A subassembly with a supporting element for a machine bed of a lathe, and of a machining unit which is arranged on the supporting element and has a machining axis, wherein a solid-body joint, via which the machining unit is arranged in a movable manner on the supporting element, is provided. A lathe for plastics spectacle lenses, having a machine bed, having a tool mount or workpiece mount which is arranged at least indirectly on the machine bed, and having a subassembly which is arranged at least indirectly on the machine bed, wherein the workpiece and the tool can be oriented in relation to one another via the solid-body joint.