In a reply that for reasons unknown is not appearing here, David Reiss asking whether renaming Annulus to something else in the package would fix things.
Naturally, that's the first thing I tried, renaming the function GTAnnulus. And indeed an expression such as
Graphics[GTAnnulus[{1, 1}, 2, 3]]
works just fine. However, when the same, renamed, function GTAnnulus is called by the MechanicsTools function Pulley, I still get the error. (Yes, I did edit and save MechanicsTools.m so as to rename calls there to be to GTAnnulus rather than to the original Annulus)
It may be that there's some deeper bug in the definition of Pulley there.