A speed reducer includes an internal gear, an input shaft coaxial with the internal gear, and an eccentric disk on the input shaft and rotatable inside the internal gear. A cage, at an end of an output shaft, coaxial with the input shaft, and rotatable between the internal gear and the eccentric disk has pockets fewer in number than the internal gear's internal teeth. Rollers are received in the respective pockets such that when the input shaft rotates once, the rollers circumferentially move by a distance equal to one internal tooth width, causing the output shaft to be rotated at a reduced speed. The root radius of the internal gear, the radius of the circumcircle of the rolling bearing, and the outer diameter of the rollers are determined such that roller gaps defined between the rollers and the tooth bottoms of the internal gear are controlled to reduce vibration.