The work deals with a numerical method for the kinematic analysis of the spatial multi-link mechanical systems (linkages). According to the proposed method, three specific points determine the spatial position and orientation of the central element of the mechanism (i.e. the rod). The kinematic equations system contains the geometric constraint equations and the rigid body conditions of the rod (i.e. constant distances between the three specific points). The corresponding non-linear system is solved by using the Newton-Kantorovich approach. The case study is developed by considering a complex wheel guiding mechanism used for vehicle suspension system. Index Terms-Multi-link mechanism, kinematic analysis, analytical algorithm, guiding linkage.