A teat cup carrier is designed to be able to co-operate with a feed platform, which teat cup carrier is freely movable relative to the feed platform. The teat cup carrier carries, besides teat cups, further milking elements for milking an animal, the further milking elements including at least a milk storage vessel for storing milk, a milking vacuum source and a pulsation vacuum source. The milk storage vessel is provided with a milk outlet. The freely movable teat cup carrier is in particular a self-propelled (autonomous) mobile teat-cup-carrying robot and comprises a control unit for controlling the functioning of the mobile teat-cup-carrying robot.