Two quick thoughts.
1) Almost any pair of glasses will fit through a hole in a piece of cardboard that is much smaller than the diameter cylinder needed. The ends of the temples (that's techie for the earpieces) protrude out in some unusual ways that will permit dropping through a hole---but be bound by a cylinder. (TP roll anyone?)
One of the big causes for glasses becoming loose is a glasses case that puts pressure on the temples when the case is closed.
First of all you have to be smarter than the machine.