## 2 Structure Design of the 2 ZBX-2A Vegetable Transplanter
### Design of Opening and Closing Control Mechanism of Planting Duckbill
#### 2.3.2 Parameter Design of the Opening and Closing Control Mechanism  
In the process of solanaceous vegetable transplantation, the cam opening and closing sequence should cooperate closely with the movement of the double-crank five-bar planting mechanism in a rhythmical manner to ensure transplantation accuracy. Thus, the cam movement should meet the following requirements:  
Planting section (push section) _UV_: When the roller \(T\) and cam contour \(U\) make contact at the beginning of the transplantation, the pendulum rod swings clockwise around point \(O_{1}\) and drives pull line \(RP\) so that the two duck mouths quickly open. At point \(V\), plug seedlings fall into the soil and are planted. At this time, the opening distance of the duckbill reaches the maximum. Hold section (far rest section) _VW_: At this stage, the distance between the planting duckbill should always be kept at the maximum so as to prevent the planting duckbill from touching the planted plug seedling and causing the seedling to fall, thus improving the plug seedling planting rate. Connecting seedling section (return section) _WX_: The pendulum rod rotates counter clockwise towards \(O_{2}\) under the function of spring \(O_{2}U\). When the planting duckbill moves to the highest point \(X\), its mouth closes gradually. The planting duckbill closes completely as the roller falls back to the \(T\) point position. At the same time, the rotary delivery mechanism drops the solanaceous vegetable plug seedling into the closed planting duckbill. Seedling transport section (nearest section) _XU_: The pendulum is in a static state, while the duckbill is kept in a closed state for seedling transportation. According to the principle of the inversion method, the line between \(O_{1}\) and \(O_{3}\) was taken as the \(y\)-axis of the coordinate system (Figure 8). During the inversion movement, when the swing rod rotated at the \(\delta\) angle relative to the cam, the swing rod was at the position shown in the graph \(O^{\prime}{}_{1}T^{\prime}\), and its angular displacement was \(\delta\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(l_{M\uparrow}/\)mm & 86.5 & \(\varphi/^{\circ}\) & 11.6 & \(X_{O3}/\)mm & \(-\)204 \\ \(l_{X\!M}/\)mm & 18.6 & \(\gamma/^{\circ}\) & 17 & \(X_{O1}/\)mm & \(-\)184 \\ \(l_{K\!P}/\)mm & 32.5 & \(\alpha/^{\circ}\) & 24 & \(Y_{O3}/\)mm & 97.5 \\ \(l_{O1\!T}/\)mm & 110.3 & \(\eta/^{\circ}\) & 67 & \(Y_{O1}/\)mm & 220 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the planting duckbill. Figure 7: DEM simulation of the interaction between the plug seedling and the planting duckbill. Since the vegetable transplanting machine works at a high speed with a light load, the planting process needs to be stable and quick during the operation of the planting mechanism. Thus, the quantic polynomial motion law was selected to design a cam contour curve in order to avoid vibration. Combined with the kinematics of the cam mechanism, the cam parameters and the cam contour curve were obtained (Equation (10)). \[\left\{ \begin{array}{l}x_{T}=l_{O_{1}O_{3}}\sin\delta-l_{O_{1}T}\sin(\delta+ \alpha+\varepsilon)\\ y_{T}=l_{O_{1}O_{3}}\cos\delta-l_{O_{1}T}\cos(\delta+\alpha+\varepsilon)\\ \end{array} \right. \tag{10}\]  
Since the pressure angle of the mechanism is an important index in the measurement of the difficulty in the movement of the mechanism, the maximum pressure angle of the cam should not exceed the critical pressure angle \(\alpha_{c}\) in practical design. The cam mechanism pressure angle was determined as follows:  
\[\alpha=\arccos\frac{L_{O_{1}T}^{2}+L_{O_{1}O_{3}}^{2}-r_{0}^{2}}{2L_{O_{1}T}L_{ O_{1}O_{3}}} \tag{11}\]  
where \(\alpha\) is the cam pressure angle; \(L_{O_{1}T}\) is the length of the pendulum rod; and \(L_{O_{1}O_{3}}\) is the distance between the fixed end \(O_{1}\) and the cam rotation center \(O_{3}\).