This is a great example of how language evolve. Do you know the original meaning of "crank"? It means to turn some kind of simple machine, usually by hand. So, image you have to do some simple task such as copying a notice. Before anyone invented printing machines, you had to write each copy by hand. Then someone invented a way to print the notice, you just have to turn - or crank - the handle and it makes 100 copies. They all come out of the machine one by one. So you crank out a lot of completed tasks quite easily. Today, I can crank out answers to questions on italki, thanks to the magic of the internet!

It just means to get through something fast and easy. People say "I cranked that out pretty fast," which means I finished it up fast (like a term paper, work assignment, a task at work, something like that).

It means accomplish or get done. Crank through might be a reference to very old cars that had to manually turned (cranked) to start the engine. That's a guess though.