There were some works on dynamical nonholonomic systems, but few works on a control method generally applied to these systems. In our previous work, we analyzed nonlinear behaviours of a 2DOF free-joint manipulator with a periodic input and developed a positioning of the both joints by modulating the amplitude of the input. The strategy was effective but very heuristic and cannot be applied to the other systems. In this paper, we apply the averaging method to the system and derive its behaviour from the averaged system. We also discuss its feedback control and design a feedback stabilization to a desired manifold. Even though its concept is the same as in , the control strategy is analytically constructed. The feedback control is designed by a Lyapunov function for the averaged system and it is also effective for the real system.