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Geometry Lesson Requested: Drawing a Simple 2D Spiral
December 04, 2013, 09:25:08 AM
Hello All,  A little geometry lesson requested:

Does anyone know how to draw a simple 2D spiral-- I'm thinking like the spirals of a traditional electric stove/cook-top.

If TurboCAD has the tool do draw it automatically, I assume it is in the most recent Pro and/or Platinum versions, and not in Deluxe or Designer.

Optimally, I would like to learn the arithmetic and geometry behind it, and learn a method of applying those so that I can draw a 2D Spiral in version-19-Deluxe, using basic 2D tools, including the Construction Tools.

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For this example, I would like to specify:  The overall "diameter" to be 200mm, and the spacing between the "360Â°-intervals" to be 10mm.

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In addition to advising on how to draw it in 2D using basic TurboCAD tools, can someone explain how to create it in real life.  I'm sure "they've" been drawing, producing, spiral objects for hundreds if not thousands of years, so it seems that it has to be able to be done.

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Thanks for your interest in this Topic.  -Alvin

If a tool does indeed exist in the most recent TurboCAD Pro and/or Platinum versions, if someone wants to-- just for kicks and reference-- post an image of a 2D Spiral they created using one of those TurboCAD tools and an explanation of how they created it... that'd be cool.

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Alvin Gregorio
---TurboCAD: V21PP; V20.2PP; V19DL; V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)

December 04, 2013, 09:29:15 AM
It's called the Helix tool (good for 2D and 3D). See attached image.

December 04, 2013, 09:42:14 AM
It's called the Helix tool (good for 2D and 3D). See attached image.

Thanks Don.  That was easy enough.  It's even available in version-19-Deluxe.  It's in the 3D tools... didn't think to look there; a spiral is simply a "flat" helix... I guess.  Generous of "them" to include that tool in Deluxe.

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I'll have to go on the 'net and try to learn how to draw a 2D Spiral "by hand"-- in CAD or in real life.  Just one of my obsessive-curiosities, really.  I've always wondered how they are drawn-- what's the math and geometric principle/formula behind them.  (and I've always wanted to get my 2D stove-top symbols more realistic.)

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Thanks again Don!  -Alvin

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Alvin Gregorio
---TurboCAD: V21PP; V20.2PP; V19DL; V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)

December 04, 2013, 10:04:32 AM
It's called the Helix tool (good for 2D and 3D). See attached image.

Cool Tool...

Using the Rail Sweep with it... all sorts of things can be done--  even in Deluxe.

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Alvin Gregorio
---TurboCAD: V21PP; V20.2PP; V19DL; V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)

December 04, 2013, 10:29:59 AM
Alvin,

While I am not a math/geometry wizard, I do remember coming across a way to do this some time ago.  I just did a little searching and found out that the place I saw this was on a website I found when I was building my dust collection system.  It's pretty simple really. See attached screenshot.

Dan

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December 04, 2013, 11:44:16 AM
Alvin,

While I am not a math/geometry wizard, I do remember coming across a way to do this some time ago.  I just did a little searching and found out that the place I saw this was on a website I found when I was building my dust collection system.  It's pretty simple really. See attached screenshot.

Dan

Oh yeah.  I see that.  Thanks Dan.  -Alvin
« Last Edit: December 04, 2013, 11:54:40 AM by Alvin Gregorio »

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Alvin Gregorio
---TurboCAD: V21PP; V20.2PP; V19DL; V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)

December 04, 2013, 12:38:18 PM
Does this help?

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December 04, 2013, 02:14:25 PM
Does this help?

Well... I'd like to see a few more revolutions, but I see where you're headed.  Thanks Cliff; that was pretty astute of you to come up with that method.  -Alvin

(With having the Helix Tool available, I doubt that I'll ever be able to justify using any other method.
Hmmm....  wonder how the "pencil-&-paper" draughtpersons were taught to draw a spiral back in the day.  Probably a variation on the "string method" that Dan posted earlier.)

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Alvin Gregorio
---TurboCAD: V21PP; V20.2PP; V19DL; V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)

December 04, 2013, 04:33:37 PM

(With having the Helix Tool available, I doubt that I'll ever be able to justify using any other method.
Hmmm....  wonder how the "pencil-&-paper" draughtpersons were taught to draw a spiral back in the day.  Probably a variation on the "string method" that Dan posted earlier.)

Just as Cliff's screenshot shows, using a "French curve" to draw the actual spiral.

Henry H

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December 04, 2013, 04:36:36 PM

(With having the Helix Tool available, I doubt that I'll ever be able to justify using any other method.
Hmmm....  wonder how the "pencil-&-paper" draughtpersons were taught to draw a spiral back in the day.  Probably a variation on the "string method" that Dan posted earlier.)

Just as Cliff's screenshot shows, using a "French curve" to draw the actual spiral.

Henry H

Interesting.  I didn't get this far in my 4 years of high-school drafting (1977-1981).  I'll have to pull out a French-Curve and try it.

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Alvin Gregorio
---TurboCAD: V21PP; V20.2PP; V19DL; V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)

December 04, 2013, 06:06:42 PM

(With having the Helix Tool available, I doubt that I'll ever be able to justify using any other method.
Hmmm....  wonder how the "pencil-&-paper" draughtpersons were taught to draw a spiral back in the day.  Probably a variation on the "string method" that Dan posted earlier.)

Just as Cliff's screenshot shows, using a "French curve" to draw the actual spiral.

Henry H

Interesting.  I didn't get this far in my 4 years of high-school drafting (1977-1981).  I'll have to pull out a French-Curve and try it.

More trouble than it's worth. A lot more. Let TurboCAD draw it, then print the result.

Henry H

P.S. You can draw a reasonable approximation using a series of semicircles. See attached screenshot.
« Last Edit: December 04, 2013, 06:24:49 PM by Henry Hubich »

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December 04, 2013, 06:45:57 PM
It looks like Cliff's is a logarithmic spiral, a cartesian spiral. The simple helix (and Henry's approximation is an arithmetic or archimedes spiral.

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mike
TC user since v3. MacMini 5.1. 2.3 GHz. 16 Gig RAM.
TC 19 Pro 64 bit. Windows 7.