## 2 Mechanism Introduction and Modeling Analysis
### Seedling Dropping Process Segmentation
#### 2.3.1 Kinematics Analysis of Seedling Separation Process  
The dropping motion process of pot seedlings at each position is not consistent. For example, the pot seedlings at the No. 1, 2, 4, and 5 positions have segmented trajectories, while the pot seedlings at position No. 3 have straight trajectories. Neglecting the air resistance and the friction between the blade and the inner wall of the seedling cylinder during the dropping of the pot seedling at position No. 3, it can be regarded as a free-dropping motion with an initial velocity of 0 m/s. The starting point of the dropping seedling is the plane where the seedling carrying plate is located, and the end point is the seedling planting groove. Since the No. 1 and 2 positions are symmetrical with the No. 4 and 5 positions, the dropping trajectories of the No. 1 and 2 positions are similar. Therefore, to simplify the analysis process, the kinematic analysis was performed under a segmented trajectory with position No. 1 as an example, and for the linear trajectory, the No. 3 position was analyzed separately. As shown in Figure 9a, the pot seedling at the No. 1 position falls freely from point A to point B, with a dropping height of \(L_{AB}\) and a unilateral deformation of \(\epsilon_{1}\). The relative velocity of the pot seedling before the collision is \(v_{1}\), and the relative velocity of the pot seedling after the collision is \(v_{2}\). The vertical upward direction is the positive direction, and  
Figure 9: Stage analysis of seedling dropping process in No. 1 position. (**a**) Seedling falling freely from position A to position B. (**b**) Sliding along the inner wall of the seedling cylinder after collision at position B. (**c**) Oblique throwing motion of seedlings after sliding to position C. (**d**) Seedling falls into the planting groove E after a second collision at position D.  
in the vertical direction, according to the momentum theorem, the following equation can be obtained  
\[(F_{1}-mg)\Delta t_{1}=(-mv_{2}\cos\alpha)-(-mv_{1}) \tag{4}\]  
where \(F_{1}\) is the impact force on the body of the pot seedling, N; m is the mass of the pot seedling, g; \(\Delta t_{1}\) is the collision time, s; \(v_{1}\) is the relative velocity of pot seedlings before collision with point B, m/s; \(v_{2}\) is the relative velocity of pot seedlings after the collision with point B, m/s; and \(\alpha\) is the sliding angle of the pot seedling, \({}^{\circ}\). The collision force can be obtained as follows:  
\[F_{1}=m(\frac{v_{1}-v_{2}\cos\alpha}{\Delta t_{1}}+g) \tag{5}\]  
For the convenience of calculation, the air resistance of the pot seedling when sliding from point A to point B and the friction between the pot seedling blade and the inner wall of the seedling cylinder were neglected. The pot seedling and the slideway were approximately subjected to a free-dropping motion before the collision. That is, the velocity of the pot seedling before the collision is  
\[v_{1}=\sqrt{2 gL_{AB}} \tag{6}\]  
As shown in Figure 9b, after the collision, the pot seedlings slide along the inner wall of the seedling cylinder, with the center of the weight of the canister as the study point. During the sliding process, the pot seedlings are subjected to a friction force \(f_{1}(x,y)\), support force \(N_{1}(x,y)\), and their gravity G. The planting requires the potted seedling to fall to the ground to maintain a stable state and to rely only on the gravity of the potted seedling to pull it from the sliding starting point to the planted seedling. In the process from position B to position C, the friction \(f_{1}(x,y)\) of the pot seedling performs negative work, and the pot seedling performs a variable motion in the system.