Equation driven curve

[Tadas]

Hi,

does any could help me to create 3d equation driven curve of heating coil path, acc. image and capture of drawing ? The half pipe is going to be welded on dished head.

Thanks in advance

[Dwight]

Tadas

I am no help with equation-driven curves, but this does look as if a spiral sketch projected onto a surface would be just what you want.

Dwight

[Tadas]

Hi,

You are right, but is it possible in that way to keep equal step (pitch) between revolutions.

[HerrTick]

I have used Dwight's solution to make conic springs. It has some advantages. You get a graphic representation of the results. Also, you can decouple F(x,y,z) into F(x,y) and F(z).

As far as the equal step between revolutions, that depends entirely on your equation. SW has a spiral function embedded in the helix function that can do this in 2D, which is much simpler than ginning up your own equation. You could derive the cone angle for z by making a cross-section layout sketch.

[Dwight]

Tadas

To add to what HerrTick said, the actual step distance will lengthen slightly as you get to steeper parts of the surface, but the projected step distance can be kept equal.

Dwight

[DanPihlaja]

I have seen this guy do wonders with equation driven curves:

@zxys001

Maybe he can chime in.

[Tadas]

The wrap feature helps a bit. Precision of step could be an issue.
I'm looking the ways to workaround. First attempt. One of edges I'm going to use for sweep of round profile.
Thanks for replays.

[josh]

Based on the sketch you posted, you have a spiral on a portion of a sphere.

I searched:

equation of spiral on sphere

and the first result was:

https://www.intmath.com/blog/mathematic ... 07.83%20cm.

[Dwight]

https://www.intmath.com/blog/mathematic ... 07.83%20cm.

Josh

That's a nice little article. Thanks for posting the link.

Dwight

[Tadas]

Thank You. I've tested functions and that works. Does any knows how to change step of revolutions ?

Based on the sketch you posted, you have a spiral on a portion of a sphere.

I searched:

equation of spiral on sphere

and the first result was:

https://www.intmath.com/blog/mathematic ... 07.83%20cm.