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A Fractal Flexural Mirror Support

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#1 Oberon

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Posted 13 December 2019 - 08:16 AM

This is just an idea for now. But its perfectly serious. And infinitely scaleable.

So how does it work?

Essentially it exploits the ease with which a flat plane can twist, yet support a load edge on. 

gallery_217007_7148_208309.png


Edited by Oberon, 13 December 2019 - 08:18 AM.

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#2 PrestonE

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Posted 13 December 2019 - 08:39 AM

I assume that you have run and FEA on this Jon???

 

Best Regards,

 

Preston



#3 Oberon

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Posted 13 December 2019 - 08:53 AM

Only in my head. I don't have the luxury of FEA, which would be great for optimising material thickness, in particular for that short little section where the Tee's join at an angle. Thats the only point that really needs watching, and even there I suspect I worry too much. The motions involved are utterly microscopic, and there are plenty of ways to beef the structure up to take a load and to keep all support points in the right place without risking its function should that be necessary.


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#4 Pinbout

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Posted 13 December 2019 - 09:35 AM

it sovles any rotation of the triangles that always occur with conventional design.

 

but the pivot on the angled cuts sux...a lot.

 

why the name fractal.



#5 PrestonE

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Posted 13 December 2019 - 09:45 AM

Ok, I understand the structure...but exactly where is the Non Mirror side supported?

 

Best Regards,

 

Preston



#6 TOMDEY

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Posted 13 December 2019 - 11:08 AM

So... it's just another name for 2-D cascaded Whiffletrees. And yes to Preston's consul to do the Finite Element Analysis (aka statics analysis) on the thing as built and used. Indeed, this is what the MEs usually start out with, and then improve with low-impedance joints etc. etc. And at that stage... they come to look just like the ones we are familiar with. The moniker "Fractal Flexure" doesn't really add anything new to the concept.    Tom


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#7 Pinbout

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Posted 13 December 2019 - 12:18 PM

Oberon - just saw a hail storm from Queensland , baseball sized hail destroyed a home, ripped threw roofs.


Edited by Pinbout, 13 December 2019 - 12:18 PM.


#8 phonehome

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Posted 13 December 2019 - 01:34 PM

Oberon,

 

My first take is it would require all the support points to be perfectly co-planar.  I suppose one way this could be accomplished is with co-sanding of all the pads simultaneously.  If there is any vertical misalignment in the support or in the flatness of the mirror then force will be unequal on the support points due to the very twisting [acting like a spring].  On conventional supports the pivot bearings more-or-less equalize the support point force.

 

Ed


Edited by phonehome, 13 December 2019 - 01:34 PM.


#9 Oberon

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Posted 13 December 2019 - 04:07 PM

Ok, I understand the structure...but exactly where is the Non Mirror side supported?

 

Thats up to you. But typically, for example, if you look at Merope’s structure you will see a solid ring around the mirror which could easily be adapted with fixtures for this sort of support. That big triangle below would be redundant from a mirror support pov. That would not benefit Merope but for my binoscope where I am pushing the boundaries to minimize mirror height it offers a significant improvement. The edge of the mirror could be so low it virtually scrapes the ground when tilted.

 

med_gallery_217007_5817_214721.jpg



#10 Oberon

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Posted 13 December 2019 - 04:08 PM

why the name fractal.

Its a repeating and ever diminishing pattern of identical shapes.


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#11 Oberon

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Posted 13 December 2019 - 04:11 PM

Oberon,

 

My first take is it would require all the support points to be perfectly co-planar.  I suppose one way this could be accomplished is with co-sanding of all the pads simultaneously.  If there is any vertical misalignment in the support or in the flatness of the mirror then force will be unequal on the support points due to the very twisting [acting like a spring].  On conventional supports the pivot bearings more-or-less equalize the support point force.

 

Ed

A flexure works because at the microscopic level of movement required to be functional there is virtually no force applied, exactly the opposite to stiction. The primary objective is to provide reliable improved performance (as in more equal support) than a conventional support subject to stiction can be trusted to provide; this is the primary reason why flexures are attractive, why flexures are employed. My personal objective is to create the flattest possible very high performance support, so to achieve both in the one design is engineering Nirvana. 

Now I’ve just got to build it...


Edited by Oberon, 13 December 2019 - 05:31 PM.

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#12 Benach

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Posted 13 December 2019 - 07:08 PM

Its a repeating and ever diminishing pattern of identical shapes.


