A method that has been proposed for the design of a control system of a muti-link arm is the optimum approach applied to the system linearized around its nominal trajectory, i.e. the dynamic trajectory that the manipulator should follow. This method works, in as much as the initial deviation from the reference trajectory is small enough. When such is not the case, it is necessary to take into account the quadratic term in the approximation, and the paper proposes a small parameter technique to solve the corresponding optimum control problem which otherwise involves cumbersome calculations.