Three-Dimensional Analysis of Vehicle Stability Using Graph Theory

Stability of long combination vehicles

“…In the kinematic model for a mechanism, the successive screws displacement method is used (Tsai, 1999;Lee, 2001;Erthal, 2010;Moreno et al, 2015Moreno et al, , 2016aMoreno et al, , 2016b. Table 1, l 13 is the distance between the fifth-wheel and the front axle, l 1,2,7,8 are the dynamic rolling radii of tyres, t 1,3 are the front and rear track widths of the trailer, respectively, t 2,4 are the front and rear axles widths of the trailer, respectively, b is the lateral separation between the springs, b 1 is the fifth-wheel width, d 1 is the offset of the cargo, θ i is the revolution joint angle rotation i, l 3,4,9,10 are the instantaneous height of the leaf spring, L is the wheelbase of the trailer, a is the distance from the front axle to the centre of gravity, l 12 is the height of the CG above the chassis and ψ is the trailer/trailer angle.…”

“…In this study, the formalism presented by Davies (1983a) was used as the primary mathematical tool to analyse the mechanisms statically. The Davies method appears in many publications in the literature and further details regarding its use can be found in Davies (1983aDavies ( , 1993bDavies ( , 2000, Tsai (1999), Erthal (2010), Mejia et al (2013) and Moreno et al (2015Moreno et al ( , 2016aMoreno et al ( , 2016b. The Davies method was selected because it offers a straightforward way to obtain a static model of the mechanism, and this model can be easily adapted using this approach.…”

“…In our previous research (Moreno et al, 2015(Moreno et al, , 2016a, we analysed the last trailer of LCVs, and reported that the SRT factor represents a three-dimensional phenomenon, and that longitudinal parameters and LLT play important roles in relation to the SRT factor calculation.…”

“…Following the methodology developed in our previous work (Moreno et al, 2015(Moreno et al, , 2016a(Moreno et al, , 2016b, we developed a three-dimensional simplified model that considers different characteristics of trailer, and the road, such as: the suspension, tyres, fifth-wheel (FW), chassis, bank angle, longitudinal slope angle and trailer/trailer angle, to calculate the three-dimensional SRT factor for a trailer in different situations.…”

“…There are several methodologies, which allow us to obtain a complete static analysis of the mechanism; however, in this paper the formalism described by Davies (1983a) is used as the primary mathematical tool to analyse the mechanisms statically. The Davies method appears in many publications and further details regarding its use can be found in the literature (Davies, 1983a;Tsai, 1999;Erthal, 2010;Mejia et al, 2013;Moreno et al, 2015Moreno et al, , 2016aMoreno et al, , 2016b. The Davies method was selected since it allows the static model for the mechanism to be obtained in a straightforward manner and it is also adapted using this approach.…”