any help on how to sketch this please?

[Anonymous]

Hope I'm posting in correct forum. This is a rolling circle cutter (used to make discs for dumplings) I am modelling and wondered if anyone was able to help with the geometry please? I started down the path of cycloids but realised very quickly that I was way out of my depth.

[davebYYPCU]

Four cylinders and a pipe.

Attach your file, so I can show you, need your sizes.

Might help....

[TrippyLighting]

@davebYYPCU with that construction method I am interested to see how you ensnare when rolling the thing over dough that you end up with perfect cookie circles.

[TrippyLighting]

I've only modeled the cutting blade so it will cut exactly round cookie.

Scratch that 😉 Need to clean my glasses LOL 😉

[davebYYPCU]

And you want real world results, too?

Not finished, need size of the bits.....

[TrippyLighting]

It will cut cookies, but they unlikely will be exactly round 😉

[davebYYPCU]

Got to agree with that, but hey,

its in the pic, (must sorta work - right?)

[Anonymous]

Thanks very much Peter but it's not actually the shape  - it would have to tumble end over end to cut & the actual bend is not a semi circle, but I liked your approach. I'd love to know the actual geometry/formula(?) behind it to be able to sketch. modelling won't be a problem, just the dims and geometry. Here's some further info if the thing  intrigues you as it does me. Many thanks

DIMs as best as I could measure.

https://a360.co/37KrIYJ 

[TrippyLighting]

Yes, I know that the model I posted is not the correct shape 😉

That is why I deleted most of my initial post, but I was not able to remove the attachment.

I believe this should be easy to do without much math using the sheet metal environment, but I ran out of time last night, and this morning ... well ... I've got some day job stuff to attend to. 

If no one beats me to it I'll get to it tonight,

[chrisplyler]

To actually cut circles, it's easy. Just a 180-deg arc, extruded up and down enough, and then intersected with another 180-deg arc from the side. The only "math" necessary is deciding on the desired radius or diameter. This will produce a shape that, when two of them are back to back, will roll like a cylinder (assuming they are stiff enough not to deform under whatever pressure is applied).

And sure, you could do it with sheet metal, but you would want to have a very tiny straight/flat flange built in, so that it will unfold or generate a flat pattern.

https://knowledge.autodesk.com/community/screencast/caa5d30d-66ee-455b-a470-51c3bfe576e9

[Anonymous]

That's Great Chris, thanks very much. I'm wondering, though: the side elevation of yours is a circle but the cutter I have is an oval and the front elevation of my cutter is a lot flatter too. I'm not disputing whether yours will cut a circle (though I might be! 😉) but how can both be doing it I wonder...?

[TrippyLighting]

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@Anonymous wrote:

 I'm not disputing whether yours will cut a circle (though I might be! 😉) 

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You shouldn't. It definitely cuts round cookies. I came up with the same solution but decided not to create a redundant post after @chrisplyler posted.

It simply is more difficult to recreate with non circular curves, but can be done.

[MichaelT_123 · Accepted solution]

Hi Mr Monoandmaude,

Your suspicious is justified, although cookies could be still good, given a proper recipe.

The equation of the curve describing the circular cookie cutter profile is:

        θ  = r/R * sin( t )

        x  = R*cos(θ)

        y  = r*cos(t) 

        z  = R*sin(θ)   

where t={0,π}, r-circle radius, R-roller radius

Regards

MichaelT

[TrippyLighting]

Pretty cool! how would you translate that into CAD geometry ?

[TrippyLighting]

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@MichaelT_123 wrote:

Hi Mr Monoandmaude,

Your suspicious is justified...

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Yep, I had thought this was a trivial problems (and for you it likely is) but it isn't a geometrically simple as I had fooled myself believe!

[chrisplyler]

Same.

So I modeled myself up some dough, with some circular cutouts all in a roll. I motion linked up the handle (slider) and the roller (revolute) at a ratio of PI*dia = 360deg. I rolled the sucker across the dough. Nope, doesn't match.

It seems I had suffered from intellectual geometric brain farting. Now that I've SEEN it not work, my brain thinks, "Duh, of course it won't work." But before I saw it, I was certain it would work.

Anyway, I'll tell you what my solution DOES do. It efin' ROLLS like a mfin' boss.

[TheCADWhisperer]

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@chrisplyler wrote:
So I modeled myself up some dough, with some circular cutouts all in a roll. 

---

Homemade doughnuts got @chrisplyler a working away.

I’ll wager we haven’t seen the end of this effort.

I want to see the solution cut the holes too.

[TrippyLighting]

@Anonymous so this will cut a perfect circle. The interesting thing is that with my very first approach I was already halfway there.

The problem can be described as a circular cookie, which is wrapped around a cylinder.

The diameter of the cookie (d1) is half of the circumference of that cylinder so the diameter of that cylinder d2 = 2 * d1 / PI.

I turn that into a sheetmetal part (symmetric with K-factor 0.5) to derive that surface.

That surface is the (infinitely thin) cookie wrapped halfway around that cylinder.

Now I can model the cutter.

I project the outline of the wrapped cookie into a sketch. This does not create a circular curve, which is where my confusion was.

That sketch is extruded into a surface, mirror and and the excess trimmed away.

This should cut perfectly circular cookies.

[chrisplyler · Accepted solution]

AHA! Of COURSE you've got to wrap the X-dia cookie around a 2X/PI-dia imaginary pipe with the sheetmetal to create the inverse of the cutter. I'll smack myself in the forehead now!

Of course, you've also got to make the K-factor of your sheetmetal = 0, otherwise it won't wrap precisely halfway around.

Cuts circles AND rolls like a cylinder:

https://knowledge.autodesk.com/community/screencast/ffae834f-43a3-47ea-9698-e680746c4f72

[TrippyLighting]

That is a great screencast/model to show how it actually works!