Embodiments are directed to a threaded gear assembly and a hand-held applicator for cleaning a teat of a milk-producing animal. In an embodiment, a threaded gear is provided which comprises a disk-shaped member having a perimeter and a plurality of radiating teeth circumferentially arranged and integrated with the perimeter of the disk-shaped member, the plurality of radiating teeth being configured to impart torque. The threaded gear includes a bore hole in a center of the disk-shaped member, the bore hole including internal threading along a surface within the bore hole.