# Archimedean spiral

**URL:** <https://discourse.shapr3d.com/t/archimedean-spiral/36352>\
**Category:** Modeling Questions\
**Created:** [February 2, 2025, 10:39am UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352 "2025-02-02T10:39:29Z")\
**Posts on this page:** 15\
**Page:** 1

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**Author:** ![msdn80](https://avatars.discourse-cdn.com/v4/letter/m/90ced4/32.png) [@msdn80](https://discourse.shapr3d.com/u/msdn80)\
**Post date:** [February 2, 2025, 10:39am UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/1 "2025-02-02T10:39:29Z")

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Hello,

I’m designing a chuck for my lathe and I need to draw an archimedean spiral.

Is there a quick way to do so in Shapr3D?

I have searched and looks like there isn’t…

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**Author:** ![arroniow](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/arroniow/32/30268_2.png) [@arroniow](https://discourse.shapr3d.com/u/arroniow)\
**Post date:** [February 2, 2025, 3:21pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/2 "2025-02-02T15:21:48Z")

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Hope this helps.  
Two sketches, one on each axis.  
Then a revolve.  
With manual adjust of the revolve using the grabs, you can make it look how you want.

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**Author:** ![msdn80](https://avatars.discourse-cdn.com/v4/letter/m/90ced4/32.png) [@msdn80](https://discourse.shapr3d.com/u/msdn80)\
**Post date:** [February 2, 2025, 4:20pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/3 "2025-02-02T16:20:14Z")

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Thanks for your help. Apologies, I was not clear. The Archimedean spiral I’m looking to draw is as in here:

> **[Archimedean spiral](https://openhome.cc/eGossip/OpenSCAD/ArchimedeanSpiral.html)**
>
> As I said in the summary of Spiral moving fish, when I published Moving fish, someone said: “C...

The radius increases with each increment of a radial angle, I need 7 convolutions (for a lathe chuck). I could design it with lines 3.6 degrees apart from the same center and 0.01mm to achieve a 1mm gap between each convolution but that’s over 700 manual touch points, so I was wondering whether there is anything faster that can be done with Revolve.

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**Author:** ![TigerMike](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/tigermike/32/32650_2.png) [@TigerMike](https://discourse.shapr3d.com/u/TigerMike)\
**Post date:** [February 2, 2025, 6:13pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/4 "2025-02-02T18:13:01Z")

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Here’s a method that can work. Credit goes to @Tippy for what he shared back in 2021.  
I recreated his method here…

And here’s the link from 2021.

> [@Spiral](https://discourse.shapr3d.com/t/spiral/1441/17):
>
> I’d like to share my take on producing a spiral by using a revolve body and a cone. Notes: The number of revolution of the revolve body dictates the MAX number of revolutions in the final spiral. The height of the cone will dictate the FINAL revolution count in the spiral. Similarly, the base of the revolve body dictates the MAX outside diameter. The base of the cone dictates the FINAL outside diameter of the spiral Here are the steps: …

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**Author:** ![arroniow](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/arroniow/32/30268_2.png) [@arroniow](https://discourse.shapr3d.com/u/arroniow)\
**Post date:** [February 2, 2025, 6:39pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/5 "2025-02-02T18:39:28Z")

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That is a nice trick, I like it.

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<div class="post-metadata">

**Author:** ![msdn80](https://avatars.discourse-cdn.com/v4/letter/m/90ced4/32.png) [@msdn80](https://discourse.shapr3d.com/u/msdn80)\
**Post date:** [February 2, 2025, 7:41pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/6 "2025-02-02T19:41:16Z")

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Yes, that seems to work. Many thanks. Now I need to figure out how to draw a spiral with lines 1mm in thickness and 1mm apart, with inner circle of 24mm… I’m playing around with it, but with 7 revolutions my iPad Pro is taking ages to project… It’s going to be a long night 🙂

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**Author:** ![TigerMike](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/tigermike/32/32650_2.png) [@TigerMike](https://discourse.shapr3d.com/u/TigerMike)\
**Post date:** [February 2, 2025, 7:49pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/7 "2025-02-02T19:49:20Z")

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Agree. And, here’s a BONUS!  
A nice way to make a helical spring.

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**Author:** ![arroniow](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/arroniow/32/30268_2.png) [@arroniow](https://discourse.shapr3d.com/u/arroniow)\
**Post date:** [February 2, 2025, 10:56pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/8 "2025-02-02T22:56:49Z")

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It sounds like you want a clock spring.  
1mm thick spring steel, around a 24mm boss and 7 turns.  
Drawn with Arcs and then sweep.

