A positioning device in a gantry-type construction, include two parallel linear guides with integrated linear drives, each of which supports an X-carriage in a manner allowing movement in an X-direction, and having a cross bar which is joined to the two X-carriages and which, with the aid of an integrated linear drive, supports a carriage in a manner allowing movement in a Y-direction perpendicular to the X-direction. In addition, the positioning device has a toolholder which is guided on the Y-carriage in a Z-direction and bears a tool for processing a workpiece located in an X-Y plane, the tool being located next to the cross bar so as to be offset in the X-direction. A force frame, disposed above the tool in the Z-direction, transfers a process force acting on the tool, to the carriages, without deforming the cross bar by a torque.