A balancing machine drive apparatus for driving rotational movement of a workpiece rotatably mounted about a rotational axis by a looping belt includes a frame at least partially surrounding, transaxially to the rotational axis, a workpiece mounting position and having an opening closable by an arch and through which the mounting position is accessible, the drive apparatus including guide devices on the frame and/or arch to guide the belt such that, when the arch is closed, the belt winds at least partially around a workpiece in the mounting position on a cylindrical circumferential workpiece region, and a drive device for the belt. The arch is held on the frame so as to be movable between open and closed positions. A balancing machine for balancing a workpiece includes a mounting apparatus in order to rotatably mount the workpiece about a rotational axis in a mounting position, and the drive apparatus.