It can't work without a ratchet, Jeromeo. When you push the "forward" pedal, the belt tension will just pull that tensioning pulley backward (toward the clutches), slackening the belt, which will then slip.
See if you can identify exactly which parts are missing. Also, find the series of teeth on the bar running through the middle of the tensioning spring. The ratchet engages with these teeth. They often get worn, so the ratchet no longer clicks into them.
