# Multi-Criteria Optimization of an Innovative Suspension System for Race Cars
## 3 The Kinematic Optimization of the Suspension Mechanism  
The kinematic optimization was carried out by considering the bi-contour mechanism, as shown in Figure 9, which was obtained from the spatial variant of a five-bar suspension mechanism (whose planar scheme is that shown in Figure 4) to which the toe link (6) was added for both the front and rear axles. The resulting suspension system had three active degrees of mobility, and another two passives (the rotation of links \"3\" and \"6\" around their own axes). The passive rotations could be canceled by adding additional kinematic constraints: \(\varphi_{3}=0\), \(\varphi_{6}=0\). When the car moves, the vertical travel (up-down) of the wheel determines the modification of the suspension mechanism configuration, which generates undesirable movements, namely displacements of the wheel center along the transversal and longitudinal axes (corresponding to the wheel track and wheelbase variations), as well as modifications of the wheel axis orientation (corresponding to the toe angle, camber angle, and bump steer angle variations). Figure 8: Optimization flowchart. Canceling or at least minimizing these variations are objectives for kinematic optimization, given the negative effects they can have on the dynamic behavior of the car, such as depreciation of stability, increasing rolling resistance, additional stress, and wear in the system, which have been stated in many works, such as [7; 13; 17; 18; 20; 30; 39; 40]. Therefore, the following statements were considered in the kinematic optimization of the suspension mechanism shown in Figure 9:  
* The vertical movement of the wheel is an independent kinematic parameter. It is controlled by a \(\mathrm{Y_{K}}=\mathrm{f(t)}\) kinematic restriction, simulating the wheel passing over a 50-mm (\(\pm 25\) mm) obstacle, which is transposed in the form of a sinusoidal function, \(\mathrm{Y_{K}}=25\)-sin(t), \(\mathrm{t}\)--time [s];
* The variations of the camber (\(\Delta\gamma\)) and caster (\(\Delta\beta\)) angles were canceled by applying kinematic restrictions: \(\Delta\gamma=0\), \(\Delta\beta=0\) (further, for the purpose of physical implementation, these fictive kinematic restrictions would be replaced/substituted by geometric constraints through the guiding rocker MM\({}_{0}\), as schematically shown in Figure 7--see \"Section 4\" of the work);
* The goal of the optimization was to minimize the variations of the wheel track (\(\Delta\)E), wheelbase (\(\Delta\)L), and bump steer angle (\(\Delta\delta\));
* The global coordinates (X, Y, Z) of the joints that link the suspension mechanism bars to chassis (A, B, C, D--see Figure 9) are defined as design variables for optimization, assuming that the joint locations to wheel carrier are established/given by constructive aspects (i.e., the wheel carrier geometry). The kinematic optimization was treated separately on the front and rear wheel suspension mechanisms, using quarter-car models. The optimization of the suspension system was realized with the help of a multi-objective parametric design process, by using the MSC.ADAMS suite of software, including ADAMS/Insight, a powerful optimization software [41], and ADAMS/View, which was used to develop the multi-body system (MBS) model of the suspension system [42]. The optimization study was based on design of experiments (DOE) technique, which provided methods and tools for efficiently planning and running a series of experiments on the suspension system design and analyzing the results [41]. In what follows, a general presentation of the optimization method was made, and subsequently it was implemented for optimizing the guiding mechanisms of the front and rear wheels of the single-seater race car. The parametric design through the DOE technique was performed by following the steps indicated in reference [41]. Figure 9: The bi-contour spatial mechanism used in the kinematic optimization. In ADAMS/View, a design objective was defined by creating its corresponding measure (wheel track, wheelbase, and bump steer variations).