John H wrote:
The bimini top on my Key West uses a mounting like this"

http://tinyurl.com/9ozwsy

This bracket allows the frame member mounted therein to rotate from front
to back without placing undue stress on the mounting screws. Note, I said
screws, not through bolts.

However when underway, even slowly, or just at anchor with a small amount
of ripple in the water, the bimini top sways from side to side. The side to
side motion gets transmitted directly to the screws in the brackets, and
causes them to loosen. I'm sure it's just a matter of time before they
strip or worse.

I'm wondering if there aren't some fittings made that would have a ball
socket or some such to allow complete forward and back movement *and* some
degree of lateral movement.

Anyone know of such a thing? Help!

We need to reduce or eliminate the sway.
What is the frame made of?
Show a picture of the frame, set up with the canvas on it.