## 1 Introduction  
In the relative movement to the car body (chassis), the non-steered wheels of vehicles (usually the rear ones) are guided by multi-link mechanisms, in which a number of binary elements or kinematic chains are interspersed between the wheel carrier and chassis (car body) [1]. The connections of the guidance bars to the adjacent parts are ordinarily made by bushings, in which, as a result of the forces and torques to which they are subjected, linear and angular elastic deformations occur in all directions (such a connection is, in fact, a compliant one, with six degrees of freedom (DOF)). Frequently, to simplify the theoretical models, the bushings are modeled by spherical (ball) joints, thus neglecting the linear deformations (which are, however, very small compared to the angular ones) [2; 3; 4; 5; 6; 7]. In the case of the triangular guidance bars, with double articulation to the chassis and/or wheel carrier, as the case may be, the two afferent spherical connections determine, in fact, a revolute joint. From a kinematic point of view, the guidance mechanism must ensure the vertical movement (travel) of the wheel, so the required degree of mobility is \(\mathrm{M}=1\). In order to obtain such mono-mobile mechanisms, various structural synthesis methods are presented in the literature, depending on the type of mechanism, the number of guidance points on the wheel carrier and chassis, and the type and number of kinematic chains interspersed between these parts [8]. The need to obtain simple and safe guidance mechanisms has led to the use of the types of guidance shown in Figure 1, with a large variety of wheel guidance mechanisms (some of which are used in practice) being obtainable by connecting/combining these basic chains. The dynamic model of the wheel suspension system is obtained by completing the structural model with the mass and inertia properties of the component bodies, the arrangement parameters and characteristics of the elastic and damping elements, and the external forces acting on the car, depending on the specific running mode. Under the action of external forces and the reaction forces in the system, the suspension mechanism will occupy a certain position in relation to the chassis, called the equilibrium (balance) position. Establishing this position is necessary to assess the behavior of the vehicle in various operating/loading regimes, and to determine the reactions in joints in order to properly size them. Such a problem is approached in the literature mainly using energetic methods, based on the minimum energy potential in the equilibrium position, or by kinetostatic analysis methods, decomposing the suspension mechanism into components and expressing their equilibrium equations [9; 10; 11; 12; 13; 14; 15; 16]. The equilibrium position can also be determined by using automatic analysis algorithms, which are integrated in the commercial MBS (Multi-Body Systems) software environments, such as ADAMS, DYMES, or SIMPACK. These virtual prototyping tools provide important benefits in the simulation and optimization of the mechanical and mechatronic systems, but their high cost and the need for effective training are still limiting factors [17; 18; 19; 20]. This paper deals with an analytical method for determining the equilibrium position of the non-steered wheel suspension systems, which is based on the virtual mechanical work principle [21; 22]. An algorithm for the analysis of relative movements in the guidance mechanism is developed, with the purpose of determining the deformations (and subsequently the reaction forces) in the elastic elements. Not only the methods themselves but also the mode in which they are integrated in a unitary algorithm are elements of originality. This paper actually continues a previous study [23], which dealt with a method for the quasi-static analysis of beam axle suspension, a dependent suspension design in which the set of two wheels is connected laterally by a single beam.