# Modeling Movement Stability of Machine-Tractor Units Based on Modular Type Tractor
## 5 Conclusions  
1. A mathematical model of the movement in the horizontal plane of a tractor-based wide-width unit has been developed, consisting of the energetic (highly energy-saturated tractor--EM) and technological (additional traction axle--TM) modules. The amplitude and phase frequency characteristics calculated based on this model form the basis for analysing the influence of the EM and TM joining methods (locked or hinged) on the stability of the movement of the MTU when exposed to a turning moment from the machines used--one central and two side row-crop cultivators.
2. The adequacy of the developed mathematical model was verified. - Mathematical modeling has established that blocking the TM vertical hinge significantly increases the stability of the wide-width MTU motion based on a modular tractor. The practical implementation of this method of joining energy and technological modules in the horizontal plane makes it possible to exclude resonant AFC peaks and reduce their value when the unit is exposed to disturbances in the frequency range of 0.65-5.50 s\({}^{-1}\). At an oscillation frequency of the turning moment of 2.5 s\({}^{-1}\), the AFC when the TM hinge is locked is 2.82 times less than when it is free (unlocked). - Blocking the vertical hinge of the TM increases the delay in the response of the MTU to a disturbance. At an oscillation frequency of 1.5 s\({}^{-1}\), this delay is 0.6 s, and at a frequency of 0.5 s\({}^{-1}\), it increases by more than 3 times, reaching a level of 1.9 s.
3. The high movement stability of the MTU based on a modular tractor is mainly due to the size of its wheelbase. With a locked joining EM (tractor KIY-14102) and TM, the value of this parameter (5.00 m) is 2.08 times greater than that of one EM. As a result, the unit movement stability consisting of three cultivators (type KRN-4.2) and the KIY-14102 tractor may be insufficient. At oscillation frequencies of the disturbing influence less than 1.5 s\({}^{-1}\), the operation of such a unit can be characterized by a complete loss of directional stability.  
Further research will study the controllability of the units' motion based on a modular tractor. First of all, this concerns its design, in which the EM steered wheels are turned simultaneously with the TM frame. Optimal coordination of the turnings of these modular tractor links in time and amplitude will provide it with the required controllability of motion as part of various designs of machine-tractor units.  
Conceptualization, V.N., G.G., N.T. and V.G.; methodology, G.G., N.T. and V.K.; validation, O.S., R.S. and V.S.; formal analysis, G.G., V.N., N.T. and O.S.; project administration V.N. and V.K.; supervision, O.S., R.S. and V.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
**Data Availability Statement**: All data generated or analyzed during this study are included in this published article.  
**Acknowledgments:** The authors would like to thank the team of the TREATY project \"Nurturing deep tech talents for clean and sustainable energy transition\" in the framework of the EIT HEI initiative \"Innovation Capacity Building for Higher Education\" for the technical support provided during the research.  
**Conflicts of Interest:** The authors declare no conflicts of interest.