A sleeving apparatus includes a worm gear. The worm gear has a plurality of threads, the worm gear receptive of a bead between adjacent threads of the plurality of threads. A plurality of flexible diaphragms are positioned along the worm gear. Each diaphragm of the plurality of diaphragms is configured to position a wire in alignment with a central bead opening of the bead. With rotation of the worm gear about a worm gear axis, the bead advances onto the wire with the wire passing into the central bead opening. The plurality of diaphragms are configured to allow passage of the bead through each diaphragm of the plurality of diaphragms.