Eh, not to pretend that I'm a smartass but I see just three identical shapes and I do not see any selfduplication.
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#13 m. allan noah

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Posted 13 December 2019 - 07:15 PM

Eh, not to pretend that I'm a smartass but I see just three identical shapes and I do not see any selfduplication.

Oh, you're clearly not pretending :)



#14 Oberon

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Posted 13 December 2019 - 07:22 PM

Eh, not to pretend that I'm a smartass but I see just three identical shapes and I do not see any selfduplication.

 

Look again.

 

Spot the T.

 

More may be added for more points of support ad-infinitum.



#15 TOMDEY

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Posted 14 December 2019 - 03:33 AM

Look again.

 

Spot the T.

 

More may be added for more points of support ad-infinitum.

Jonathan, Fractal is good and has many utilitarian applications.

 

Problem is --- your "fractal series" experiences mutual interference if you attempt to go even one single step in regression or progression. Which is to say, it can't work --- at least as shown. Add to that the further constraints required of N-step symmetric whiffles and the whole things falls apart. Those constraints are each contact point auto-adjusting to equal loads on all (each and every) and equal mass cons above each. This is then further optimized to achieve some pre-selected optimization single-valued metric (e.g. least Strehl impact, minimax surf slope, minimax surf displacement, min RMS wavefront hit... some metric of goodness)... Additionally, the severe boundary condition of side-support and (presumably) round homogeneous, isotropic thin disc-shaped object being supported (aka not an infinite planar object) etc. etc.

 

What I'm getting at... so far, you have a nice buzz-word and a bit of a cartoon... but not nearly enough detail to even begin to critique whether there is any merit to the concept. Show yourself (and us) the detailed geometry two or three steps further --- and how you avoid mutual interference? In mathematical jargon --- you still need to present (by induction) an infinite series that is not self-interfering.

 

What has not been shown (only flatly stated) is "Infinitely Scalable".    Tom


Edited by TOMDEY, 14 December 2019 - 03:36 AM.

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#16 Oberon

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Posted 14 December 2019 - 05:49 AM

Tom, I'm primarily interested in supporting a 16" mirror on 18 points (a pair of actually), so all my design work will reflect that. However I see no reason why as a matter of principle (execution being a practical constraint) that the design principles don't naturally follow for larger structures with more support points, exactly as our more conventional whiffle-trees already do.

 

I disagree with your assertion of mutual interference, and I disagree that it can't work. It works almost the same way as a standard whiffle-tree with ball or point bearings, except that there are no sliding or rolling parts, no friction and no stiction. The only real difference is that motions are always constrained in one axis per component, unlike a standard 18 point whiffle tree where the triangles move in two axis. This is catered for in my design by the "triangle" being replaced with a "T" in which the 2 components each permit one axis of movement.

 

So far as regression is concerned (the fractal nature of the design), if I removed the 6 x smaller T shapes I would have a 6 point mirror support. The 6 support points would be exactly where the larger T's currently join the smaller T's, and the only flexure working would be the 3 x vertical components of the 3 remaining T's (the 3 pieces extending in radially from the outside). In other words, it would function exactly the same way as a standard whiffle-tree style 6 point support system (but without the stiction).

Right now I don't see why it wouldn't work the same way in progression, but I'll admit I haven't really tried to go there (haven't even sketched it up) and aren't really interested in doing so at the moment. Sorry. 


Edited by Oberon, 14 December 2019 - 06:29 AM.

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#17 Oberon

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Posted 14 December 2019 - 06:48 AM

I thought I would try out some potential materials starting with a 0.9mm steel ruler, just to get a feel for what to expect. Using my spider test bed means that the test length of steel rule is 220mm. Hanging off the back is a small bucket for weights. Moment is 75mm.

 

gallery_217007_7148_91588.jpg

 

Having centered the laser on 5mm rules paper I drop a 3.4 gram aluminium weight into the bucket...

 

gallery_217007_7148_99187.jpg

 

...to see the laser spot move 35mm! Woah...thats 10mm per gram! 

 

gallery_217007_7148_55867.jpg

 

OK, so we have a sensitive enough test procedure and will follow up with some real data.


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#18 don clement

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Posted 14 December 2019 - 12:57 PM

hokusai.jpg


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#19 Dale Eason

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Posted 14 December 2019 - 01:04 PM

Very interesting replacing the normal whiffel-tree bearings with flexure.  Took a little while to see that.  But I did even before your last post explaining it in more detail.  Once I just looked at the point support pattern I could see the exact mapping of the standard triangle and levers of the conventional cell.  Cool.  Neat observation by you that it was a fractal as well.  Again very cool.

