Pushing out a plate-shaped workpiece part that has been cut free

A machine for separative machining of a plate-shaped workpiece, the machine comprising:

• a first movement drive to move the plate-shaped workpiece in a first direction, the first movement drive including a first bearing face configured to bear at least a first part of the plate-shaped workpiece and a second bearing face configured to bear at least a second part of the plate-shaped workpiece;
• a machining head configured to cut free a workpiece part from the workpiece such that a center of area of the workpiece part that is surrounded by an external contour line that defines an outer border of the workpiece part deviates from a centroid of the external contour line;
• a second movement drive to move the machining head of the machine in a second direction;
• two workpiece bearing supports to hold the plate-shaped workpiece, the two workpiece bearing supports being separated from each other by a gap that extends along the second direction between the two workpiece bearing supports;
• a push-out piston having a push-out rod, wherein the push-out rod is movable at least in the second direction within the gap to be positioned at a predefined push-out position;
• and
• a controller that is configured to arrange components of the machine so that the push-out position either coincides with the centroid of the external contour line that defines the outer border of the workpiece part, or is offset from the center of area of the workpiece part in a direction toward the centroid of the external contour line of the workpiece part.