Summary

The hinge connecting the head of my desk lamp to the arm broke, leaving the head dangling. I made a new one. It's not perfect (it's a little bit loose around the head, and the peg the hinge is on is too short), but it works.

Lamps get hot. I won't be responsible if your lamp melts this holder and burns your house down. You have been warned.

Instructions

Travel back in time to 2002.
Buy a Martha Stewart "Architect's Work Lamp".
Use it until the hinge breaks.
Print each part listed at the bottom of the OpenSCAD file (I used ABS).
Glue holder_top to the top of holder_bottom (I used ABS/acetone slurry).
Insert hinge_inside into the larger hole in hinge_outside from the bottom(without gluing).
Insert the square peg on holder_bottom into the hole in hinge_inside from the top (optionally gluing it).
Slide the holder over the head of the lamp, putting the power cable and the remnants of the old hinge through the gap opposite the new hinge.
Turn the holder so the old hinge remnant is trapped between holder_bottom and holder_top (see photo).
Remove the other side of the old hinge from the arm by removing the screw.
Insert the small hole in hinge_outside in the resulting gap, and replace the screw.

Desk Lamp Hinge Fix