It's just a standard early model short shaft Ryobi of 31 cc. It probably began life as a Ryan or Lawnboy string trimmer.

It would be a good engine for your Bridi Stick

You might want to put a different rear mount on it. You can get them here http://www.carrprecision.com/Pages/prod02.htm
# Ryobi 31cc 2-cycle motor mount with screws - $ 25.00

# Ryobi 31cc carburetor spacer with gasket - $ 8.00