5string - check the part this ribbed end goes into. There should be matching ribs that would cause this to be a 'force fit' = tight enough to have to use force to put it in but not so tight that you can't get it out. If those ribs are plastic, chances are good that you will need a putty, plastic wood or just glue to secure this into place. It's my guess that someone 'twisted' this rod out and stripped down the ridge tops or even the entire set of those teeth.
If they are in good shape, then there is probably something else amiss but I can't guess what. If that nipple that goes into the securing part protrudes, you can carefully make a groove for a clevis pin (the circular thing that acts like a cotter pin on the other end). doing this would not be easy as the line would need to be straight all the way around and the right size pin found. My guess is that the nipple only goes up to the upper surface of the part it enters.
Another way to make this work, though more complicated, is to have a machinist drill a small diameter hole in the tip end of this, tap it, then use a bolt and washer on the upper side to hold it in place, or a thumbscrew and washer. This would be the most secure method that is also remove-able from the enlarger, though also the trickiest to implement.