That "frame " is called a hay cage.  You put them up and dumped the hay in and it made your stack the right size and shape.  We never had one but some of the neighbors did. 

We used a "Jayhawk" to make our stacks when I was a kid and we got in the stack to place the hay in the right places where needed, (holes) and to pack it to make a good solid stack.  My uncle started using a loader on an M and then he could "pack" the hay with the loader by pushing down on the stack with the loader instead of somone in the stack doing it with your feet. 

 We used a dump rake on occasion to pick up a lot of hay that may have gotten scattered by wind or if the side rake did a poor job for some reason.  We still have an old dump rake sitting around "just in case"!