Using the Stasis Rune, target the large gear on the left and freeze it when the platform that it's spinning is straight, and run across.
Using this rune, you can freeze certain objects - either to stop moving parts from advancing, or to build up momentum on an object when Stasis is released. In particular the moving platform ahead will move too rapidly for you to cross - so inspect the pedestal to the left with your Sheikah Slate to obtain the Stasis Rune. Entering the Owa Daim Shrine you'll find it to be almost clockwork in its design - with many moving parts and gears moving platforms in a large hall.
