A power toothbrush appliance, comprising: a handle with a first toothbrush housing portion containing a power actuator which includes a stator having a first moment of inertia, and a handle rotor portion, wherein the actuator in operation generates torque for driving the handle rotor portion, and wherein the stator and the handle rotor portion move in opposing directions during operation of the appliance, the appliance further including a first spring element or assembly having a first spring constant connecting the stator to the first housing portion or element fixed to the housing; and a brushhead assembly, wherein the brushhead assembly comprises: a brushhead shaft having a bristle member at a distal end thereof for cleaning of teeth, and a brushhead rotor portion with a connecting rotor interface portion at a proximal end thereof for removably connecting the brushhead rotor portion to the handle rotor portion, wherein the handle rotor portion and the brushhead assembly form an appliance rotor having a second moment of inertia; a second toothbrush housing portion configured to mate with the first toothbrush housing portion in response to the brushhead assembly being connected to the handle, the first and second toothbrush housing portions defining an appliance housing; and a second spring element or assembly having a second spring constant between and connected to the brushhead rotor portion and the second housing portion or an element fixed to the second housing portion, wherein a ratio of the first and second spring constants is sufficiently similar to a ratio of the first and second moments of inertia that, when the brushhead assembly is connected to the handle, there is substantially no resulting torque transmitted to the appliance housing during operation of the power toothbrush appliance and hence substantially no vibration of the appliance housing during operation of the power toothbrush appliance. a handle with a first toothbrush housing portion containing a power actuator which includes a stator having a first moment of inertia, and a handle rotor portion, wherein the actuator in operation generates torque for driving the handle rotor portion, and wherein the stator and the handle rotor portion move in opposing directions during operation of the appliance, the appliance further including a first spring element or assembly having a first spring constant connecting the stator to the first housing portion or element fixed to the housing; and a brushhead assembly, wherein the brushhead assembly comprises: a brushhead shaft having a bristle member at a distal end thereof for cleaning of teeth, and a brushhead rotor portion with a connecting rotor interface portion at a proximal end thereof for removably connecting the brushhead rotor portion to the handle rotor portion, wherein the handle rotor portion and the brushhead assembly form an appliance rotor having a second moment of inertia; a second toothbrush housing portion configured to mate with the first toothbrush housing portion in response to the brushhead assembly being connected to the handle, the first and second toothbrush housing portions defining an appliance housing; and a second spring element or assembly having a second spring constant between and connected to the brushhead rotor portion and the second housing portion or an element fixed to the second housing portion, wherein a ratio of the first and second spring constants is sufficiently similar to a ratio of the first and second moments of inertia that, when the brushhead assembly is connected to the handle, there is substantially no resulting torque transmitted to the appliance housing during operation of the power toothbrush appliance and hence substantially no vibration of the appliance housing during operation of the power toothbrush appliance. a brushhead shaft having a bristle member at a distal end thereof for cleaning of teeth, and a brushhead rotor portion with a connecting rotor interface portion at a proximal end thereof for removably connecting the brushhead rotor portion to the handle rotor portion, wherein the handle rotor portion and the brushhead assembly form an appliance rotor having a second moment of inertia; a second toothbrush housing portion configured to mate with the first toothbrush housing portion in response to the brushhead assembly being connected to the handle, the first and second toothbrush housing portions defining an appliance housing; and a second spring element or assembly having a second spring constant between and connected to the brushhead rotor portion and the second housing portion or an element fixed to the second housing portion, wherein a ratio of the first and second spring constants is sufficiently similar to a ratio of the first and second moments of inertia that, when the brushhead assembly is connected to the handle, there is substantially no resulting torque transmitted to the appliance housing during operation of the power toothbrush appliance and hence substantially no vibration of the appliance housing during operation of the power toothbrush appliance.