## 3 Simulation and Analysis of the Sugarcane Leaf-Picking Process
### Analysis of Changes in the Sugarcane Leaf Bending Angle  
In order to observe the bending effect of the elastic teeth on both sides of the sugarcane leaf, points A and B on the sugarcane leaf were extracted in post-processing. Point A is the midpoint of the bend, wherein the sugarcane leaf contacts the elastic teeth, and point B is the midpoint of the end of the sugarcane leaf. The extraction point of the sugarcane leaf bending angle is shown in Figure 12.  
Then, the angle of bending of the sugarcane leaf on both sides (i.e., the angle between the bent section of the sugarcane leaf and the horizontal direction) was given by  
\[\alpha=\arccos\frac{z_{2}-z_{1}}{\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y _{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}} \tag{4}\]  
In Equation (4), \(\alpha\) represents the cane leaf bending angle (\({}^{\circ}\)). \(x_{1}\), \(y_{1}\), \(z_{1}\) represent the coordinate values of point A. \(x_{2}\), \(y_{2}\), \(z_{2}\) represent the coordinate values of point B.  
Figure 13 represents the curve of the change in the bending angle of the sugarcane leaf during the picking process. From 0-0.14 s, the sugarcane leaf contacted the elastic teeth and the ground. The sugarcane leaf was subjected to the resultant force of the elastic teeth moving obliquely upward and the friction force of the ground. The bending angle of sugarcane leaf increased rapidly. The rate of change of the sugarcane leaf bending angle reached its maximum when the elastic teeth moved to 0.03 s. From 0.14-0.18 s, the middle part of sugarcane leaf was gradually bounced by the elastic teeth. The sugarcane leaf produced some rebound and the bending angle of the sugarcane leaf was reduced more slowly. From 0.18-0.22 s, the sugarcane leaf made contact with the underside of the guard and broke away from the ground at 0.19 s. The sugarcane leaf was subjected to the forces of the elastic teeth and the guard plate during this time, and the bending angle increased more slowly. From 0.22-0.58 s, the sugarcane leaf moved upwards with the rotation of the elastic teeth. Some rebound occurred in the sugarcane leaf on both sides. The overall trend in the bending angle of the sugarcane leaf showed that it was gradually becoming smaller. From 0.58-1.34 s, the sugarcane leaf was lifted by the elastic teeth to the uppermost part of the guard plate and then pushed downwards by the elastic teeth. The sugarcane leaf detached from the elastic teeth at t = 1.09 s, and then slid along the guard plate. At t = 1.26 s, some areas of the sugarcane leaf began to collide with the door frame. At t = 1.34 s, the bending angle of sugarcane leaf reached a maximum value of 27.75\({}^{\circ}\). The overall trend in the folding angle of the sugarcane leaf during this period was gradually increasing. From 1.34-1.8 s, the sugarcane leaf slid down the guard plate to the end of the guard plate. The area wherein sugarcane leaf hit the door frame became larger.  
Figure 12: Extraction point of sugarcane leaf bending angle.  
Figure 13: Change in the bending angle of the sugarcane leaf during the picking process.  
The sugarcane leaves bounced some distance after the collision. The overall trend in the bending of the sugarcane leaf during this period is a gradual decrease. Finally, the bending angle changed to 12.34\({}^{\circ}\).