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Creating logarithmic spirals using a conic and a helix. Need some math help!
john_concannon
Member Posts: 6 ✭
I've been trying to create logarithmic spirals in Onshape, and have found a few special features that other users have kindly developed, but none of these met my needs. You can project a regular (Archimedean) spiral on to a sketch easily enough using a conical helix:
But I wanted a logarithmic spiral (i.e. one where the distance between the turnings increase in geometric progression) and unfortunately you can't project a helix on to anything other than a cone or a cylinder. So instead, I used the loft feature to create a surface from a helix to its axis. I then created a horn shaped object by rotating a sketch with a conic about its axis. I then subtracted (Boolean) the horn from the surface. I could then 'use' (i.e. project) the inside edge of the surface on to a sketch in a perpendicular plane:
https://cad.onshape.com/documents/8f65c1667813235a037348da/w/e6d6a886e68d914a56993e10/e/b02f51d28e59bd8b08e851b9
In this way the spiral shape is determined by only three variables: The radius of the horn's base:
the number of turns (rotations) the helix makes:
and the Rho of the conic used to sketch the horn's cross section.
The height of the horn has no influence.
What I would like to do is understand the relationship between these variables and the spiral's logarithmic ratio (the geometric progression of the distances between the turnings of the spiral), so that I can (a) figure out what variables to use to create a golden spiral (i.e. with a ratio equal to the golden ratio) and then perhaps at some future point once I've learned how, (b) incorporate these variables into a feature script that draws logarithmic spirals using just these three variables.
So, can anyone point me in the right direction?
But I wanted a logarithmic spiral (i.e. one where the distance between the turnings increase in geometric progression) and unfortunately you can't project a helix on to anything other than a cone or a cylinder. So instead, I used the loft feature to create a surface from a helix to its axis. I then created a horn shaped object by rotating a sketch with a conic about its axis. I then subtracted (Boolean) the horn from the surface. I could then 'use' (i.e. project) the inside edge of the surface on to a sketch in a perpendicular plane:
https://cad.onshape.com/documents/8f65c1667813235a037348da/w/e6d6a886e68d914a56993e10/e/b02f51d28e59bd8b08e851b9
In this way the spiral shape is determined by only three variables: The radius of the horn's base:
the number of turns (rotations) the helix makes:
and the Rho of the conic used to sketch the horn's cross section.
The height of the horn has no influence.
What I would like to do is understand the relationship between these variables and the spiral's logarithmic ratio (the geometric progression of the distances between the turnings of the spiral), so that I can (a) figure out what variables to use to create a golden spiral (i.e. with a ratio equal to the golden ratio) and then perhaps at some future point once I've learned how, (b) incorporate these variables into a feature script that draws logarithmic spirals using just these three variables.
So, can anyone point me in the right direction?
0
Best Answer

Optionsmahir Member, Developers Posts: 1,292 ✭✭✭✭✭The equation for a logarithmic spiral is r = ae^(bθ). This can either be implemented via custom FS, or you can use my Parametric Curve FS to generate it. Here's an example.
3
Answers
What exactly are you having trouble with? If you can make it in the part studio, it can be either instantiated or recreated via FS.
Learn more about the Gospel of Christ ( Here )
CADSharp  We make custom features and integrated Onshape apps! cadsharp.com/featurescripts 💎
Not sure I can help you with understanding the variables. But I can help with FeatureScript.
Here is an example of how to create a spiral from scratch within FS using solid modeling approaches:
https://cad.onshape.com/documents/abb998532f54a132a42bea8b/w/b0d311a0342c2b1e722bdaf1/e/79973a...
And here is an example of how to model it in the part studio, and simply instantiate it using your custom feature:
https://cad.onshape.com/documents/bf218127a4290c050e205e75/w/42342e313f737ad5d1388f67/e/dd21cb39f...
Learn more about the Gospel of Christ ( Here )
CADSharp  We make custom features and integrated Onshape apps! cadsharp.com/featurescripts 💎
Boom! @mahir knows his spirals!
Learn more about the Gospel of Christ ( Here )
CADSharp  We make custom features and integrated Onshape apps! cadsharp.com/featurescripts 💎
And thank you Michael, I'll return to your examples when I start learning to write feature scripts.
Here's an example  I'm using Radians so t is bounded between pi and pi (2 pi radians in a single rotation)
The document is here: Single rotation parametric curve
John