Abstract: Milking machine methods and apparatus facilitating automatic attachment to the dairy cow's udder, incorporate upstanding thin-walled flexible conical teat cup entrance portals, with the four teat cups preferably positioned upright in a trapezoidal configuration, free for lateral and longitudinal movement horizontally, while resisting vertical displacement. Leaf-spring retainer arms positioned vertically edgewise provide resilient adjustable teat cup positioning. A claw manifold guides milk received from the teat cups in laminar flow streams, minimizing foaming turbulence. A robotic manipulator may be used to attach these milking machines to the udders of a plurality of dairy cows.