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Biologically important ciliated fiber-type structures act in very complicated biological and physical situations. In this article, we model these structures and a process that is carried out by a collection of fibers, assuming that each of the fibers is connected by a small "muscle" to the surface on which the fibers are growing. The muscles act, and the fibers perform mechanical movements over the surface. Synchronization between the mechanical movements of the fibers is necessary for their mutual action, whose macroscopic relevance may be (as in the case of the cilia), for example, pushing some small obstacles in the needed direction over the (wet) surface. Synchronization only in time in the operation of the different muscles cannot be sufficient for such an effective collective mechanical action. The same direction of movement of the free ends of the fibers is also required. For this unidirectional activity, all of the muscles have to be placed at the same side of the fibers. This is a requirement of an orientational symmetry.