A bicycle gearing system includes input and output shafts, two planetary gear systems, and a clutch mechanism. The clutch mechanism includes three clutch presser plates for frictional engagement with two clutch disks and a clutch base. A motor rotates a camshaft formed with cams selectively engageable with cam followers for driving the clutch presser plates to rotate. Steels balls are provided within cavities formed between the clutch presser plates and a clutch housing to convert rotation of clutch presser plates to linear force for frictional engagement with the two clutch disks and the clutch base. Different angles of rotation of the camshaft produce different clutch and gear combinations and different gear ratios.