point of the panicle of the deformed crop (point \(B_{2}\)) and be as close to it as possible. To describe the cutterbar configuration, a coordinate system \(XO_{1}Y\) was established. Figure 2: Rice plant (**a**) deformation and (**b**) force analysis before cut by the upper cutterbar. \(x_{uc}\), \(y_{uc}\) are the horizontal and vertical coordinates of the upper cutterbar blade midpoint in mm, respectively; \(F\) is the reel acting force exerted on stalk, and \(F_{h},F_{\tau}\) are its component forces on horizontal and tangential direction, N; \(G\) is the gravity of the panicle, and \(G_{h}\), \(G_{\tau}\) are its component forces on horizontal and tangential direction, N; \(M_{G}\) is the additional torque when the \(G\) is moved to point \(A_{2}\), N-mm; \(h_{B1}\) and \(h_{B2}\) are the heights of the panicle lowest point before and after deformation, mm; \(\Delta_{C}\) is the plant deflection at the height of the upper cutterbar, mm; \(p\) is the distance between crop and auger center, mm; \(l_{time}\) is the length of the reel time, mm. To calculate the deformation of the whole rice crop, the assumptions that the plant is bent elastically by the reel and the panicle is moved translationally were made. To facilitate the calculation, another coordinate system \(\Delta O_{2}Y\) describing the rice crop deformation was established. The force analysis of the rice crop bent to \(O_{2}A_{2}\) is illustrated in Figure 2b. The forces acting on the crop include the force \(F\) exerted by the reel and the weight of the panicle \(G\), which are acted on point \(A_{2}\) and the center of the panicle, respectively. The weight \(G\) can be moved to point \(A_{2}\) with an additional torque (\(M_{G}\)). Furthermore, \(F\) and \(G\) can be decomposed into horizontal forces \(F_{h}\), \(G_{h}\) and tangential forces \(F_{\tau}\), \(G_{\tau}\). The tangential forces give the elongation on the surface of the stalk at point \(A_{2}\), but the effect on the bending is considered to be very slight [20]. Thus, the tangential forces are neglected in the deformation calculation. The torque \(M_{G}\) can be transformed to a horizontal force \(F_{M}\) acting at point \(A_{2}\). Therefore, the resultant force at point \(A_{2}\) can be presented as follow:  
\[F_{re}=F_{h}+G_{h}+F_{M} \tag{1}\]  
The curve of the stalk \(O_{2}A_{2}\) as shown in Figure 3 can be fitted by substituting \(F_{re}\) into Equation (2), the large deflection formula [13], which can be solved by the fourth-order Runge-Kutta method [13; 16],  
\[\frac{d\Delta}{dy}=\frac{h_{A1}\cdot y-\frac{y^{2}}{2}}{\sqrt{\left(\frac{EI} {F_{re}}\right)^{2}-\left(h_{A1}\cdot y-\frac{y^{2}}{2}\right)^{2}}} \tag{2}\]  
where, \(\Delta\) is the deflection of the stalk, mm; \(y\) is the vertical coordinate of the stalk, mm; \(EI\) is the flexural rigidity of stalk, N\(\cdot\)mm\({}^{2}\). To obtain the values of \(F_{re}\) and \(EI\), rice stalk deflection experiments detailed by [PERSON] et al. were conducted and the vertical and horizontal displacement of point \(A\) can be calculated by Equations (3) and (4) [15]. In the calculation of \(EI\), the rice stalk was partitioned into eight equal segments on vertical  
Figure 3: Rice plant partition and calculation. \(F_{re}\) is the resultant force of \(F_{h}\), \(W_{h}\) and \(F_{M}\), N; \(h_{A1}\) and \(h_{A2}\) are the heights of point \(A\) before and after deformation, mm;  
according to the Simpson's Formula, as shown in Figure 3; the angle between tangent line of point \(K_{i}\) and \(Y\) axes can be presented as Equation (5) [15].