I'm unsure which is the common post and which are the travelers. I THINK the common is the black post on top... but I really don't know. I though the travelers were parallel to each other. Can you tell from the pictures which one is the common wire?
Black is the common.
This can be confirmed with a multimeter on an unconnected switch. Testing for resistance, there should be infinite on the two brass terminals regardless of the switch position. The connection between the black and each brass should change from infinite to direct connection with the flip of the switch.
The common wire is associated with the differently colored screw on a 3-way switch, so it's the black screw in your case. (Ignore the green ground screw, of course.)
As others suggested, and in accordance with your situation, the black is the common wire, and the red is the traveler wire (assuming this is for a three way switch).