The great evolution of the data-processing tools during the last years allowed for the development of the computer aided design in the field of mechanical structures. Controlling the clearance in joints between parts, is one of the required objectives to provide accurate relative movements and to minimize geometrical errors. For that purpose, a new method of static study allowing for the computation of the equilibrium positions of various elements in spatial mechanisms constituted by parallel joints and subjected to mechanical loadings is proposed. The isostatic study takes into account the presence of the clearance in the mechanism joints. The method is based to the minimization of the potential energy by means of some algorithms of optimization. The results obtained show the effectiveness of the method.