Sense Position of String Intersecting 2d Plane

I am trying to sense the XY position of string intersecting a 2d plane (square or circle) to keep a machine grinding head at the same/level position. I am trying to find a way to sense this position, the camera will not work because the Machine will be used outside and have a different light level or get extremely dusty.

what are the known paramerters from this setting? Where is the thing you want to know the position of?

The string will run from one end of the base to the other as a line to level the ground off of, the square that the string goes through will be around 3in by 3in to sense how far off the grinder head has drifted.

Yes, but what do you measure? Do you know the height above ground (if that is ground)where the string starts/end? do you know the position of the 2 black posts? and where is the grinding head? do you have a picture of the situation? how big is this thing? how far away from the string do you intend to place whatever-measures-position?

OP's graphic

Now I don't want to be picky, but where do you see the square of 3x3in and the grinder head? When the stakes are known and the strings height on each stake is known, and orientation and position of that disk and the distance between stakes then the searched point is alsow known. As the point is not known, what oter variables are known?

I redrew up the diagram and hopefully this will help you.

Sorry, still don’t get it: the string is fixed? the plane moves in Z-direction relative to the plane? The grinding wheeel is in that plane, a bit away from the string?

Yes the sting is fixed as a level line and the 2d plane moves in the z-direction and as it moves along the plane I need to get the XY position of the intersection of the string.

The thread will move the fingers up/down left/right as the machine advances. Read sensors to get X-Y position.

In this does the string itself have to move the sensors or do the sensors use distance and light to sense where the string is. Because if the sting has to move a sensor the level will get offset and the head will cut at the wrong level.

The Z movement, are we talking in the range of 1-10 mm, or mor in the range 0f 0.01 to 0.1 mm? To mee it looks like more the second scale, is it?

The movement is can be over 10ft to 100ft, the machine is to level gravel for foundations.

What's the disired accuracy?

Within a couple of mm so 1 to 2 mm, that is what is needed to get a level line, but if I could get even more some way that would be even better.

But your string has a sag of more than 1-2 mm per meter. Isn't that a bit unrealistic? Anyway, how do you move your machine? Or the grinder? Can you post a real world photo of the situation?

The sting does not sag all too much when we measured. The base is a tracked base, and the head moves up and down with 2 linear actuators, one on each side. I have a new picture drawn up but can not figure out how to get it uploaded.

Here is the new diagram.

That's a good one! Do you have pressurized air at the engine? if yes, then you still use a laser (in place of the string) + camera to detect the position.

Oh, forgot: headroom above the engine is clear and you can attach a device to it?