The invention relates to a device for grinding a surface to be ground having at least one recess (40), along a grinding plane, the device comprising: a milling ruler (50) that is straight and flat in the direction of its length and a milling cutter (51) that is translationally movable in the direction of the length of the milling ruler; a frame (70) comprising the milling ruler (50), the latter being rotatable about a point of rotation (52) on the frame (70) in a plane of rotation that is parallel to the grinding plane; and the direction of the length of the milling ruler being included in the plane of rotation. The grinding device is essentially characterised in that: the milling ruller (50) is in addition mounted so as to be translationally movable in a direction that passes through the point of rotation (52) and is parallel to the direction of the length of the milling ruller (50) and parallel to the grinding plane.
