A tool for the design of a periodic motion in underactuated systems via generating a self-excited oscillation of a desired amplitude and frequency driven by a variable structure control is reviewed. In this chapter, we overview the capabilities of the two-relay controller to induce oscillations in dynamical systems. In this chapter, we will focus on underactuated mechanical systems with degree of underactuation one, that is,
– 1 actuators only. Threemethods to set the frequency and amplitude of oscillation and its application to one-degree of underactuation systems are reviewed: describing function method, Locus of the perturbed relay system design (LPRS), and Poincaré map based design. Theoretical and practical open problems are also discussed.