## 4 Kinematic Simulation of the Fertilization Mechanism
### Analysis of the Movement Characteristics of the Fertilizer Applicator  
#### 4.3.1 Motion Analysis of Duckbill Opening and Closing Controller  
After setting the relevant parameters, simulation steps were determined for each movement. The simulation results included the opening angle of the duckbill controller, the displacement of the entire fertilizer applicator, and speed curves. These are represented in Figure 24, 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. The opening angle of the duckbill controller directly reflects the timing of fertilization and is a crucial control factor in the fertilization process. The displacement parameter of the fertilizer applicator, when observed in conjunction with the opening angle, can indicate the fertilization spacing. By monitoring the changes in these parameters, the fertilizer application situation during work can be reflected, thereby evaluating the accuracy and uniformity of fertilization. From the data in Figure 24, the minimum opening angle of the duckbill controller was approximately 14\({}^{\circ}\), marking its closed state. After this point, the lever disengaged,  
Figure 24: Simulation results of duckbill opening and closing controller. **(a)** Parameters when the speed of the work vehicle is 2 km/h. **(b)** Parameters when the speed of the work vehicle is 3 km/h. **(c)** Parameter when the speed of the work vehicle is 5 km/h. closing the mouth and ending the fertilization process. The angle change curve for the controller remained smooth across different speeds, with each working cycle returning to the minimum opening angle. This shows that the opening and closing of the duckbill mechanism operates normally. According to the data in Figure 24, when the operating vehicle speeds are 2, 3, and 5 km per hour, respectively, the opening angles of the duckbill controller in one working cycle are approximately 66\({}^{\circ}\), 58\({}^{\circ}\), and 48\({}^{\circ}\), respectively, which are obtained by subtracting the minimum angle from the maximum angle in one working cycle. As the speed of the operating vehicle increases, the rotation speed of the fertilizing disc also increases, after the rolling bearing assembly in the duckbill controller disengages from the previous lever, it will contact the next lever more quickly during the falling process, which leads to a smaller opening angle of the duckbill controller and thus shortens the fertilization interval time. Although the vehicle speed increases, the fertilization interval time is correspondingly reduced. The interaction between the two ensures the stability of the fertilization spacing. It can be clearly seen from the data in the right figure that, under different vehicle speeds, the displacement difference corresponding to the two adjacent highest points on the opening angle curve of the duckbill controller, which is the fertilization spacing, was stably maintained at around 500 mm (the set fertilization spacing). This fully demonstrates that the design of the duckbill controller is scientific and reasonable, effectively guaranteeing the stability of the fertilization spacing. In actual field conditions, the vehicle speed often changes due to terrain and soil unevenness. The simulation analysis showed the fertilization device's strong adaptability. For example, on downhill slopes, the speed increases, causing the fertilizing disc to rotate faster, which narrows the duckbill controller's opening angle and shortens the fertilization interval time. Conversely, when traveling uphill and the vehicle decelerates, the fertilization interval time is extended. This automatic adjustment helps maintain a stable fertilization spacing and ensures uniform fertilization.