An eccentric speed variator includes a first rotor, a second rotor, a third rotor, a cylindrical pin, and a flange. The second rotor has a hole formed therein. The third rotor rotates eccentrically to change a relative rotation phase between the first and second rotors. The cylindrical pin extends through the hole of the second rotor to establish mechanical engagement between the second and third rotors. The flange is secured to or integrally formed with an end of the cylindrical pin. In operation, when the flange contacts the outside wall of the second rotor, it serves to minimize inclination of the third rotor relative to the second rotor, thereby reducing local friction between the second and third rotors to eliminate undesirable mechanical vibration or noise. This structure also enables parts of the cycloidal speed reducer to be decreased, which leads to a reduced size of the cycloidal speed reducer.