A mouthpiece assembly for cleaning teeth, comprising: an upper mouthpiece for receiving a first set of teeth from the maxillary dental arch of a user and for simultaneously cleaning multiple tooth surfaces of the first set of teeth, and including an upper channel having two opposite vertical upper walls (22, 24) adapted to extend along side surfaces (28, 30) of the first set of teeth and a central upper wall in between facing horizontal surfaces of the first set of teeth; a lower mouthpiece for receiving a second set of teeth from the mandibular dental arch of the user and for simultaneously cleaning multiple tooth surfaces of the second set of teeth, and including a lower channel having two opposite vertical lower walls (36, 38) adapted to extend along side surfaces (42, 44) of the second set of teeth and a central lower wall in between facing horizontal surfaces of the second set of teeth; a bite block housed between the upper mouthpiece and the lower mouthpiece and including a vertical block section having an upper end extending freely through a first opening in the central upper wall and configured to engage at least one tooth of the first set of teeth, and a lower end extending freely through a second opening in the central lower wall and configured to engage at least one tooth of the second set of teeth; a driving mechanism for driving movement of the upper mouthpiece and the lower mouthpiece to clean the tooth surfaces; and wherein the bite block, the at least one tooth of the first set of teeth, and the at least one tooth of the second set of teeth create a static arrangement relative to movement of the upper mouthpiece and the lower mouthpiece when the user bites on the bite block, and wherein movement of the upper mouthpiece and the lower mouthpiece driven by the driving mechanism is uninhibited when the user bites on the bite block. an upper mouthpiece for receiving a first set of teeth from the maxillary dental arch of a user and for simultaneously cleaning multiple tooth surfaces of the first set of teeth, and including an upper channel having two opposite vertical upper walls (22, 24) adapted to extend along side surfaces (28, 30) of the first set of teeth and a central upper wall in between facing horizontal surfaces of the first set of teeth; a lower mouthpiece for receiving a second set of teeth from the mandibular dental arch of the user and for simultaneously cleaning multiple tooth surfaces of the second set of teeth, and including a lower channel having two opposite vertical lower walls (36, 38) adapted to extend along side surfaces (42, 44) of the second set of teeth and a central lower wall in between facing horizontal surfaces of the second set of teeth; a bite block housed between the upper mouthpiece and the lower mouthpiece and including a vertical block section having an upper end extending freely through a first opening in the central upper wall and configured to engage at least one tooth of the first set of teeth, and a lower end extending freely through a second opening in the central lower wall and configured to engage at least one tooth of the second set of teeth; a driving mechanism for driving movement of the upper mouthpiece and the lower mouthpiece to clean the tooth surfaces; and wherein the bite block, the at least one tooth of the first set of teeth, and the at least one tooth of the second set of teeth create a static arrangement relative to movement of the upper mouthpiece and the lower mouthpiece when the user bites on the bite block, and wherein movement of the upper mouthpiece and the lower mouthpiece driven by the driving mechanism is uninhibited when the user bites on the bite block.