## 3 Algorithm for Finding the Static Equilibrium  
The equilibrium configuration of the suspension system in relation to the car body (considered as the fixed reference part) is determined on the static model (Figure 3), which is defined by kinematic elements (bodies), geometric constraints (joints), and elastic elements. Determining the equilibrium configuration consists in establishing the independent positional parameter (the wheel guidance mechanisms having one degree of mobility), which corresponds to the vertical displacement of the wheel center (\(Z_{\text{Gs}}\) or \(Z_{\text{Gd}}\)). The external loading of the suspension system is carried out by forces applied to the wheels (\(\text{F}_{\text{s,d}}\)), in the theoretical contact point with the ground (\(\text{K}_{\text{s,d}}\)), corresponding to the specific operating regime (such as stationary, traction, braking, skidding). These are balanced by the reaction forces or torques in the elastic elements of the suspension system, as follows:  
* The forces in the springs (\(\text{F}_{\text{as,d}}\)), which are applied in \(\text{Q}_{\text{s,d}}\);
* The torsional (\(\text{M}_{\text{fb}}\)) and conical (\(\text{M}_{\text{fc}}\)) torques in the bushings (which are modeled by spherical joints, with elastically restricted rotations);
* The forces in the buffers for limiting the suspension travel (\(\text{F}_{\text{bs,d}}\)), which are applied in \(\text{T}_{\text{s,d}}\);
* The forces in the anti-roll bar (\(\text{F}_{\text{ws,d}}\)), which are applied in the connection points \(\text{W}_{\text{s,d}}\) of the anti-roll bar to the connecting rods. With the exception of the forces in the anti-roll bar, which depend on both independent parameters (i.e., the vertical coordinates of the wheels' centers, \(Z_{\text{Gs}}\) and \(Z_{\text{Gd}}\)), the other elastic forces depend only on the parameter corresponding to the left or right side of the suspension (by case, \(Z_{\text{Gs}}\) or \(Z_{\text{Gd}}\)). It must be noted that due to the anti-roll bar, which is connected between parts from the left and right guidance mechanisms, it is necessary to consider the transverse half-car model of the suspension system (such as the one shown in Figure 3, where the anti-roll bar is connected by rods to the lower guidance arms), which considers the suspension systems of both axle wheels, and not just the quarter-car model corresponding to the suspension of a single wheel [31; 32; 33]. Although, under the action of wheel reaction forces, not only do the elastic elements of the suspension deform but so do the tires and sometimes even the bars of the guidance mechanism. These deformations are not taken into account in the determination of the equilibrium position, which considers them negligible compared to the deformation of the suspension elements. It should be mentioned that in the automotive industry, there are some experimental tests carried out on a so-called full-vehicle road simulator (test rig),  
Figure 3: The static model of the non-steered wheels’ suspension system. in which the wheels are disassembled/removed, and the external forces are applied (by some actuators) directly to the wheel spindle level [34]. Such an actuating mode is largely equivalent to the \"rigid tire\" assumption used in this work. Therefore, the mechanical work developed by the wheel reaction forces is transformed only into mechanical work of deformation of the elastic elements of the suspension.