The power appliance (10) for cleaning teeth includes a drive system (16) and a substrate (10) for supporting a field of bristles (14) which contact teeth for cleaning. The drive system is connected to the substrate, moving the substrate in operation to produce an action of the bristle field against the teeth. The assembly, which includes internal stiffeners (60, 62, 64) in one embodiment, has two physical states, including a first state in which the substrate is softened so as to be formable to conform to the geometry of the teeth, and a second hardened state following its conformance to the teeth in which the substrate is sufficiently rigid to effectively transmit a driving motion to the bristles.