A portal-type positioning device includes two parallel linear guides provided with integrated linear drives, which support a separate X-carriage in a manner that allows movement in the X-direction, as well as a cross beam which is connected to the two X-carriages and movably supports a carriage in a Y-direction that extends perpendicular to the X-direction, with the aid of an integrated linear drive. In addition, the positioning device has a tool holder, which is guided on the Y-carriage in a Z-direction and holds a tool for machining a workpiece situated in an X-Y plane, the tool being disposed next to the cross beam at an offset in the X-direction. A force frame disposed above the tool in the Z-direction transmits a process force acting on the tool to the carriages LX1, LX2 without deforming the cross beam by a torque. The process force is applied by an electromagnet which acts between the force frame and the tool holder.