Fix a shelf above the door, parallel with the runner.
Attach a rear bike wheel with tyre and sprocket/cassette to the door so that the tyre is pressing on the underside of the shelf.
Attach old crank and and chainwheel to door at convenient height.
Attach chain between sprocket and chainwheel.
Attach pedal spindle to crank.
Turn crank to open/close the door
Like this: