An apparatus for revealing the geometry of operative cylinders, in particular during the grinding operation of the same, includes a pair of movable clamps which can be moved away from and towards each other with respect to a fixed intermediate structure, the clamps having tilted surfaces in opposite directions to each other according to a swallowtail arrangement with respect to a cylinder being measured, positioned between them and between a surface of the fixed intermediate structure, the surfaces of the movable clamps and the surface of the fixed intermediate structure always being kept in contact with the cylinder, whether still or rotating, wherein the fixed structure also has, in its interior, parts of a group which interact with each other to correlate the movement of the clamps.