Technological peculiarities of cultivation and harvesting of some agricultural crops make it necessary to use asymmetric machine-and-tractor aggregates. However, for the time being there is no sufficiently complete, analytical study of the steady movement of such machine-and-tractor aggregates. This necessitates the development of a theory of stable movement of the aggregates which would allow choosing their optimal kinematic and design parameters. On the basis of the results of mathematical simulation, a system of linear differential equations of the second order is obtained describing transverse displacement of the center of masses of the aggregating wheeled tractor and turning of its longitudinal axis of symmetry by some angle around the indicated center of mass, as well as the deviation angle of the rear-trailed harvester from the longitudinal axis of the tractor at any arbitrary moment of time. This system of differential equations can be applied for numerical calculations on the PC, which will make it possible to evaluate the stability of the movement of the asymmetric machine-and-tractor aggregate when it performs the technological process.

The harvest techniques and the employed machines are important factors in reducing soil loss due to root crop harvesting. Furthermore, the deviation of the working organs of the self-propelled sugar root harvesting machines from the axis of the row also leads to significant losses and damage to sugar beetroots. Therefore, the self-propelled machine units must move in a horizontal plane with a high degree of accuracy. The purpose of this study is to increase the efficiency of the self-propelled harvester by analyzing its plane-parallel motion and evaluating its constructive and kinematic parameters. In order to determine the influence of these parameters on the plane-parallel motion of the self-propelled root harvesting machine, its mathematical model has been calculated. Furthermore, experimental tests were executed in order to evaluate the degree of damage to sugar beetroot crops during their digging, depending on the magnitude of the deviations of the center of the digging tool. The results of this trials highlighted that if the crop row deviates from the conventional axis line by 10 mm, the root crop damage exceeds is 21.7% and at deviations by 70 mm, the damage exceeds 67%. The theoretical study of the trajectory of the center of the outside digging tool and the experimental evaluation of its work (in terms of the quality of harvesting with deviations in its trajectory of motion) formally confirm the coincidence of all the studies—both theoretical and experimental. The use of the model of the plane-parallel movement of the self-propelled root harvesting machine then improves the quality parameters of the technological process.

The beet leaves and tops, which currently are excluded from the production process of sugar, could be an interesting opportunity for the production of renewable energy. Usually, the defoliators are joined with root collar remover machines, which are installed in front of the tractor. In working conditions on soils having natural roughness these front-mounted beet topper machines carried by tractors are affected by angular oscillations in a longitudinal-vertical plane that strongly affect the cutting uniformity. A theoretical study of these oscillations was carried out in this paper using Lagrange II kind equations, with the aim to assess the design and kinematic parameters of a front-mounted beet topper, corresponding to more stable and suitable movements in the longitudinal-vertical plane. A numerical simulation was then performed adopting the developed mathematical model. In order to improve the efficiency of this harvesting machine, a significant role is assumed by the soil preparation. In this work the stiffness and damping parameters of the feeler wheels pneumatic tires have been considered constant but further studies are in progress to assess their effective importance and influence for reducing the vibration of the front-mounted beet topper machine with the final aim to achieve a better machine design.

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It is purposeful to increase the efficiency of the 80-100 hp tractors (traction class 1.4) in sowing agricultural crops by increasing the working width of the technological part, using wide-span sowing machineand-tractor aggregates. However, their movement characteristics on the turning strips in many respects determine their technical and economic performance, as a whole. It has been found out by the conducted research that a motivated choice of the parameters of wide-span sowing machine-and-tractor aggregates allows them making manoeuvres of turns on the turning strip in an optimal mode, which promotes reducing the length and time for turns by 4.5-11.2 % and the width of the turning strip by 4.9-12.1 %. In order to improve the turning ability of a two-machine sowing aggregate, it is desirable to apply ballasting (i.e., installation of additional loading) of the front axle wheels of the tractor. Thus, additional loads with a mass of 180 kg, installed on it, can reduce the turning radius of the aggregate. The most noticeable result of ballasting is achieved, when the turning angle of the driven wheels of the tractor is greater than 0.32 rad. At the maximum value of the control action (α = 0.5 rad) the reduction in the turning radius of the aggregate, due to ballasting the front axle of the tractor, is 0.8 m (i.e. 15 %). It has been theoretically established that, in case the speed of the movement is increased from 1.0 to 3.0 m⋅s-1 , the turning radius of the unit tends to decrease. Such a result is because the increase in the drift angle of the rear wheels of the tractor outstrips the increase in the drift angle of the tires of its front wheels.