Imagine a piece of paper in the shape of a right triangle.
Imagine that it's special paper, of zero thickness.
If you hold one square edge parallel to the axis of a cylinder, and wrap the other square edge around the cylinder, the hypotenuse will form a helix.
Assume the cylinder is of the pitch diameter of the spiral shaft.
Now, the problem has been unwrapped into a wedge; you can probably figure the kinematics from there.
Mike Halloran
Pembroke Pines, FL, USA