# Design and Evaluation of a Shaping and Pruning Machine for Dwarf and Densely Planted Jujube Trees
## 2 Materials and Methods
### Design of Shaping Frame
#### 2.5.2 Design of Shaping Adjustment Frame  
The structure of the shaping adjustment frame is shown in Figure 8. In operation, the horizontal distance of the pruning device is controlled by the above or following adjustment  
Figure 7: Schematic diagram of shaping and pruning frame structure. (1) Left connecting seat for side pruning assembly. (2) Long vertical beam. (3) Crossbeam for pruning frame. (4) Crossbeam for adjustment frame. (5) Swinging cylinder. (6) Connecting seat for shaping and pruning frame. (7) Fixing sleeve for oblique beam. (8) Top pruning diagonal beam. (9) Connecting seat for top pruning assembly. (10) Fixing sleeve for frame beam. (11) Right connecting seat for side pruning assembly. hydraulic cylinder (that is, the horizontal distance between the pruning position and the edge of the tractor). The position of the inner sleeve for the vertical beam relative to the outer sleeve for the vertical beam is adjusted by telescopic lifting of the cylinder, so as to control the pruning height (that is, the height of jujube trees from the ground). The range of lifting cylinder is determined according to the upper limit of pruned jujube tree height (2200 mm). The hinge point of the outer sleeve for the vertical beam is 350 mm above the ground. Considering that the combination method for the inner and outer sleeves for the vertical beam is for sloping when the pruning machine is operating, the designed measuring range of the lifting cylinder is 800 mm, the installation distance is 850 mm, and the adjustment range of the vertical beam height is 1450-2250 mm (that is, the adjustment of jujube pruning height). To ensure that the horizontal adjustment distance of the pruning machine meets the requirements, the maximum adjustment angle needs to be determined. The adjustment frame was analyzed geometrically. The adjustment frame geometry was simplified to facilitate calculation, as shown in Figure 9. In order to ensure that the pruned jujube branches will not be scratched and pulled by the tractor or that the side pruning assembly \(EF\) will not overlap with the outside edge of the tractor, the distance between \(CD\) and EF was set to 150 mm. When pruning the maximum diameter of canopies and the highest height of trees, the value of adjustment angle \(\alpha\) is the largest. At this time, the above adjustment cylinder has no expansion, and the following adjustment cylinder reaches the maximum expansion state. In order to find the angle \(\alpha\), a triangle \(\Delta OAB\) is drawn. The length of \(OB\) is 2775 mm, which is obtained through the proportion drawing method, and the length of \(OA\) and AB are known. The expression for the adjustment angle is established according to the cosine theorem, as shown in Equation (10):  
\[\cos\alpha=\frac{OA^{2}+AB^{2}+OB^{2}}{2 OA\times AB} \tag{10}\]  
Figure 8: Structural diagram of shaping adjustment frame. (1) Fixed base for adjustment frame. (2) Following adjustment cylinder. (3) Outer sleeve for vertical beam. (4) Lifting hydraulic cylinder. (5) Inner sleeve of vertical beam. (6) Above adjustment cylinder. (7) Crossbeam locking assembly. (8) Crossbeam for adjustment frame. (9) Mounting holes for shaping and pruning frame. As obtained from Equation (10), \(\alpha\approx 106.5^{\circ}\). To obtain the geometric relationship between the stretching length of the cylinder \(x\), the original length of the adjusting cylinder \(l\) and the installation distance of the cylinder \(l_{ab}\), the geometric relationship of the adjustment cylinder was analyzed, as shown in Figure 10.  
From the geometric relations, Equations (11) and (12) can be obtained:  
\[\left\{ \begin{array}{c}l_{b1f1}=l_{dlc1}=l_{a1d1}\cdot\sin(180^{\circ}-\alpha) \\ \hskip 14.226378 ptl_{c1f1}=l_{b1c1}-l_{b1f1}\\ \hskip 14.226378 ptl_{a1e1}=l_{a1d1}\cdot\cos(180^{\circ}-\alpha)\\ \hskip 14.226378 ptl_{d1f1}=l_{b1e1}=l_{ab}+l_{a1e1}\\ \hskip 14.226378 pt(l+x)^{2}=l_{c1f1}^{2}+l_{d1f1}^{2}\end{array} \right. \tag{11}\]  
Figure 10: Schematic diagrams of the geometric relationship for adjustment cylinder.