A coupling device has a flexible member that is vertically connected to a rotating shaft and of which the length can be varied in an inward and outward direction with respect to the rotating shaft, an elastic member that is connected to the flexible member and causes the flexible member to receive an elastic force in the outward direction with respect to the rotating shaft, and a cam member that is rotatably connected to the rotating shaft and delivers a rotating force of the rotating shaft to a rotating member. The cam member has a through-hole having an initial-position portion in which the flexible member is positioned at the initial stage and a displaced-position portion which has a smaller diameter than the initial-position portion and of which the diameter is constant about the rotating shaft, and an another through-hole having an initial-position portion in which the flexible member is positioned and a return-position portion of which the radius decreases from the initial-position portion.