Harry and his wife from Saanichton, B.C. write:
The pivot points on this sewing box are just screws into the wood. As the boxes pivot in and out, the screws unscrew and fall out. What to do?
I love little challenges like this, and your drawing was great.
What we need to do is either fix a pivot that has no screw action, or freeze the rotation of the screws.
A rivet, even a pop rivet could do the job if the wall of the box is not too thick. The problem with a pop rivet is that there is a large bump on one end, and that would probably interfere with stuff inside.
If we want to stick to using wood screws, I see two possibilities. First is that you could drill down from the top edge and intersect the screw inside the box wall. Then you could actually run a long screw, or even a not so long "set screw" that you could seat in with an Allen key. You just have to drill the hole a little tight so that the set-screw would bite it's teeth into the wood without splitting the side.
If that is too delicate an operation in the side of 7/16 inch wood, you could freeze the head of the screw to the metal arm, and let it rotate a little in the wood, back and fourth, but not unscrew. This could be done neatly by drilling a very small hole through the part of the screw head that hangs out from the shank and through the metal arm. Then squeeze a little brass pin into the hole to lock the two together.
I hope one of these ideas can help to keep your sewing stuff inside the box where it belongs and not on the floor.