###### Abstract
This method is used in various multi-body software, like ADAMS, due to their simplicity and low degrees of freedom compared to FEM. A widely used approach is the SAE X-link model [28]. A simpler model, the 03-link model, is utilized in [29] to study the leaf spring. Experimental tests, including both static and dynamic tests, have validated the developed model. The advantage of this method lies in its ability to easily construct a simplified model that accurately replicates the kinematic and compliance properties of the leaf spring. However, this method does consider the hysteresis effect from friction between the leaves. The study [30] was based on the 03-link model, which introduces torsional friction at the revolute joints to address this issue. The optimization of key parameters is accomplished through a combination of ADAMS and OPTIMUS software. The comparison analysis between the simulation and test results of the leaf springs shows a good correlation. Another model used in [31] is a five-link model where the leaf spring is discretized in five rigid elements and mathematical development is used to find leaf spring performances. The results of this method are compared with those obtained using the sophisticated finite element method with SIMPACK Software, and a good correlation between the methods is observed. The equivalent model consists of finding the corresponding leaf spring model, which contains simple elements such as a coil spring and a shock absorber, while retaining the same characteristics as the reference model. This approach aims to facilitate the study of leaf springs without requiring much time for modeling and simulation, as is the case with discretization methods and finite element methods (FEMs). This method is used in [18] to replace the transversal leaf spring and the longitudinal leaf spring, which are placed in the front and rear suspension of the vehicle, respectively, with coil springs using ADAMS software, and it is validated by simulation in ADAMS and experimentally by comparing the new model's results with the original model. All the previously cited methods have been validated through experimental tests, and each has its advantages and disadvantages. Generally, the experimental testing procedure used to validate these methods consists of placing a leaf spring on a device known as a \"Static Stiffness Test stand\" (SST) [32]. This device includes a hydraulic actuator that applies a vertical force to the center of the leaf spring, and the associated vertical displacement is recorded via the displacement sensor [33]. Then, the results of the chosen method are compared to those found through the experimental tests to validate it. To conduct this experiment, it is necessary to first disassemble the leaf springs from the vehicle and mount them on a SST device. Then, the leaf spring characteristics are determined. To avoid disassembling the vehicle's leaf springs, which is time-consuming, and to eliminate the need for using an SST device to carry out the test, we proposed a method that involves conducting experimental tests on the leaf springs as they are installed in the vehicle. Therefore, the experimental test is not performed directly on the leaf springs, but on the entire suspension system, where a lifting device, scales, and displacement sensors are necessary to conduct this test. The advantage of this method is that it gives more accurate suspension system results under real operating conditions. However, this method requires prior knowledge of all the characteristics of the elements constituting the suspension system and may require experimental tests on certain elements if certain characteristics are not known. In addition, the use of scales allows for the indirect measurement of forces, which can increase the measurement error, unlike the use of the SST device which allows for the direct measurement of the force applied by the actuator. This method can be used to validate the ADAMS model of the leaf spring.