Modeling the angular capability of the ball joints in a complex mechanism with two degrees of mobility

The paper puts forward a complex linkage mechanism with two degrees of mobility and three kinematic loops, which is used for the guiding (suspension and steering) system of the vehicles. The geometric parameters and the coordinates frames that define the mechanical system are presented, as well as the specific kinematic functions. For this complex mechanical system, the angular capability of the ball (spherical) joints is defined by two angles. The equations for these angles have been determined by matrix algebra tools, considering the transformation matrices between the bodies reference frames. The diagrams of the angular capability of the ball joints, which are represented in angular coordinates, describe the form, orientation and size of the sockets from the spherical casings. Wears, shocks, functional locks or the compromising of the joint strength can occur if scarce sockets are implemented. The risk points, in which the angular parameters have maximum values, have been determined, the simulation being performed for a real system (vehicle).