Four glasses are placed in the four corners of a square rotating table, each glass is either up or down. You wish to turn them all in the same direction, either all up or all down. You may do so by grasping any two glasses and, optionally, turning either over.

There are two catches:
1) You are blindfolded and
2) the table is spun after each time you touch the glasses.
Assuming that a bell rings when you have them all facing the same way, how do you do it?