Tools, machines, and methods for processing planar workpieces

A tool for processing a planar workpiece, comprising:

• an upper tool having a clamping shaft and an upper main body that lie on a common, upper positioning axis;
• a processing tool arranged on the upper main body opposite the clamping shaft, which comprises two fixed processing edges that are parallel to each other and delimit an indentation between them that extends along a holding-down surface of the entire upper main body, wherein the processing tool further comprises a processing surface within the indentation between the two fixed processing edges that extends along the entire upper main body;
• a lower tool having a lower main body with a rest surface for the planar workpiece and a lower positioning axis oriented perpendicular to the rest surface;
• a counter tool body on the lower main body, the counter tool body having a counter roller with at least one counter edge opposite the two fixed processing edges of the processing tool;
• and
• a processing device that is provided adjacent to the at least one counter edge, and that has at least one curved counter surface oriented aligned with the two processing edges of the processing tool,
• wherein the upper tool and lower tool are moveable towards one another in a stroke direction to process the planar workpiece arranged therebetween.