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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
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
Although the curve start perpendicular to the arc, Creo accuracy doesn't show it perfectly perpendicular, not even with curvature analysis. Setting accuracy to absolute at .00005 helps, but still show nearly 2 degrees off perpendicular. I have evaluated several involutes and they all have this inaccuracy at the start.
However, I did find this feature in one of the gears on the web that was worth sharing...
How to extend an equation curve in a subsequent sketch:
I don't why uploaded video files seem to fail half the time