## 2 Materials and Methods
### Design of Sorting and Conveying Mechanisms  
In order to convey the sugarcane grasped by the manipulator in a relatively uniform and orderly state, the sorting and conveying device is designed as a three-stage operation stroke, which includes the lifting conveyor belt, the cane collecting board, and the sorting mechanism, and its structure is shown in Figure 3. The lifting conveyor belt is made of serrated rubber tracks, which can separate the canes and prevent them from rolling back down. According to engineering experience and the actual conveying situation in the early stage, the lifting and conveying angle is set to 30\({}^{\circ}\). The sugarcane is lifted by the lifting conveyor belt at a steady pace while in operation, allowing it to be transported in a comparatively uniform condition. The sugarcane that is transported by the lifting conveyor belt is received by the cane collecting board, which also has a pallet at the bottom to keep the sugarcane from falling and a gap that corresponds to the hook claw of the sorting mechanism so that the sugarcane can be hooked and then passed through smoothly. The sorting mechanism, which primarily consists of the frame, chain sprocket, flexible steel bar, sorting rake, and so forth, is the essential part of sorting and conveying. To guarantee the stability of the apparatus, it uses three sets of chain sprockets positioned side by side, and the driving shaft is put together using an inverted triangle design. To keep sugarcane from falling into the sorting mechanism during operation, there is a flexible steel bar and sorting rakes below the cross-connection, as well as an equally spaced sorting rake along the chain. The length of the hooks can somewhat regulate the quantity of sugarcane that is grabbed, and Figure 4 displays the geometrical parameters of the sorting hooks. Each sorting rake has four hooks that are evenly spaced throughout the rake and are capable of  
Figure 1: Overall structure of step-by-step sugarcane leaf stripping equipment. Figure 2: Flow chart for sugarcane leaf stripping machine operation. efficiently grabbing the shorter cane and determining the positional deviation of the cane. The three parts of sorting and conveying work together, so that the sugarcane in the pile is transported stably and uniformly to complete the sorting task, and the parameters of the sorting conveyor structure are shown in Table 1.  
Assuming that the cane falls from the lifting conveyor belt to the cane collecting plate at an effective height of \(h\), the rebound effect can be determined using the mechanical energy conservation theorem just before the cane collides with the cane collection plate:  
\[mgh=\frac{1}{2}mv_{1}^{2}-\frac{1}{2}mv_{0}^{2} \tag{1}\]  
where \(m\) is the mass of the sugarcane, \(v_{1}\) is the cane's speed prior to impact with the ramps, and \(v_{0}\) is the initial velocity of falling sugarcane. The collision between the cane and the cane collector plate is not entirely elastic due to the significant difference in their elastic moduli and the kinetic energy loss that occurs during the collision process. The coefficient of restitution, or e, is the ratio of the separation velocity and the approaching velocity of the two objects prior to and following the collision along the direction normal to the contact place, and it can only be obtained using the material of the collision object:  
\[e_{0}=\frac{v_{1}\cos\alpha}{v_{y}} \tag{2}\]  
where \(\alpha\) is the inclination of the cane plates, and \(v_{y}\) is the cane's velocity after rebounding perpendicular to the sloped plate. Using the kinematics equation and the cane's center of mass at the moment of impact as the origin, a coordinate system is created in the x-axis direction:  
\[\left\{ \begin{array}{l}v_{x}=v_{1}\sin\alpha\\ L_{1}=v_{x}t_{1}+\frac{1}{2}\delta\sin\alpha\cdot t_{1}^{2}\\ L_{2}=v_{x}(t_{1}+t_{2})+\frac{1}{2}\delta\sin\alpha\cdot(t_{1}+t_{2})^{2}\\ \end{array} \right.