<p>A dynamic surface control method for constructing control laws in an underactuated mechanical system has been developed. A specific choice of control parameters and filter constants makes it possible to avoid the increase in the order of the auxiliary system and the related complication of both the system of differential equations and the control law (the so-called “explosion of complexity”). Control law for the rotation of the electric motor ensuring the global stabilization of the manipulator motion in the vicinity of the predetermined time-dependent trajectory has been proposed. The nonlinear dependence of the elastic transmission force on displacement as well as the parameter uncertainties in the model have been taken into account. Using the Lyapunov function method, the robustness of the control has been proved, and the robustness region in the system parameter space has been determined. In general, a combined analytical and numerical approach to the analysis of mechanical systems that can be classified as a single-link manipulator with an elastic joint has been developed.</p>