Abstract: A method and apparatus for mechanically controlling the flame cutting and/or connection welding of workpieces. The difficulty encountered during the mechanized burning of holes in vessels, containers or tanks and the welding of connecting members into these holes is that the cutting and welding apparatus need to be guided in such a way that not only do they not contact the surface of the vessel, container or tank, but they are also kept a fixed distance from this surface. Therefore, control of the cutting and/or welding process is effected in conformity with the actual dimensions of the workpiece that is being worked on. In particular, this control is undertaken in conformity with the circumferential line of the hole for a given connecting member, and also in conformity with the curved surface of the vessel, container or tank. The peripheral line of the connecting member is first sensed and is graphically or electromagnetically recorded.