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.