## 4 Conclusions  
The article presents an outline of the methodology that allows the analysis of the braking safety of a set of vehicles (articulated vehicle) in the form of a relatively simple mathematical model. The presented simulation calculations for selected braking cases of vehicles sets in the form of a tractor-semitrailer, reflecting realistic conditions (vehicle parameters, operational situations in traffic), indicate the possibility of such an assessment. It is possible to evaluate the basic indicators of braking efficiency (braking distance, braking intensity, braking time) as well as features indicating the risk of loss of motion stability (force in the coupling, state of rotation of the wheels of the set's vehicles). A preliminary comparison of the simulation results with the available results of experimental tests (taken from [14; 15; 16]) indicates a good agreement in terms of the main indicators of braking efficiency.  
The greatest threat, both related to the braking efficiency and the increase in the force in the coupling, is associated with the lack of braking of the semitrailer axles or a significant reduction in its load. The weight and location of the centre of gravity of the load have a large impact on braking safety. The positioning of the load can significantly increase or decrease the force in the coupling. The order in which the axles are locked is also important. The braking reaction time of the semitrailer affects the maximum value of the horizontal force in the coupling during the braking initialization phase. However, in the phase of fully developed braking, it is no longer relevant to this force. Another thing is the moment when the maximum value of the horizontal force occurs (so the moment when the risk of jack-knifing the tractor-semitrailer is the highest). It usually takes place in the final phase of actuating the brakes before the phase of fully developed braking.  
The condition of the pavement has no direct effect on the horizontal force in the coupling. However, it determines the maximum deceleration value, which affects the indicators of braking efficiency and thus changes the values of the coupling forces. ABS reduces the risk associated with braking safety in this context, but does not completely eliminate it.  
The presented simulations were only an example of the capabilities of the model and the program written in the Matlab environment. An essential feature of the proposed method and model is its versatility--you can easily change the configuration of the vehicles set--the towing vehicle (truck/tractor) and towed (trailer/semitrailer), number and type of vehicle axles. It is also important to reproduce the actual characteristics of the pneumatic braking system and the ability to set various operating conditions as well as obtain relatively quick results on potential threats during braking. However, one should also remember about certain limitations related to the above-mentioned simplicity of the model (rectilinear motion is considered, relative movements of unsprung masses, interactions resulting from road surface inhomogeneity, etc. are omitted).In the course of future works, further development of the method and its testing on other set configurations and operating conditions are planned.  
Conceptualization, P.R. and M.G.; methodology, P.R. and M.G.; software, P.R.; validation, P.R. and M.G.; formal analysis, P.R. and M.G.; investigation, P.R. and M.G.; resources, P.R. and M.G.; data curation, P.R. and M.G.; writing, P.R. and M.G.; writing--review and editing, P.R. and M.G.; visualization, P.R. and M.G.; supervision, M.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.