Not sure if this is perfectly a physics question:
A rope is wrapped around a cylinder of diameter D. The cylinder is slightly eccentric so that the distance between the axis of the cylinder and the axis of rotation is e. As the cylinder rotates, it pulls the rope. At t=0, the far end of the rope is at position 0.
What is the function of the rope position with respect to the angle of rotation of the cylinder? (This is not a homework question BTW)