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We continue to investigate the possibility of slow (quasi-static) locomotion of multi-link systems along a horizontal plane owing to changing configurations. We have shown previously that the quasi-static motion of a two-link system, occurring when the angle between its links varies, is uncontrollable and that the trajectories of the system's vertices are uniquely defined by the initial position of the system. We consider here a symmetrical three-link system such that all its links have a common point. The control torques act between the links of the system. We show that there exist enough possibilities for quasi-static motion of the system. One can arrange the motion with the central vertex of the system moving along a prescribed line on the plane. As an example, we consider here two gaits of the three-link system allowing it to move along a straight line and to rotate on a spot.