The Involute Curve.
There is another approach used to simulate rolling action. Consider what happens when you place one end of a
straight line (with a length equal to half the circumference of the
circle) on the perimeter of a circle and then rotate that line around
the perimeter of the circle until the other end touches the perimeter
of the circle.
If you observe what happens to the end of the line, you will see
how it moves away from the circle. If you trace a line along the
path taken by the end of the straight line as it rolls around the
circle, the result is an Involute Curve (with Displacement in Inches on the both axes).