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Epicyclic Trammel


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  • Silver Contributor


Quite fascinating.

Are there any real world objects that use an epicyclic trammel?

 

...and if If "Epicyclic trammel" are not a rock band, someone really ought to form it : )

 

 

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Archimedes made a 2 slot trammel that drew ellipses.

 

https://en.wikipedia.org/wiki/Trammel_of_Archimedes

 

I made one in C4D a while ago that had 3 slots

 

 

Recently I saw this device on YouTube, and thought I'd try it with 2 spinners

 

screenshot.png.a4a0af29327fc1104f72fe810dee08d1.png

 

I imagined I'd need some trig to make it work, but it seems the small object just has to rotate 2X the speed of the large one. Not sure why... 

 

I got a bit carried away, adding planetary gears 😀

 

I think epicyclic gears are used in electric screwdrivers, and Sturmey-Archer 3 speed bike hub gears.

 

Epicyclic gear math can be a bit difficult, but you're welcome to look at my methods

 

trammel 9.c4d

 

here's a regular epi system that has sliders for speed

 

epi.c4d

 

 

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  • Silver Contributor

Thanks Jed - I'm always interested to see files like these. Facinating stuff.
You might enjoy this youtube channel that I stumbled across today - a retired Vietnamese engineer making animated video of various mechanical setups - over 3,000 of them I believe!

 

https://www.youtube.com/user/thang010146

 

 

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@MikeA thanks for the link - there's a ton of ideas there. Thang knows his stuff.

 

After I made the model in post 1, it bugged me that although it worked, I didn't really understand why the red spinning part had to rotate at 2X the speed of the larger part, and even why the cylinders stayed in sync in the slots. I have managed to solve it with a bit of simple geometry if you're interested -

 

 

turns out the size of the red part doesn't matter -

 

spinner-test-small.gif.524acf3f588c2b53c6789595f2f45b11.gif

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  • Silver Contributor

I very much enjoyed that Jed - and you would have made a great maths teacher!

If you concentrate on that red spinner above it's quite hard to convince yourself it's not moving left or right : )

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@MikeA - I had a go at one of thang010146's YouTube  designs

 

 

I'm always impressed at how well C4D can handle difficult dynamics situations. I don't think I'd be able to animate those cogs with math.

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  • Silver Contributor

@jed

I've only just seen this - been snowed under with work the last week. Oddly enough out of all thang's video this elliptical gears one was one I watched!  As you say, quite impressive that C4D handles this so well. Thang has some incredible knowledge of these mechanical designs.

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The elliptical gears use a tooth from the standard C4D cogwheel. The ellipse ratio is 1.35, and I used XPresso to measure the spline length and scaled it to an integer multiple of the cog pitch - an odd integer in this case so they line up. I put the rotation axes at one of the ellipse focus points (using math from Wiki for position). Using the focus was just a guess, but seems to work 😀

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