An apparatus for cleaning a floor includes a housing, wheels by which the apparatus is adapted to move; a motive device for moving the apparatus, a steering mechanism, and a cleaning assembly including a cleaning unit and an offset mechanism adapted to move the cleaning unit to or from an offset position projecting beyond one lateral side of the apparatus. In another embodiment, an apparatus for cleaning a floor includes a housing, wheels by which the apparatus is adapted to move, a motive device for moving the apparatus, a steering mechanism, and a cleaning assembly including a cleaning unit and a swing mechanism indirectly linking the cleaning unit to the steering mechanism such that when the apparatus is in an operative mode, the cleaning unit reorients its position in synchronization with the path of travel of the apparatus. Optionally, a lifting device may raise and lower the cleaning assembly.