# Transverse Movement Kinetics of a Unit for Inter-Row Crops--Case Study: Cultivator Unit
## 1 Introduction  
One of the most essential and responsible agricultural technological operations is the inter-row cultivation of row crops. Its application aims to solve several problems: (I) weed control; (II) reduce soil moisture loss by destroying its capillary structure in the capillary structure of the upper layer capillary structure; (III) aeration of the soil root layer. Weeds steal nutrients, water, and sunlight, reducing both the quality and the quantity of crop yields [1]. Taking up the necessary space from weeds can make crop plants more susceptible to diseases and even pests [2; 3]. Previous research shows that a lack of weed control can cause up to 90% crop loss [4; 5]. The most commonly used weed control methods include chemical, mechanical, and a combination of these two methods [4]. In many countries, chemical control using herbicides dominates, increasing production costs and negatively affecting the natural environment [6]. At the same time, herbicide residues in soil negatively affect the quality [7], as well as of drinking water [8], and have a harmfuleffect on soil microorganisms [9]. According to the resolutions of the European Green Deal on crops by 2030, we are to strive to reduce the use of chemically synthesized plant protection products by 50%. Therefore, there is a visible need to develop alternative methods of weed control that retain moisture in the soil and aerate it. There are known non-chemical methods for weed control, e.g., intercropping, flaming, or steaming, but these methods are not economically justified [10]. Furthermore, thermal methods of weed control are very expensive (energy-consuming) and inefficient [11; 12]. Taking into account the care of the natural environment and the requirements of the modern market for healthy food [13], the development of mechanical weed control methods is also becoming increasingly important in conventional agricultural systems [14; 15]. It should be emphasized once again that chemical control does not retain moisture in the soil (does not reduce moisture loss) and does not create conditions for increasing the aeration of the root layer. Although inter-row cultivation can solve all three problems, practical implementation requires determining the best parameters. One of the important parameters is the ability to reduce or even completely eliminate damage to crop plants, even if the rows in the crops are not perfectly straight. To systematize the boundary conditions of inter-row cultivation, many countries have developed agrotechnical requirements with respect to the straightness of sowing (planting) of crops. In Ukraine, for example, the crop trajectory is acceptable if the variance of its amplitude oscillations does not exceed 12.5 cm\({}^{2}\), and in frequency, most of them (at least 95%) are in the range of 0-25 m\({}^{-1}\)[16]. On the other hand, the mechanical control of processing inter-row spacing of crops raises requirements for the technical devices used for its implementation. If this unit consists of a tractor and a cultivator, the tractor's tires must fit into the row crops' inter-row width. With relatively narrow row spacings (45 cm, for example), the tractor should be equipped with double tires and the ballast (if necessary) of its front axle should be carried out [17], taking into account the requirements of \"ecophilic\" tires. Special devices are required to design an asymmetric machine-tractor unit in the case of the tractor track with a width ratio in the form of an odd number [18]. Most inter-row units consist of a self-propelled vehicle and rear-hitched cultivator(s). Units with rear-driven machines have different designs and their own set of work devices [19; 20; 21; 22]. Recently, robotic machines have been used more and more frequently [23], which are characterized by good efficiency despite small operating widths and save time for the operator because they do not require its participation during agrotechnical procedures.