A hand-held applicator of a system for cleaning teats of a milk-producing animal, said hand-held applicator comprising: a housing having an internal volume within which a plurality of brushes (186A, B, C) are positioned for engaging a teat of the milk-producing animal having been inserted in the volume for cleaning; a gear assembly including a plurality of gears (1288A, B, C) operatively connected to the respective brushes, wherein each gear that is operatively connected to a respective brush comprises: a disk-shaped member having a perimeter; 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 on an adjacent gear; and a bore hole in a center of the disk-shaped member, said bore hole having a hole circumference and a gear collar, said gear collar having an inner circumference which surrounds the hole circumference at the open end of the bore hole, the bore hole including internal threading along a surface within the bore hole wherein each gear is operatively connected to the respective brush; each brush comprising a shaft portion, said shaft portion being adjacent to and extending past an end brush flange, said shaft portion having external threading corresponding to the internal threading of the corresponding gear and each gear is rotated in a respective first direction or each brush is rotated in a respective second direction for threaded engagement between the gear and the corresponding brush, and wherein a respective second direction for one brush is opposite to a respective second direction of another brush; wherein in operation of the hand-held applicator, each gear rotates in its respective first direction to impart a torque onto the brush to rotate each brush in the respective first direction; and wherein the end brush flange assists in sealing the bore hole when the end brush flange is in surface-to-surface contact with a top end of the gear collar. a housing having an internal volume within which a plurality of brushes (186A, B, C) are positioned for engaging a teat of the milk-producing animal having been inserted in the volume for cleaning; a gear assembly including a plurality of gears (1288A, B, C) operatively connected to the respective brushes, wherein each gear that is operatively connected to a respective brush comprises: a disk-shaped member having a perimeter; 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 on an adjacent gear; and a bore hole in a center of the disk-shaped member, said bore hole having a hole circumference and a gear collar, said gear collar having an inner circumference which surrounds the hole circumference at the open end of the bore hole, the bore hole including internal threading along a surface within the bore hole wherein each gear is operatively connected to the respective brush; each brush comprising a shaft portion, said shaft portion being adjacent to and extending past an end brush flange, said shaft portion having external threading corresponding to the internal threading of the corresponding gear and each gear is rotated in a respective first direction or each brush is rotated in a respective second direction for threaded engagement between the gear and the corresponding brush, and wherein a respective second direction for one brush is opposite to a respective second direction of another brush; wherein in operation of the hand-held applicator, each gear rotates in its respective first direction to impart a torque onto the brush to rotate each brush in the respective first direction; and wherein the end brush flange assists in sealing the bore hole when the end brush flange is in surface-to-surface contact with a top end of the gear collar. a disk-shaped member having a perimeter; 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 on an adjacent gear; and a bore hole in a center of the disk-shaped member, said bore hole having a hole circumference and a gear collar, said gear collar having an inner circumference which surrounds the hole circumference at the open end of the bore hole, the bore hole including internal threading along a surface within the bore hole wherein each gear is operatively connected to the respective brush; each brush comprising a shaft portion, said shaft portion being adjacent to and extending past an end brush flange, said shaft portion having external threading corresponding to the internal threading of the corresponding gear and each gear is rotated in a respective first direction or each brush is rotated in a respective second direction for threaded engagement between the gear and the corresponding brush, and wherein a respective second direction for one brush is opposite to a respective second direction of another brush; wherein in operation of the hand-held applicator, each gear rotates in its respective first direction to impart a torque onto the brush to rotate each brush in the respective first direction; and wherein the end brush flange assists in sealing the bore hole when the end brush flange is in surface-to-surface contact with a top end of the gear collar.