The invention relates to a device for machining workpieces, especially for chip removing machining. The device includes a spindle which is mounted on a first end of a pivoting arm in such a way that it can be linearly displaced in a direction parallel to the rotation axis of the spindle, and a console on which the pivoting arm is mounted by its second end in such a way that it can rotate about an axis parallel to the rotation axis of the spindle. The console can be displaced in a direction which is perpendicular to the displacement direction of the spindle in all of the pivoting positions of the pivoting arm.