# 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?
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.
dimension in the sketch and N is the number of coils.
Figure 3 3. Next create a swept protrusion using the outside edge of the surface as your trajectory: Select #Feature, #Create, #Protrusion, #Sweep, #Solid and #Done. Use the default options for the feature and when selecting the trajectory, use #Tangent Chain and select the outside edge of the surface. Now sketch your desired section on the cross-hairs (centerlines) as seen below.
Figure 4 4. Finally, the surface and datum curves may be placed on a layer and blanked to show the resulting helical coil.
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 =3D 8 primary_rad =3D 8 secondary_turns =3D 2 secondary_height =3D 60 theta =3D t * 360 * secondary_turns r =3D 40 + primary_rad * cos (theta * primary_turns) z =3D 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.
ve
y

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