An annular device includes an annular main body defining a through hole, a battery mounting portion arranged in the through hole, and a battery cover. The battery mounting portion protrudes from an inner surface of the main body in the through hole, includes a first arcuate element with an outwardly curved surface and a second arcuate element with an outwardly curved surface opposite to each other and cooperatively defining a receiving space. The battery cover is operable to clasp the battery mounting portion, includes a first arcuate member and a second arcuate member opposite to each other. At least one first protrusion is formed on an inner surface of the first arcuate member, at least one cutout is defined in an outer surface of the first arcuate element, and the first protrusion can be fit into the cutout. The second arcuate member clasps the second arcuate element.