How to create a Conical Log Spiral?
-
Hi Y'all,
I'm new around here and I hope my question is appropriate for the forum and someone can help me with this.
I posted this in a discussion about the Helix Along Curve plugin yesterday, but haven't received any response.
I am trying to find a way to model a conical helix where the helix maintains a constant and specific pitch angle to a conical surface. It is also known as a conical log spiral.
The helix I am describing has the coils get closer together as they approach the apex of the cone. Here is an example:
I have searched these forums and all of the Googles on the Interwebs and had no luck finding a solution for SU. I have found plugins that draw helices with evenly spaced turns along an axis (Helix Along Curve, Screw, SPgears), but I need a way to build it by defining the pitch angle rather than the number of turns. The closest that I have been able to get is through Helix Along Curve, shown below, but this won't exactly work for what I need to model.
Can anyone help me with this, please?
-
See if this is anywhere close to what you are looking for. I have no idea what angle you want and I'm not sure I have the math skills to draw a specific angle.
SS
-
@s shepherd said:
See if this is anywhere close to what you are looking for. I have no idea what angle you want and I'm not sure I have the math skills to draw a specific angle.
SS
[attachment=0:21kl0pw5]<!-- ia0 -->conic spiral.jpg<!-- ia0 -->[/attachment:21kl0pw5]
Hi SS,
I appreciate your response.
I think I was using the term "pitch angle" incorrectly and causing confusion, since it's a totally different thing when talking about bevel gears. What I really meant was coil angle or helix angle.
I'm looking for an isosceles cone of 10 degrees taper (20 degrees apex) with a constant helix angle of 17 degrees to the base plane or 73 degrees to the cone axis. FWIW, my model will end up being a truncated cone.
Your model appears to have equidistant turns, like mine, rather than equiangular. The turns of a conical log spiral should get noticeably closer together with each turn toward the apex. You can see in our models how the spiral becomes more acute to the cone axis as it approaches the apex, while the angle is more obtuse at the base.
This one really has me stumped!
-
Okay, I think I'm getting warmer.
-
@s shepherd said:
Okay, I think I'm getting warmer.
[attachment=0:3d7s499l]<!-- ia0 -->conic spiral 2.jpg<!-- ia0 -->[/attachment:3d7s499l]
Hi Scott,
YES! How did you do it? Please let me know.
-
I knocked up this rough approximation just using a normal helix.
One turn then change the pitch and repeat, then fredoscale, box taper to make it a cone.
It's a bit of a work around, but you should be able to get just what you want with a bit of thought. I can't think of a plugin that makes the shape automatically, but I'm sure it could exist.
-
-
that's a sort of weird shape.. i think it's something like an arc being wrapped around a cone..
using shapeBender, you can get this:
though doing it like this is wrong.. the upward spiral isn't conical because it bulges..
i can see a way to do this manually which would work right but it wouldn't be quick.. i'll post up an example later if i get some time to draw it.
-
Hi everyone,
Thank you for your responses.
Scott gave me some insight on how to construct the equiangular spiral manually, in segments. It's tedious, but works very well to create the desired shape. Thank you, Scott!
In the meantime, I found the Spirix plugin, which can generate true LOG10 conical spirals, among many other shapes, very quickly. https://sites.google.com/site/spirixcode/home It has a lot of interesting parameters to generate complex coils, twists, etc., with mathematical precision.
Advertisement