# Transverse Movement Kinetics of a Unit for Inter-Row Crops--Case Study: Cultivator Unit
## 3 Results and Discussion
### Theoretical Study of the Row-Crop Cultivators' Turn Kinematics
Similar reasoning is valid for the front row cultivator (Figure 6). For this, under the conditions \(\alpha=3^{\circ}\), \(\delta_{A}=\delta_{B}=2^{\circ}\), and \(B_{p}=8.4\) m, zero displacement of the outside working devices can be achieved at \(l_{p}\approx-0.8\) m. This can be achieved by shifting the sections of the front cultivator back by a specified distance with respect to the axis of the tractor's front wheels. As a result, we find that, taking into account the specific values of the row-crop MTU design parameters included in Equations (1) and (2), it is possible to choose such an arrangement of the inter-row cultivator working devices, at which their transverse displacement will be close to zero. With the lateral placement of the cultivators as part of a row-crop MTU, the central machine can be placed behind and in front of the tractor. Based on the data analysis in Figure 4, a frontal cultivator is preferable when the tractor's steering wheels' turning angle is increased up to \(3^{\circ}\). The theoretical analysis shows that with an increase in the \(\delta_{A}\) parameter from 1 to \(3^{\circ}\), the outside left and right working devices of cultivators react oppositely. Namely, if the values of \(h_{p}\) and \(h_{o}\) transverse displacements increase for the rear machine, then the values of similar \(d_{p}\) and \(d_{o}\) displacements decrease for the front cultivator (Figure 7). At the yaw angle of the tractor's steering wheels' tires \(\delta_{A}\approx 2.5^{\circ}\), there is an approximate equality of the indicated transverse displacements, i.e., \(h_{p}\approx h_{o}\approx d_{p}\approx d_{o}\). This provision means that with a turning angle of the tractor wheels \(<2.5^{\circ}\), the difference in the lateral deflections of the external right and external left working devices of the cultivator is so small that it can be neglected. Figure 6: Dependence of transverse displacements of the working devices of the front-hitched row cultivator from the coordinate of its placement relative to the tractor. The algorithm for further use of the \(\delta_{A}\) parameter set value can be as follows. Considering the dynamic of MTU movement of the row in the horizontal plane, it is possible to determine the lateral force (\(T_{B}\)) acting on the tractor's steering wheels. The product \(\delta_{A}\cdot T_{B}\) gives the value of the tire yaw resistance coefficient (\(k_{B}\)). After determining this parameter, guided by the methodology described by [29], it is possible to calculate the required air pressure on the tires of the steering wheels of the tractor. Similarly, you can carry out this step when determining the tires of the air pressure in the rear wheels. From the above, using only a centrally located cultivator or its combination with side ones can provide four different row-crop MTU diagrams (Figure 8). Figure 8: Row MTU design variants: (**a**) a cultivator mounted at the front, (**b**) a cultivator mounted at the front and two cultivators at the rear, (**c**) a cultivator mounted at the rear, and (**d**) two cultivators mounted at the front and one at the rear. Figure 7: Dependence of the transverse displacements of the working devices of the row cultivator from the tractor’s steering wheels’ tires’ yaw angle. In general, the operating width of the side (\(B_{po}\)) and central (\(B_{pc}\)) cultivators may not be the same. The following equation describes the ratio of these parameters:  
\[B_{po}=k\cdot B_{pc},\]  
where \(k\) is the proportionality coefficient, \(0<k\leq 1\). In the MTU design of the row described, for example, in [17], the coefficient \(k\) is 0.25.