Appliance of type razor, clipper, depilator and/or "exfoliator", comprising an appliance body including a motor and a transmission (9, 11, 25), and comprising several removable heads adaptable on this body, at least one of the removable heads comprising a subassembly movable according to a reciprocating translational motion and at least another one of the removable heads comprising a subassembly movable according to a rotational motion; - the transmission (9, 11, 25) comprising a member for transforming motion, driven in rotation by the output shaft of the motor or by a gear which comprises the transmission (9, 11, 25), the subassembly movable according to a reciprocating translational motion comprising a coupling means (20, 21) which can be coupled with said member for transforming motion when adapting the head including the subassembly on said appliance body and which can be uncoupled from this member for transforming motion when removing this head from said appliance body; and - the transmission (9, 11, 25) comprising a member for transmitting rotational motion, independent from said member for transforming motion, the subassembly movable according to a rotational motion comprising a coupling means which can be coupled with said member for transmitting rotational motion when adapting the head including this subassembly on the appliance body and which can be uncoupled from this member for transmitting motion when removing this head from said appliance body. appliance characterised in that: - said member for transforming motion consists of a cylindrical cam, comprising a groove inclined relative to the axis of revolution of this cam; - said coupling means of the subassembly movable according to a reciprocating translational motion consists of a lug attached to the movable subassembly and comprising a free end portion intended to be engaged in the groove of said cam when adapting the head on the appliance body. - the transmission (9, 11, 25) comprising a member for transforming motion, driven in rotation by the output shaft of the motor or by a gear which comprises the transmission (9, 11, 25), the subassembly movable according to a reciprocating translational motion comprising a coupling means (20, 21) which can be coupled with said member for transforming motion when adapting the head including the subassembly on said appliance body and which can be uncoupled from this member for transforming motion when removing this head from said appliance body; and - the transmission (9, 11, 25) comprising a member for transmitting rotational motion, independent from said member for transforming motion, the subassembly movable according to a rotational motion comprising a coupling means which can be coupled with said member for transmitting rotational motion when adapting the head including this subassembly on the appliance body and which can be uncoupled from this member for transmitting motion when removing this head from said appliance body. - said member for transforming motion consists of a cylindrical cam, comprising a groove inclined relative to the axis of revolution of this cam; - said coupling means of the subassembly movable according to a reciprocating translational motion consists of a lug attached to the movable subassembly and comprising a free end portion intended to be engaged in the groove of said cam when adapting the head on the appliance body.