In the apparatus for creating a swinging motion, one ends of two opposed sides of a flexible link are secured to a stationary member and the opposite ends of the sides are connected to a driven shaft. A cam member is slidably mounted on a drive shaft and arranged between the two sides so as to continuously engage them when the cam member is rotated by the drive shaft. The cam has gradually varying configuration and when it is shifted along the drive shaft, the swinging angle is varied. By suitably constructing the cam member it is possible to stop the swinging motion and reverse the phase thereof.