There appears to be a groove for a C-clip on the shaft. Could a hose clamp be used on the shaft? Enough room and clearance?
It appears you lost part of the quick link on the chain. It and a C-clip should be available at a motorcycle shop or small engine repair shop. Possibly a hardware store. The C-clip will require an installation tool. Like a pair of pliars.
I believe on a quiet night,
I can hear the fish laughing.
I have to tell you THAT IS NOT the motor that came with that trike. That is a home made Sprocket attachment on a regular motor for a two wheeler. I mean even the shaft is angled. TAKE A PICTURE of the WHOLE REAR END of that thing.
HERE IS WHAT IT SHOULD LOOK LIKE: Alleyoop THE REAR AXLE:
Here is what is on the trike a 150cc Drum Brake Two Wheel Motor. Trikes have TWO motor mounts in the front AND on the Rear, Two wheel scooters only have One Motor Mount on the Rear.
To help the situation that setup needs a piece of on the Shaft that extends to the LEFT so it does not move more than 1/8 of an inch in either direction. That is why the Chain broke it moved to much to the left.
I am sure there was a "C" Clip on that grove on the shaft but it was not strong enough to hold the pressure put on it and it popped off or broke off.
Alleyoop
Here is HOW to At Least get it back on the road. The best fix so it does not move more than 1/8 of a inch is a piece of metal to fit the open space. Try a Gas pipe and cut it to length Allow for at least 1/16 of movement left and right for alignment.
REMEMBER the Front Sprocket Must be Aligned with the REAR SPROCKET on the Differential OTHERWISE you will always break the chain.
CLICK ON THE PICTURE TO EXPAND IT SO YOU CAN READ WHAT I WROTE.
Look at end of sprocket 3 bolts metal tin bent over to hold to bolts from unscrewing. I have something like that but is attached to a bracket just wondering is a a bracket broke loose and fell off? and maybe that's why gear slides around?
His 3 bolts are holding the SPROCKET onto the back plate. The sprocket is a stand alone piece that bolts onto the shaft that has a plate to bolt a sprocket to it. Alleyoop