Centering machine for workpieces, namely optical lenses with curved optical surfaces, with two centering spindles (22, 30), the centering spindle shafts (24, 34) of which, each driven in rotation and accommodated in centering spindle housings (26, 32), are axially aligned with respect to a centering axis and each accommodate a cup-shaped clamping bell (36, 38) at mutually facing ends, a stroke device, by means of which one of the centering spindle shafts (24, 34) can be adjusted axially in a sensitive manner along the centering axis with respect to the other of the centering spindle shafts (24, 34) in order to align one of the workpieces between the clamping bells (36, 38) in a bell clamping process, in which the clamping bells (36, 38) are applied to the workpiece with slight pressure in a probing phase before the workpiece is automatically displaced in a direction transverse to the centering axis in an alignment phase as a result of the curvature of its optical surfaces until it has assumed a position between the clamping bells (36, 38) which permits the minimum distance between the clamping bells (36, 38) under the given geometric conditions, a clamping device for applying a clamping force to one of the centering spindle shafts (24, 34) in order to clamp the workpiece aligned between the clamping bells (36, 38) in a clamping phase following the alignment phase, and at least one processing unit (58, 60) movable relative to the centering axis with a tool for edge processing of the workpiece clamped between the clamping bells (36, 38), characterized in that the centering spindle shaft axially adjustable by way of the stroke device is rotationally drivable by means of a rotary drive arranged as the stroke device to be coaxial with respect to the centering axis, so that due to the arrangement, which is centered with respect to the centering axis, of the rotary drive merely a torque about the centering axis can be generated, without application of a transverse force to the centering spindle shaft. two centering spindles (22, 30), the centering spindle shafts (24, 34) of which, each driven in rotation and accommodated in centering spindle housings (26, 32), are axially aligned with respect to a centering axis and each accommodate a cup-shaped clamping bell (36, 38) at mutually facing ends, a stroke device, by means of which one of the centering spindle shafts (24, 34) can be adjusted axially in a sensitive manner along the centering axis with respect to the other of the centering spindle shafts (24, 34) in order to align one of the workpieces between the clamping bells (36, 38) in a bell clamping process, in which the clamping bells (36, 38) are applied to the workpiece with slight pressure in a probing phase before the workpiece is automatically displaced in a direction transverse to the centering axis in an alignment phase as a result of the curvature of its optical surfaces until it has assumed a position between the clamping bells (36, 38) which permits the minimum distance between the clamping bells (36, 38) under the given geometric conditions, a clamping device for applying a clamping force to one of the centering spindle shafts (24, 34) in order to clamp the workpiece aligned between the clamping bells (36, 38) in a clamping phase following the alignment phase, and at least one processing unit (58, 60) movable relative to the centering axis with a tool for edge processing of the workpiece clamped between the clamping bells (36, 38), characterized in that the centering spindle shaft axially adjustable by way of the stroke device is rotationally drivable by means of a rotary drive arranged as the stroke device to be coaxial with respect to the centering axis, so that due to the arrangement, which is centered with respect to the centering axis, of the rotary drive merely a torque about the centering axis can be generated, without application of a transverse force to the centering spindle shaft.