A Brief History of the Marque
Rinne-Motorengesellschaft mbH of Berlin, 1925-1930, was primarily an engine manufacturer of air-cooled and water-cooled two-strokes of 124, 173 and 247cc which they supplied to other motorcycle firms including Bücker, Lesshafft, Leto, Wecoob, Slevogt and Schlimme. They also built complete motorcycles designed and raced by Max Hucke, the last of which was produced in 1928.
The 131cc engine was air-cooled and horizontal, and was mounted in a very elegant loop frame with a cylindrical tank.
The 8545¹ site reports that they built Lastendreiräder (cargo tricycles) in 1923.
N.B. Possibly related to Flugzeugwerke Albert Rinne.