Peter wrote:
I've got a clamp-on, adjustable swing arm desk lamp with fully enclosed
friction hinges connecting the base, the arms, and the shade. There are
no springs, tension knobs, screw holes, or any other apparent method of
adjusting the friction. The hinge closest to the base has worn and no
longer supports any extended lamp position. I don't even see any way to
disassemble the hinges. I've spent hours with Google trying to get help,
but no luck. The manufacturer has not been of help either. Any bright
ideas?

You could always try exploratory surgery with a Dremel Tool.
A picture or brand and model might help us figure out how it
was assembled.

TDD