I finally got this... Obviously math is -not- my strong suit.
"Unwrapping a string from a cylinder..."
The sketch will show you the basis of the formula. The curve equation is stand-alone from the sketch.
Creo 2.0 attached
YouTube link
Video Link : 5126
Curve Equation:
/* Ref_r is the fixed radius of circle being unwound
REF_R=1
/* Segment is arclength per degree of the circle being unwound (2*PI*R)
SEGMENT = 2 * PI * REF_R / 360
/* Right angle triangle A = Radius B = ArcLength C =Involute radius
A = REF_R
B = t * 360 * SEGMENT
C = sqrt(A^2 + B^2)
/* The plot radius as the hypotenuse of triangle A-B-C;
/* R being a required cylindrical curve input
R=C
/* Formulating angle B = arctan(B / A); angle B of triangle A-B-C at the root circle center
TRAILANGLE = atan(B / A)
/* Leadangle is the linear sweep along the root circle; t = 0 - 1 * 360 for full circle
LEADANGLE = t * 360
/* Setback angle accounting for length B
/* Theta is the second required cylindrical curve input
THETA = LEADANGLE - TRAILANGLE
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