Mitotic chromosome motions are driven by microtubules (MTs) and associated proteins that couple kinetochores to MT ends. A good coupler should ensure a high stability of attachment, even when the chromosome changes direction or experiences a large opposing force. The optimal coupler is also expected to be efficient in converting the energy of MT depolymerization into chromosome motility. As was shown years ago, a "sleeve"-based, chromosome-associated structure could, in principle, couple MT dynamics to chromosome motion. A recently identified kinetochore complex from yeast, the "Dam1" or "DASH" complex, may function as an encircling coupler in vivo. Some features of the Dam1 ring differ from those of the "sleeve," but whether these differences are significant has not been examined. Here, we analyze theoretically the biomechanical properties of encircling couplers that have properties of the Dam1/DASH complex, such as its large diameter and inward-directed extensions. We demonstrate that, if the coupler is modeled as a wide ring with links that bind the MT wall, its optimal performance is achieved when the linkers are flexible and their binding to tubulin dimers is strong. The diffusive movement of such a coupler is limited, but MT depolymerization can drive its motion via a "forced walk," whose features differ significantly from those of the mechanisms based on biased diffusion. Our analysis identifies key experimental parameters whose values should determine whether the Dam1/DASH ring moves via diffusion or a forced walk.