Abstract: In a stand (1), a work-piece spindle (2) is mounted for rotation around a vertical axis (C). On the stand (1), a slide (3) can be shifted horizontally and on the slide, a work-piece carrier (5) can be swivelled around a vertical axis (C1). On the carrier (5), a slide (6) can be shifted vertically. The slide (6) bears a linear guide element (7) able to be swivelled around a horizontal axis (A) and on which a second slide (8) can be shifted. The slide (8) bears the grinding spindle (axis B) with mounted grinding worm (9). A dressing device (12) is arranged, relative to the axis (C1), opposite the work-piece spindle (2). The machine makes easy operation possible, because all parts to be operated are quite accessible.