Wrong. I designed differently. I also tested it and it works.
What will happen is that the doorknob will have a string on it. Then the motor will pull on the string. The string will pull, opening the door.
The only problem is that if I need to pull the string. And using a gear that could potentially be a bitch unless I get a big gear.
That'd be a wench, not a gear. And you'd only need one, attached to the moter's driveshaft.
Besides, that string would get in the way if you wanted to ever do it manually, or you had like, friends over.