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The green is something like 1/2 tube where you can get those locking collars for. 3 pivot points and you are done. The head of the arm where the camera goes has a flat reference piece (a few sq in) and you use a piece of squared off wood or metal to calibrate the angle of the head (which the camera is affixed to) and the surface of the platten.

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Replace the dial indicator with a camera and make it bigger.
Fixed height means camera is set and forget as well as the lights. You just slide the angled arm up and down in relation to the center of the book on the platten. The red dots are clamps that would allow the tube to be moved about. The brown line is the wood and is cut to your preferred height. You can have several calibrated wood sticks for varying heights for paperback, paper sized, or large format.
All you *NEED* is to keep the camera 90DEG to the paltten. All that math is nice, but nothing a calibrated piece of wood wouldn't fix
