# Transverse Movement Kinetics of a Unit for Inter-Row Crops--Case Study: Cultivator Unit
## 2 Material and Methods
### Experimental Studies  
Based on the analysis of Figure 1, it is evident that \(\varphi_{p}\) and \(\varphi_{r}\) angles are functions of the the turning angle of tractor wheels (\(\alpha\)). That is, \(\varphi_{p}=k_{1}\cdot\alpha\) and \(\varphi_{r}=k_{2}\cdot\alpha\), where \(k_{1}\) and \(k_{2}\) are some coefficients of proportionality. In this study, \(k_{1}=k_{2}=0.5\) was taken. The angle value \(\alpha\) in the calculations was changed within 1-6\({}^{\circ}\). In this case, as shown by preliminary studies of the unit as part of the KhTZ-16131 tractor (Kharkiv, Ukraine) and the KRNV-8.4 row cultivator (Elvotri, Ukraine) with \(B_{p}=8.4\) m, the actual values of the coefficients \(k_{1}\) and \(k_{2}\) are quite close to the accepted ones. The values of the remaining parameters included in Equations (1)-(4) were as follows: \(L=2.86\) m; \(\delta_{A}=1\)-3\({}^{\circ}\); \(\delta_{B}=1\)-3\({}^{\circ}\); \(l_{z}=-2\); 0; 2 m; \(l_{p}=-2\); 0; 2 m.  
The physical object of the research was an MTU consisting of a KhTZ-16131 tractor and a KRNV-8.4 row-crop cultivator (Table 1). This MTU was configured according to two diagrams: (1) rigid attachment of the cultivator with the tractor in the horizontal plane (variant A) and articulated attachment (variant B). In the unit of variant A, the check chains (1) of the tractor's three-point hitch linkage were tensioned, and in variant B, they were freely slack. This allowed the cultivator with the low-linkage hitch (2) to turn relative to the tractor in a horizontal plane. The machine-tractor team from both schemes worked in the same agricultural field during the inter-row weeding of sunflower seeds. During the experimental studies, we measured (a) soil moisture and density in a layer of 0-10 cm; (b) the depth of tillage between rows; (c) the width of a one-sided protective zone; (d) the row-crop unit's movement velocity. \begin{table}
\begin{tabular}{c c} \hline \hline
**Index** & **Value** \\ \hline Tractor weight (kg) & 8200 \\ Cultivator weight (kg) & 1920 \\ Cultivator number sections & 13 \\ Distance between cultivator sections (m) & 0.7 \\ Cultivator operating width (m) & 8.4 \\ Tractor wheelbase (mm) & 2860 \\ Tractor track (\(B_{t}\), mm) & 2100 \\ Tractor fires & 16.9R38 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical characteristics of weeding machine-tractor unit. To measure soil moisture, we used a specially developed device (Figure 2a). Its operation is based on the dielectric constant, which depends on its moisture. A piston is mounted on the top cover of the device. It is designed to compact the soil. As a result, the effect of its density on humidity is neutralized. The electronic part is located on the bottom cover of the device. During the measurement process, a dose of soil is placed in the instrument glass. After the piston compacts, its humidity (%) is recorded on the electronic part. The measurement error of this device does not exceed 1%. Soil density was measured using a device developed by us in the form of a cylinder with a volume of 28.35 cm\({}^{3}\) (Figure 2b). The soil sample taken with a cylinder was weighed on a scale (EGY-100, Dneproves, Dnipro, Ukraine) set to measure in ounces (oz). Because 1 oz = 28.35 g, the EGY-100 scale displayed the soil mass, corresponding to its density in g\(\cdot\)cm\({}^{-3}\). The measurement error with this device does not exceed 0.01 g\(\cdot\)cm\({}^{-3}\). The measurement of soil density and moisture was carried out along the diagonal of the field. The measurements for each parameter were 30, and the measurement step was 5 m.  
We used a device (Figure 2c) based on Arduino Uno (Milan, Italy) to measure the depth of sunflower inter-row cultivation. This device uses an ultrasonic sensor US-025 (Guangdong, China), whose measurement error does not exceed 3 mm. During measurement, the device is installed with a support (2) in the processed background. The measuring probe (3) is lowered to the tillage depth \(l\). Arduino Uno (1) measures the \(L_{a}\) distance.