# Multi-Criteria Optimization of an Innovative Suspension System for Race Cars
## 2 Conceptual Design of the Single-Seater Suspension System  
The development of the conceptual solution for the suspension system of the single-seater race car was based on the functional particularities (including advantages and disadvantages) of the classic suspension based on the four-bar mechanism, both in the passive (Figure 2) and active version (Figure 3). The principle behind this was to define a system with a single degree of mobility (DOM = 1)--as the passive system, which could achieve adjustments specific to the mechanism with two degrees of mobility (DOM = 2)--as the active system (considering the systems in a planar configuration, as are the representations in Figures 2 and 3). The solution of the above-mentioned system was based on a five-bar mechanism that had two degrees of mobility. The initially developed suspension system, which integrated the specific pushrod-rocker assembly that helped mount the spring and damper assembly in a horizontal plane (as shown in Figure 2b) is presented in Figure 4. This would make it possible to decouple the contradictory movements (wheel track and camber angle variations) from influencing each other. The control of the second degree of mobility (with the purpose to cancel, by case, the wheel track variation or the camber angle variation) could be achieved by an actuating element (resulting in an active suspension) or by a mechanical element (passive suspension). Thus, the active suspension could be constituted, for example, by using a linear actuator, disposed between the upper connecting rod (upper control arm as per Figure 2) of the five-bar mechanism and the chassis, with the corresponding scheme shown in Figure 5.  
Figure 4: Suspension system based on the five-bar mechanism (DOM = 2). With the view to obtain a pure mechanical (passive) suspension able to provide the functional parameters (behavior) of the active suspension, an original design algorithm was developed, which was based on the following steps:  
1. In the five-bar suspension mechanism (Figure 4), the variation of the camber angle was canceled by means of a kinematic constraint of form \(\Delta\gamma=\gamma-\gamma_{0}=0\), where \(\gamma\) is the current value of the camber angle, and \(\gamma_{0}\) is the initial value;
2. Performing the kinematic analysis of the suspension mechanism by imposing the vertical travel of the wheel with the help of a kinematic restriction;
3. Obtaining the trajectory of a specific point on the upper rod of the five-bar mechanism; the trajectories of several points on the upper rod could be monitored, finally choosing the point that would generate a more convenient trajectory (it could be a semicircle for the planar variant of mechanism, or a hemisphere for the spatial variant);
4. Replacing the kinematic restriction from step \"1\" with one of the following variants: 4.1. Geometrical constraint roller-guide type (Figure 6), where the roller would be mounted on the upper rod, while the guide of which would attached to the chassis would have the shape defined by the trajectory obtained in step \"3\";
4.2. Second rocker mounted between the upper rod and the chassis (Figure 7), linked to the upper arm in the point (M) that describes the trajectory from step \"3\" and to the chassis at the geometrical center (M\({}_{0}\)) of the trajectory. Figure 5: Active suspension system based on the five-bar mechanism (DOM = 2). Figure 6: Suspension system with guiding roll (DOM = 1). Both purely mechanical solutions obtained in step \"4\" led to mono-mobile (DOM = 1) mechanisms (in the planar versions), and could be used on a single-seater racing car suspension as they are reduced in size, lighter, and are not as complex as an active suspension system. It should be noted that the mechanism obtained by the second variant in step \"4\" (Figure 7) would be viable if the trajectory defined by the interest point (M) from the upper arm approximated a semicircle or a hemisphere.