There are vending machines for books, jeans, and produce so it's only natural that vending machine burgers would pop up somewhere. And that somewhere is Japan (of course), at Tateishi Burger, which is a retro hamburger place that lets its patrons order burgers through a vending machine.
The coin-operated machine drops out a Tateishi Burger, but you can't order two at a time. If you watch the video you'll see why: these vending machine burgers require a bit of manpower, meaning the operation really isn't all that automated. They tried!