## 2 Materials and Methods
### Construction of the Cutting Device Model Based on ADAMS
#### 2.3.3 Cutting Diagram Drawing Methods  
Referring to the reciprocating cutter motion principle of the rice and wheat combine harvester, when the reciprocating cutter is in the operational phase, the area swept per unit time of the cutter is the product of the displacement per unit time of the cutter, and the forward displacement of the implement. In addition, the absolute movement trajectory of the cutter reflects the working process of the cutter, and the corresponding graph represents the cutting diagram [25].  
The orderly harvester for GLVs utilizes a wide cutter and curved teeth. When the cutter moves to the left, the right half of the curved teeth play a cutting role. On the contrary, when the cutter moves to the right, the left half of the curved teeth play a cutting role. Firstly, using the location table function in the ADAMS software to export the \(x\)-, \(y\)-, and \(z\)-axis coordinate information of each point on the path curve, and import all the coordinate information into CAD to form the cutter trajectory curve [17]. Then, according to the cutter tooth shape, edge shape, and the direction of the reciprocating motion of the cutter, the cutting diagram of the case of two adjacent teeth in one cutting stroke via CAD has been schematically presented in Figure 8.  
Figure 8: Cutting diagram of the cutter movement. Note: \(H\) represents cutter width, \(h\) is cutter tooth height, \(H_{1}\) denotes the feed distance of the cutter, and, finally, \(S\) stands for the cutting stroke.  
Figure 7: Cutter movement trajectory curves for various types of markers: (**a**) Movement trajectory of a single marker; (**b**) Movement trajectories of two neighboring markers; (**c**) Movement trajectories of multiple neighboring markers.  
By analyzing Figure 8, it is observed that, during the orderly harvesting operation of GLVs, the absolute path of the cutting device cutter movement consists of the forward motion of the machine (speed \(v_{m}\)) and the simple harmonic motion of the cutter relative to the machine. The corresponding curve can be written as [27]  
\[y=\frac{rL_{2}}{L_{1}}\mathrm{cos}(\pi x/H_{1}) \tag{6}\]  
where \(H_{1}\) denotes the feed distance of the cutter (unit: mm). The feed distance of the cutter represents the distance that the harvester advances when the moving blade moves from the extreme left position to the extreme right position (or vice versa), which is formulated as follows:  
\[H_{1}=30\times v_{m}\times 10^{3}/n \tag{7}\]  
where \(v_{m}\) signifies the forward speed of the machine (m/s) and \(n\) denotes the crank rotation speed (r/min).  
As can be seen from Figure 8, the cutting of GLVs mainly includes three cases: single cutting, repeated cutting, and miss cutting. If the area of repeated cutting is too large, it will lead to the useless cutting of the blade and high energy consumption. In addition, as the miss-cutting area would be too large and the GLVs in the miss-cutting area are pushed to the side or front by the cutter to produce tilting, the tilting of the GLVs in one case must be cut in the next trip, but, due to the excessive tilting of the GLVs being cut, it is easy to result in the stubble cutting would be high. In the other case, the area in which the GLVs are located is still a miss-cutting area, and the harvester has increased the harvest loss rate due to the missed harvests caused by the blind spot during the cutting device operation. Therefore, both miss-cutting and repeated-cutting possess adverse effects on the cutting performance; miss-cutting should be avoided and repeated-cutting should be reduced as much as possible.