A driving force transmitting device is comprised of a first rotary member, a second rotary member securely fit around the first rotary member, a third rotary member rotatably supported in the first and second rotary members for being engaged with a shaft, an anti-rotated solenoid slidably fit in a solenoid housing hollow defined by the second rotary member, and a friction clutch driven by the solenoid for transmitting torque between the first rotary member and the third rotary member.