## 2 Materials and Methods
### Innovative Design of Transplanting Mechanism
#### 2.2.1 Seedling Gripper
Figure 3: Structure drawing and operation schematic of the multi-pin grasping type seedling gripper: (**a**) overall mechanical structure: 1. fixed bracket; 2. revolute joint; 3. rubber finger; 4. pneumatic connector; 5. cylinder finger; 6. support plate; 7. support bar; 8: tightening spring; 9. support slot; 10. limit gasket; 11. extension rod; 12. pick-up pin; 13. pneumatic solenoid valve; (**b**) grasping operation: 1� air inflating: 2� pin withdrawing; 3� pin penetrating; 4� air deflating; 8� spring tightening; 6� pin grasping; 7� gripper moving; 8� pin extracting. \[\left\{ \begin{array}{l}L_{\text{CC}^{\prime}}=b-2\Delta d_{1}\\ L_{DD^{\prime}}=a-2\Delta d_{2}\\ L_{\text{CF}^{\prime}}=\sqrt{2}(b-2\Delta d_{1})\\ L_{\text{DG}^{\prime}}=\sqrt{2}(a-2\Delta d_{2})\end{array} \right. \tag{1}\]  
where \(L_{\text{CC}^{\prime}}\), \(L_{\text{DD}^{\prime}}\), \(L_{\text{CF}^{\prime}}\), and \(L_{\text{DG}^{\prime}}\) are the corresponding pick-up parameter dimensions, respectively, mm; \(a\) and \(b\) are the lower side length and the upper side length, respectively, mm; \(\Delta d_{1}\) and \(\Delta d_{2}\) are the side distances from the upper and lower pick-up pin inlets to the hole, respectively, mm. The upright inclination angle of the pick-up pin along the grasping direction was set as \(\theta\). Then, the penetration depth can be theoretically determined as follows. \[L_{CD}=\frac{h_{1}-h_{2}}{cos\theta} \tag{2}\]  
where \(L_{\text{CD}}\) is the corresponding pick-up penetration depth, mm; \(h_{1}\) is the height of the root lump, mm; \(h_{2}\) is the vertical distance from the end of the pick-up pin to the hole bottom, mm; \(\theta\) is the pick-up upright inclination angle, \({}^{\circ}\). In this study, it was assumed that the root lumps of plug seedlings were of homogeneous body. The grasping forces were equal in all directions, and the pick-up pins were applied at the force action within the rigid range. Then, the effective equilibrium condition in the clamping and extraction directions can be expressed as follows. \[\left\{ \begin{array}{l}F_{\text{J1}}=F_{\text{J2}}\\ F_{\text{S1}}=F_{\text{S2}}\\ F_{\text{J1}}\times cos\theta=\sqrt{2}F_{\text{S1}}\\ 2(F_{\text{J1}}+F_{\text{J2}})\times sin\theta\geq F_{\text{G}+A}\end{array} \right. \tag{3}\]  
where \(F_{\text{J1}}\) and \(F_{\text{J2}}\) are the holding forces imposed on the pick-up pins, respectively, N; \(F_{\text{S1}}\) and \(F_{\text{S2}}\) are the grasping forces imposed by the bundling of the tightening spring, respectively, \(N\); \(\theta\) is the pick-up upright inclination angle, \({}^{\circ}\); \(F_{\text{G}+A}\) is the resultant force from the seedling's gravity and its adhesion force in the vertical direction, N.  
The equivalent transformation was performed on the Equation (3). To successfully pull out the seedling plug, the tightening force of the spring on the pick-up pins should meet the following constraint condition. \[F_{\text{S1}}\geq\frac{\sqrt{2}cos\theta\times F_{\text{G}+A}}{8 sin\theta} \tag{4}\]  
Figure 4: Schematic drawing of grasping action on the root lump of plug seedlings: (**a**) front view; (**b**) vertical view; (**c**) water film attraction. where \(F_{S1}\) is the grasping forces imposed by the bundling of the tightening spring, mm; \(\theta\) is the pick-up upright inclination angle, \({}^{\circ};F_{G+A}\) is the resultant force from the seedling's gravity and its adhesion force in the vertical direction, N.  
Since the root lump of the plug seedling is the root-soil complex, a water film attraction has been formed between the root lump and its cell wall at some water contents [28]. The corresponding force values could be calculated as follows. \[\left\{ \begin{array}{l}F_{G+A}=F_{G}+F_{A1}+F_{A2}+F_{A3}\\ F_{A1}=2k_{1}\tau r_{1}(\tau_{\delta 1}+\tau_{\delta 2}-\tau_{\delta 1|\delta 2})\\ F_{A2}=\sum 4\pi r_{1}\gamma_{LV}\cos\delta\\ F_{A3}=\sum\frac{3k_{2}\eta\gamma_{LV}^{2}}{4!}\end{array} \right.