Ideal Harmonic Transformer

by lalbritton, published

Ideal Harmonic Transformer by lalbritton Jun 8, 2011

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20353Views 11828Downloads Found in Math


Was "Analog Sine/Cosine Calculating Machine", but then I found the actual name for this device, which I really like.

It is a thing to hold, enjoy turning the crank, and look at. If you can't find your calculator, and need to know the sine or cosine of an angle real quick, you can dial in the angle and read off of the Scotch Yokes. It also works in reverse.

I plan to paint one up, hang it on my wall, and use it to help explain Trig to my kids. I have built and assembled one.

This was initially going to be a simple design to help me learn Alibre. Simple was lost at some point, I'm afraid. I am thinking about adding a paper feed and pencil holder, so I can plot with it.

I've included a photo of two prototype versions, where I worked out the mechanical details. You can read more about them here, along with notes on why I'm making my own printed screws: http://swampcastle.blogspot.com/2011/06/sincos-prototypes.html

I also added photos of some now-funny-looking prototypes that helped me get the design to where it is today.

There are various other articles about this project on my blog: http://swampcastle.blogspot.com/


Assembly instructions are here: http://swampcastle.blogspot.com/2011/06/analog-sincosine-machine-assembly.html

If you don't have a printer, or want the parts in other materials, find them here: http://www.shapeways.com/shops/swampcastle

harmonic-transformerstl-mm.zip contains the whole set. If the file name starts with "print1", print 1 copy; if it starts with "print2_", print 2 copies. :) The "alternate" file is a one-piece version of the yoke, and replaces the yoke-T and yoke-extend files. This eliminates the need for glue, but is 11" x 4.75", so needs a large printer.

harmonic-transformer_alibre.zip contains all of the Alibre design files. I included a txt file with the names of Alibre files, listed under the name of the stl file that they appear in.

You'll want a T15 Torx screwdriver and some glue. I use an Up! printer, which has a 5"x5"x5" printing bed.

On the Up!, all bolts and pins need to be printed with fill=solid and quality=fine to provide sufficient torsional strength. Other components may be printed with the default settings of fill=loose and quality=normal. All fasteners are in one file for convenience.

File updates:
6/12/2011 9:54 pm, Central:

  • Replaced all files with higher resolution versions.
  • Added Alibre design files


  • Replaced fastener file, giving them a 10° tilt on the printer, to make them stronger (thanks for the suggestion, TeamTeamUSA).
  • Added alternate 1-piece version of the yoke.

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Awesome design but the screws seem to be tilted at an angle. I would love to print this. Can you please fix this?

The screws are intentionally at an angle, and will print just fine. The angle makes them stronger. If they are straight, the heads shear off very easily.

This is absolutely beautiful. I can’t wait to print this. It reminds me in some ways of the Antikythera mechanism. Another piece of ancient engineering I would love to print. Thank you for sharing your passion with us.

Which 3D prnter did you use for yur part printing? Looks more like Stratasys than Thing-O-Matic.

I used an Up! printer.

This is a beautiful piece of equipment. Once I get my CupCake printer I'll be printing this out first just for a wall piece in a nice frame. Thanks for your hard work..


Glad you like it. :)

The naming convention of your files is very helpful. More people should adopt it...

Morning i have tryd to yous the STL files but thy dont work is it posebel that i can get the drawings of you so i can scan them on to my cam program. I would like to see if i can cut it on my CNC my RAPMAN does not print as nice as you Printer .thats way i want to see wat it looks like if i cut them out and we can comperr them . I would love that please thanks Stan cheers

Have the updated stl files worked any better? There are no drawings for this design. It exists only as the Alibre design files. I would really like for you to be able to make one.


Check it out! I made a new set of higher resolution stl files, and ran a check on them. They may now work on your CNC. I've also included my design files, which are in Alibre format. Enjoy!


Can i be so blant to ask you if it is posable to send me the drawings on a stl or dxf files . The reason behind me asking is I have a cnc router of Heiz and want to try it on there in perspex to see if i can make the parts there . THe nuts and spacers i wil print on my Rapman and the dome .I would realy apreasehait it if you wil send me the drawings you can send it to [email protected] .i thank you and hope we can becum friends would lve to give back the feedback on your idea .I am in South-Africa and my kid is now at this stage at school were thy yous this in maths would help them just to understand the work beter thankyou very mutch regaards Stan .

All of the stl files are available already, on this Thingiverse page. You may have to log in before you can download them, but it is free. You are welcome to get a copy and make one. I look forward to your feedback.


They are Alibre files. I'll post them soon.

=-O Good morning there wat a nice idea i am printing one now as we speak my son is now at that stage in school were tyy bizee to lurn of sin ;cos and tan we wil see if this wil help .wer can we read more on this item and exacly how it works .can you please let me know it is printing very nice on my Rapman BFB wil let you know houw it went thanks Stan

I need to write a blog entry about that. For now, look at the diagrams here: http://en.wikipedia.org/wiki/Unit_circlehttp://en.wikipedia.org/wiki/U...

The crank arm is the radius of the unit circle. Each gear tooth is 2°. Point the arm at the angle you want, and then read the value on the arm. The arm at zero gives the cos, the arm at 90 (pi/2) is sin. Here's a screen shot of it with the arm at 0°, 90°, 180°, and 270°. Hope this helps for n

Inspirational work! I am delighted by the possibilities of customized adornment of technical parts that in recent history would have been streamlined and strictly functional. A renaissance in the making!


Wow. I'm a little sad it's not an openscad creation because I want to use that butterfly from the dome. I guess I'll just have to chop it out of the stl. ;)

Thanks! :) I really need to check out openscad. I've never tried it.