## 4 Kinematic Simulation of the Fertilization Mechanism
### Analysis of the Movement Characteristics of the Fertilizer Applicator
#### 4.3.3 Motion Analysis of Reverse Rotation of the Fertilizer Applicator  
In actual field operations, when reversing in the field, avoiding obstacles, or adjusting the fertilization position, it often causes the fertilizer applicator to rotate in reverse, which occurs 3-5 times on average per operation. At this time, the design of the duckbill controller ensures that the duckbill remains closed during reverse movement, preventing fertilizer spillage, avoiding fertilizer waste, and repeated fertilization in the fertilized area. This function reduces manual intervention in actual operations, improves work efficiency, and reduces the cost of use.  
To set up the simulation analysis process, assuming that the fertilizer applicator's fertilizing wheel is moving in reverse and the drive is set to the opposite direction, the values for translational motion along the X-axis and rotation around the Z-axis should have negative signs added. At this point, the movable duckbill lever touches the bearing group, causing the duckbill opening and closing controller to rotate counterclockwise, which prevents the pressing duckbill from opening, as shown in Figure 26.  
In the simulation results, we added the angle of rotation of the duckbill opening and closing controller and the displacement and velocity curves of the entire fertilizer spreader while traveling backward at speeds of \(-2\) km/h, \(-3\) km/h, and \(-5\) km/h. The selection of \(-2\), \(-3\), and \(-5\) km/h for the backward speeds was intentional as they were the same magnitudes as the forward speeds of 2, 3, and 5 km/h discussed previously, allowing for a more straightforward and meaningful comparison. The final simulation results are shown in Figure 27, where the red solid line (angle) represents the opening angle of the duckbill controller, the blue short dashed line (length) represents the movement displacement of the fertilizer applicator, and the pink dotted line (velocity) represents the movement speed of the fertilizer applicator.  
According to the data comparison in Figure 27, an analysis of the motion state of the duckbill controller as the reverse speed gradually increased revealed several key characteristics. The opening angle of the duckbill controller remained stable across different reverse speeds, consistently staying within a reasonable range. Specifically, its swing angle was stable between 50\({}^{\circ}\) and 125\({}^{\circ}\). All opening angle curves demonstrated a smooth state, exhibiting clear regularity and periodicity, with no significant huge fluctuations in the short-term throughout the process. In comparison with the curves depicting the variation in the opening angle of the duckbill controller at diverse forward speeds of the vehicle as presented in Figure 24, it was discerned that they all exhibited analogous periodic alterations and were relatively smooth, devoid of substantial short-term fluctuations.  
Figure 26: Drive in reverse.  
Based on the comprehensive analysis of the above data and related factors, it can be seen that the duckbill controller still operated smoothly and regularly during the reverse process. It could stably control the state of the duckbill, and regardless of how the reverse speed changed, it could always keep the duckbill tightly closed. Field tests demonstrated that when the duckbill moved in reverse under different soil humidity and terrain conditions, it could always maintain a tightly closed state with no fertilizer leakage. This is highly consistent with the simulation results, verifying the reliability of the duckbill's reverse movement performance in actual agricultural production and provides strong support for the stable operation of the fertilizer applicator under complex field conditions.