## 3 Design of Main Working Parts
### Seedling-Casting Device
#### 3.2.1 Analysis of Seedling Movement  
According to the cultivation mode of Codonopsis outcrop with a micro ridge covered with film, it is necessary to carry out movement analysis of the seedlings' landing process in order to ensure a small head deviation of seedlings when they are thrown into the seedbed. Figure 7(a) shows the side view of the seedling-casting process (the influence of the seedling protection plate on the seedling-casting process is not taken into consideration), in which the driving shaft of the seeding device rotates at angular speed \(\omega\), \(V_{m}\) is the advance speed of the whole machine. Suppose that after a seedling is thrown from point \(O\) of height \(H_{1}\), the head of the seedling falls to point \(P\) and the root falls to point \(Q\), and the horizontal displacement of the seedling is \(L\). Taking the horizontal direction as the \(x\)-axis and the vertical plane as the \(y\)-axis, a rectangular coordinate system is established. Air resistance is considered in the seedling-casting process, and it is known that the resistance of air is proportional to its motion speed [21], namely,  
\[f_{a}=\mu_{1}V_{t} \tag{5}\]  
where \(f_{a}\) is the air resistance (N);  
\(\mu_{1}\) is the coefficient of air resistance;  
\(V_{t}\) is the seedling speed, m/s. Without considering the slip of the conveyor belt, the instantaneous speed of seedlings leaving the conveyor belt is equal to the speed of the conveyor belt, namely,  
\[V_{t}=V_{c} \tag{6}\]  
\(V_{c}\) is the speed of the conveyor belt, m/s. The forces of seedlings during seeding operation are shown in Figure 7(b). \(OP\) is the motion path of seedlings. At the moment when the seedlings leave point \(O\), their motion is influenced by gravity (mg) and air resistance (\(f_{a}\)). Then, the accelerated speed in all directions of the seedlings moving through the air is  
\[\left\{ \begin{array}{l}a_{x}{=f_{y}/m}\\ a_{y}=\left(mg-f_{y}\right)/m\end{array} \right. \tag{7}\]  
Figure 7: Structure of seedling-casting device. 1. Seedling protection plate. 2. Cylindrical pin. 3. Connecting block. 4. Fixed pin. 5. Seedling separation plate. 6. Conveyor belt. 7. Driving shaft of seedling-casting device. 8. Driven shaft I. 9. Driven shaft II. where \(a_{x}\) is the accelerated speed of the seedling in the horizontal direction (m/s\({}^{2}\));  
\(a_{y}\) is the accelerated speed of the seedling in the vertical direction (m/s\({}^{2}\));  
\(f_{x}\) is the air resistance of the seedling in the horizontal direction (N);  
\(f_{y}\) is the air resistance of the seedling in the vertical direction (N);  
\(g\) is gravitational acceleration, m/s\({}^{2}\). The instantaneous speed \(V_{c}\) of the seedling is decomposed when the seedling leaves the conveyor belt, and the speed of the seedling in the \(x\) and \(y\) directions is  
\[\left\{ \begin{array}{l}V_{x}\!\!=V_{m}+V_{c}\cos\beta_{1}\\ V_{y}\!\!=V_{c}\sin\beta_{1}\end{array} \right. \tag{8}\]  
By integrating Equation (7), the horizontal and vertical motion velocities of seedlings in the falling process can be written as \(V_{xt}\), \(V_{yt}\), respectively,  
\[\left\{ \begin{array}{l}V_{xt}\!\!=V_{m}+V_{c}\cos\beta_{1}\!\!-\!e^{\frac{- \beta_{1}t}{m}}\\ V_{yt}\!\!=V_{c}\sin\beta_{1}\!\!+\!gt-e^{\frac{\beta_{1}t}{m}}\end{array} \right. \tag{9}\]  
\(V_{xt}\) is the motion speed of seedlings in the horizontal direction (m/s);  
\(V_{yt}\) is the motion speed of seedlings in the vertical direction (m/s);  
\(\beta_{1}\) is the angle between seeding direction and horizontal plane (\({}^{c}\));  
\(t\) is the movement time of seedlings (s). Figure 8: Analysis of seedling movement in the air. 1. Seedling protection plate. 2. Conveyor belt. 3. Cross-section of seedbed. 4. Seedbed. 5. Seedling soil-covering belt. 6. Driving shaft of seedling-casting device. 7. Seedling. By integrating Equation (7) again, the displacement of seedlings in the horizontal direction \(x\) and in the vertical direction \(y\) is  
\[\left\{