# 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  
The influence of the rear and front cultivators' operating width (\(B_{p}\)) on the deviation of their outside right (\(h_{p},d_{p}\)) and left (\(h_{o},d_{o}\)) working bodies are shown in Figure 3. The \(B_{p}\) parameter was set to 5.6, 8.4, 11.2, and 16.8 m. The values of the other parameters, included in Equations (1)-(4), were constant and equal: \(\alpha=3^{\circ};\delta_{A}=\delta_{B}=2^{\circ};l_{p}=l_{z}=2\) m.  
Calculations have established that with an increase in the rear row cultivator operating width and a change in the unit movement with the tractor's steering wheels' turning angle from \(1^{\circ}\) to \(3^{\circ}\), the transverse deviation of its outside right working devices tends to increase qualitatively (see Figure 3). In quantitative terms, this increase is insignificant: with an increase in the \(B_{p}\) value by a factor of three (from 5.6 to 16.8 m), the value of the \(h_{p}\) parameter increased by only 3.6%. The deviations of the outside left working devices of the rear cultivator decreased by the same 3.6% (curve \(h_{o}\), Figure 3). The opposite trend is observed in the behavior of the frontal cultivator's outside working devices. That is, with an increase in the cultivator operating width by three times, the transverse deviations of the outside left working devices (\(d_{o}\) curve, Figure 3) increase by 3.1%, and the deviations of the outside right ones (\(d_{p}\) curve, Figure 3) decrease by the same amount. Based on the obtained research results, it can be noted that for small values of the turning angle of tractor wheels (which is typical for MTU row work), increasing the cultivator's width by three times causes small antiphase deviations (an increase or decrease in the amplitude of lateral deviations does not exceed 4%). The change in the value of the tractor's steering wheels' turning angle is qualitatively the same, but quantitatively, it has a different effect on the changing nature of the cultivator's working devices' transverse deviations. Their values in both variants of aggregating the row cultivator with the tractor increase as the values of the \(\alpha\) parameter increase (Figure 4). But the dynamics of these processes is different. The frontal cultivator reacts more intensively to changes in the \(\alpha\) parameter. Furthermore, when the value of the turning angle of tractor wheels is less than 2.75\({}^{\circ}\), it is generally preferable because in this case, the deviations of its working devices (\(d_{p},d_{o}\)) are less than those of a rear-hitched cultivator (\(h_{p},h_{o}\)). Figure 3: The dependence of the transverse displacements of the row cultivator working devices from its operating width. During widespread GPS introduction, which guarantees fluctuations in the tractor's steering wheels' turning angle from 1\({}^{\circ}\) to 2\({}^{\circ}\), considering this factor in choosing a row-crop MTU diagram can be decisive. As noted above, the lateral arrangement of row cultivators relative to the tractor can be emulated by changing the values of the \(l_{p}\) and \(l_{z}\) parameters (see Figure 1). Analysis of dependences (1) and (2) shows that an increase in the value of the \(l_{z}\) parameter, equivalent to the distance of the rear cultivator from the tractor, increases the transverse displacements of its outside right and left working bodies (Figure 5). Figure 4: Dependence of the transverse displacements of the workhorse plant of the tractor’s steering wheels’ turning angle. Figure 5: Dependence of transverse displacements of the working devices of the rear-hitched row cultivator from the coordinate of its placement relative to the tractor. However, when the sections of the row cultivator are moved forward relative to the rear axle by a distance \(l_{z}\approx-1.2\) m, we reach the zone of absence of their transverse displacements (\(h_{p},\ h_{o}\approx 0\)). Such a result, in principle, is ideal.