Helical curve swept on a helical curve

I need to create a helical curve that is normal to an existing helical
curve. A spiral on a spiral so to speak. I have found several curve
equations that are close, but what usually happens is that the
secondary curve is not swept normal to the primary curve. The primary
curve is created by cylindrical equation like this:
r = 0.75
theta = 360 * t * 4.5
z = 0 - 19.05 * t

It is the equation that sweeps the secondary curve that eludes me.
Surely, someone must have done this before. Any ideas?

 

I don't really follow your description yet.

Does this shape look like a coil formed into a helical curve? Like if
you formed a phone cord into a spring?

David

 

Yes, exactly that. A phone cord formed into a spring is an accurate
description.

 

I have dug out an equation that I believe is what you may be looking
for.
It produces what looks like a helical phone cord wound around a
helix.
Using a cylindrical CSYS, the equation is:
primary_turns = 8
primary_rad = 8
secondary_turns = 2
secondary_height = 60
theta = t * 360 * secondary_turns
r = 40 + primary_rad * cos (theta * primary_turns)
z = primary_rad * sin (theta * primary_turns) + (t *
secondary_height)
There are definitely much more elegant ways to write this equation but
as my old brain is slowing down, I find that I need all the help (and
prompts) that I can get.
An elliptical variable sweep (about 3.5 X 1.75) gives a better visual
result than a circle when trying to follow this curve.
Hope that it is what you wanted and that I am not too late posting
it.
Peter

 

Peter,

Thanks for the formula, it is close but not quite right. I need the
orientation of the spiral to be normal to the helical sweep
trajectory. The spiral your formula produces is oriented such that
the spiral is parallel to the "sketch" plane (if there was one) as it
rotates about the main axis through the coordinate system. Think of a
plane through the axis that rotates with the sweep as the curve moves
down the z direction. I have a graphic, but do not know know how to
show it in this forum.