A crankcase for a motorcycle is divided into an upper half and a lower half. A crankshaft, a main shaft, a counter shaft, and a pivot portion are arranged substantially on a straight line along a parting plane P of the crankcase. An eccentric cam and a pivot collar are disposed in the pivot portion, and a rear swing arm is connected to the pivot shaft. The upper half and lower half are vertically mated to each other in front of and behind the pivot portion and then vertically fastened to each other. The center of the pivot collar is offset downwardly from the parting plane P.