# Research on the Trajectory and Operational Performance of Wheel Loader Automatic Shoveling
## 3 Wheel Loader Shoveling Trajectory Planning
### Parallel Shoveling Trajectory Planning  
There are many methods of shoveling materials by loaders, the most commonly used of which are the one-step shoveling method, the step-by-step shoveling method, the excavation method, and the coordination shoveling method of these four shoveling methods. Due to the minimal resistance to shoveling by the loader according to the coordination shoveling trajectory, the shoveling process is smooth, the shoveling range is more extensive, and the high full bucket rate can be ensured, so the coordination shoveling method was chosen as the automatic shoveling of the loader in this test experiment [24]. The trajectory planned according to the coordination shoveling method is further divided into the straight trajectory and the curved trajectory, as shown in Figure 6.  
AB is the horizontal shoveling stage; BC is the shoveling stage; CD is the bucket lifting stage; AD is the surface of the pile.  
Figure 5: The process of the automatic shoveling test.  
Figure 6: Coordination shoveling trajectory.  
In the loader shoveling process, the bucket is first inserted horizontally into the pile from point A to point B. then it starts to cooperate with shoveling from point B to point C. Finally, the bucket is lifted from point C to point D, and the automatic shoveling ends. In the BC section, it can be a straight trajectory or a curved trajectory. However, on the premise of meeting the same shoveling volume, the loader requires less energy to shovel according to the straight trajectory than the curved trajectory [25], so the straight trajectory is more suitable for this shoveling test to reduce carbon emissions and improve efficiency.  
The loader shovels the material according to the straight-line trajectory. If the inclination angle of the straight trajectory is greater than the resting angle of the material pile will produce Coulomb passive earth pressure and affect the full bucket rate. If the straight trajectory inclination angle is less than the resting angle of the pile, the shoveling resistance in the shovel excavation phase will increase [26]. Therefore, as shown in Figure 7, the inclination angle \(\beta\) of the straight shoveling trajectory is equal to the angle \(\alpha\) of the pile, and such a straight shoveling trajectory is called parallel shoveling trajectory. The shoveling cross-section of the parallel shoveling trajectory is shown in Figure 6, and the bucket tooth tip trajectory formed by the bucket shoveling according to the parallel shoveling trajectory is shown in Figure 8.  
Where \(Z\) is the vertical distance between the linear shoveling trajectory and the pile surface; also known as parallel shoveling depth; \(\alpha\) is the pile rest angle; \(S\) is the cross-sectional area.  
As shown in Figure 7, the parallel shoveling trajectory has three phases, the \(ab\) interval is the horizontal insertion phase, the bc interval is the shovel digging phase, and the \(cd\)  
Figure 8: Trajectory of the bucket tooth tip.  
Figure 7: Shoveling cross-section.  
interval is the lifting phase. The shoveling cross-section \(S\) consists of the surface profile of the stockpile and the bucket tip curve. According to our previous deduction inside the literature [27], The curve equation of the bucket tip can be defined as:  
\[\left\{\begin{matrix}L_{bc}=\frac{L_{ab}=\frac{Z}{\sin\alpha}}{Z\rho(1-N)B}- \frac{Z}{\sin 2\alpha}\\ L_{cd}=\frac{Z}{\cos\alpha}\end{matrix}\right. \tag{1}\]  
where \(G\) is the rated shovel weight of the test vehicle; \(B\) is the width of the bucket; \(\rho\) is the density of the material; \(N\) is the porosity of the material.  
According to Equation (1), the bucket tip position is only a function of \(Z\), provided that the material density, porosity, rest angle of the pile, bucket width, and rated shoveling weight are known. Then different \(Z\) values are selected and brought into Equation (1) to obtain the corresponding bucket tip trajectory.