 ![Clock_Spring](https://us1.discourse-cdn.com/flex002/uploads/shapr3d/original/3X/d/1/d1192296efb7b625cd6a821186e4133121bfa8d2.jpeg)

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<div class="post-metadata">

**Author:** ![msdn80](https://avatars.discourse-cdn.com/v4/letter/m/90ced4/32.png) [@msdn80](https://discourse.shapr3d.com/u/msdn80)\
**Post date:** [February 3, 2025, 7:31am UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/9 "2025-02-03T07:31:23Z")

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Yes, that’s it. I need to be able to control all dimensions. Would you be so kind to show it in a video? If it’s too much trouble, I understand.

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**Author:** ![arroniow](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/arroniow/32/30268_2.png) [@arroniow](https://discourse.shapr3d.com/u/arroniow)\
**Post date:** [February 3, 2025, 9:22am UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/10 "2025-02-03T09:22:55Z")

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Hi  
You will not be able to control all dimensions, only thickness of spring material and the height. These you can set on the sketch of the cross-section.

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<div class="post-metadata">

**Author:** ![arroniow](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/arroniow/32/30268_2.png) [@arroniow](https://discourse.shapr3d.com/u/arroniow)\
**Post date:** [February 3, 2025, 10:36am UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/11 "2025-02-03T10:36:38Z")

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Hi again  
For what it is worth, here is the video.  
I start with the circle sketched, along with a string of short guide lines with ‘=’ constraint set and the inner two ends fixed. This will allow me to change one measurement to change spring pitch.  
NOTE: You can only increase pitch, Shaper can’t decrease it.  
The spring is drawn manually with 180 degree arcs.  
Then ‘sweep’ the spring cross-section along the arcs.  
You can change the dimensions on the Cross-section sketch.

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<div class="post-metadata">

**Author:** ![arroniow](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/arroniow/32/30268_2.png) [@arroniow](https://discourse.shapr3d.com/u/arroniow)\
**Post date:** [February 3, 2025, 10:45am UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/12 "2025-02-03T10:45:36Z")

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Adjustment of the dimensions video.

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<div class="post-metadata">

**Author:** ![arroniow](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/arroniow/32/30268_2.png) [@arroniow](https://discourse.shapr3d.com/u/arroniow)\
**Post date:** [February 3, 2025, 4:51pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/14 "2025-02-03T16:51:09Z")

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> [@arroniow](#):
>
> Okay, I have added a couple more constraints and we now have a fair amount of control on coil parameters.  
> The sketch is similar to before, but using the following constraint arrangement.  
> Two fixed length lines from the origin, set the first half turn (the difference should be half the spacing pitch). Therefore a 1mm difference if the pitch is 2mm  
> Next you have three short lines on each side attached to the ends of the two previous lines.  
> All of these short lines must be linked with the ‘=’ constraint and both sides linked.  
> Now set the length of one short line (in this case I set 2mm).  
> The next step is to draw the 180 deg ‘ARCs’ which are snapped to the line end points (junctions).  
> On both sides of the drawing you will need to set a 90 deg angle constraint between each short line and the Arc that is coincident to it. This will hold the Arcs correctly when changing the pitch dimension on the left.

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<div class="post-metadata">

**Author:** ![msdn80](https://avatars.discourse-cdn.com/v4/letter/m/90ced4/32.png) [@msdn80](https://discourse.shapr3d.com/u/msdn80)\
**Post date:** [February 3, 2025, 9:41pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/15 "2025-02-03T21:41:54Z")

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Thanks so much, this is just perfect for what I need and I’m glad that others can refer to this too! Very clear video, I could easily follow and draw it. I’m very grateful, many many thanks.

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<div class="post-metadata">

**Author:** ![arroniow](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.shapr3d.com/arroniow/32/30268_2.png) [@arroniow](https://discourse.shapr3d.com/u/arroniow)\
**Post date:** [February 3, 2025, 11:18pm UTC](https://discourse.shapr3d.com/t/archimedean-spiral/36352/16 "2025-02-03T23:18:59Z")

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No problem, it was an interesting little exercise in use of constraints.  
This has made me think of missing pieces of functionality in sketching.  
It would be nice if we could make dimensions a mathematical function of others (establish a relationship between elements of the sketch).  
I suppose this would be a case of being able to set a measurement as a variable and then define it in a table.  
Next would be ‘Scripting’ which would allow users to automate the generation of patterns, etc.  
Have a great day.