A formulation which seeks steady-state equilibrium positions of constrained multibody systems driven by constant generalized speeds is presented in this paper. Since the relative coordinates are employed, constraint equations at cut joints are incorporated into the formulation. To obtain the steady-state equilibrium position of a multibody system, nonlinear equations are derived and solved iteratively. The nonlinear equations consist of the force equilibrium equations and the kinematic constraint equations. To verify the effectiveness of the proposed formulation, two numerical examples are solved and the results are compared with those of a commercial program.