 

Now if it can be assembled easily .  Hey I bet it could easily be 3D printed.  I will try it.  I do have a 3D printed cell in my 10 F3 with the standard 6 point 3 lever support


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#20 figurate

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Posted 14 December 2019 - 02:55 PM

I also think it a good idea, though this is only academic for me as I use 8"-10" full thickness mirrors. I sketched a simple fractal branching pattern, chosen so as to be (somewhat) easy to draw, that I envisioned as 3D-printed and replacing a single pivoting triangle pair in a conventional 18-point support. The drawing is intended as an example and not to be taken too literally, as all parameters can be varied almost infinitely, and even the fractal proportions themselves can be tweaked anywhere from the 'branch' to the outer 'twigs', which I show here as having raised nodes at their extremities which would form the support points. The first branching is analogous to the pivot at the center of the conventional three-contact-point triangle, which allows the two groups of supports some mutual independence.

 

The supports themselves could be as dense or sparse as desired, as stiff or compliant, and of course a three branching pattern is an option also (where I live, a frequent chore is trimming fast-growing shrubs so I am used to looking at this sort of thing).  

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Edited by figurate, 14 December 2019 - 04:32 PM.

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#21 Oberon

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Posted 14 December 2019 - 05:20 PM

Very interesting replacing the normal whiffel-tree bearings with flexure.  Took a little while to see that.  But I did even before your last post explaining it in more detail.  Once I just looked at the point support pattern I could see the exact mapping of the standard triangle and levers of the conventional cell.  Cool.  Neat observation by you that it was a fractal as well.  Again very cool.

 

Now if it can be assembled easily .  Hey I bet it could easily be 3D printed.  I will try it.  I do have a 3D printed cell in my 10 F3 with the standard 6 point 3 lever support

Exactly! I hesitated to mention 3D printing suspecting I would get howled down about material inconsistencies. But I imagine that if 3D printing can be stiff enough and consistent enough, then that opens up the options for, say, 100plus support points even on a smaller mirror. Whether thats practical or feasible or even desirable is for others to determine.


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#22 Dale Eason

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Posted 14 December 2019 - 06:30 PM

I'm not a good FEA person or even much of a mechanical engineer.  I'm an electrical engineer. Took statics and dynamic force classes too long ago.  It seems to me that it might not provide an even force at each point of contact to the mirror.  Which a correctly made whiffel-tree does.  That is because now the torsion spring nature of the bars start to work instead of just a gravity load by the mirror.  

 

Fusion360 can do FEA and it is free to people like us.  However there is a learning curve that some may not want to tackle.  Me included.  I use it to make 3D printed parts but have never tried the FEA feature.

 

Dale


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#23 TOMDEY

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Posted 14 December 2019 - 09:20 PM

I'm not a good FEA person or even much of a mechanical engineer.  I'm an electrical engineer. Took statics and dynamic force classes too long ago.  It seems to me that it might not provide an even force at each point of contact to the mirror.  Which a correctly made whiffel-tree does.  That is because now the torsion spring nature of the bars start to work instead of just a gravity load by the mirror.  

 

Fusion360 can do FEA and it is free to people like us.  However there is a learning curve that some may not want to tackle.  Me included.  I use it to make 3D printed parts but have never tried the FEA feature.

 

Dale

Yeah... that's also where I'm at. In my case, I'm an optics guy and also a mathematician, but not an ME. But, I worked closely with the MEs, including support structures for active and adaptive optics mirrors! Some applications were ground-based, some air-breathers, some extreme g fields, and some zero-g. So, I can't help but perk-up when the discussion gets around to mirror supports. There a few right ways and absolutely tons of flawed ways.

 

figurate's sketch is interesting... truly fractal... and note the dilemma that I had mentioned in my first response --- which is (trying to) get the fingertips all either equally-loaded and distributed (near-ideal) or at least each loaded in proportion to "local" weight-load (also good) or (most ideally) such that a scalar optimization metric is e.g. minimized (overall wavefront differential RMS, for example). And that (of course) deep-dives into the mathematics of it... far far from trivial.

 

So, it's an interesting topic. Pragmatically, anything that emulates one of the ~standard~ successful whiffle patterns should get the job done.

 

Oh yeah! I've built a lot of hobby whiffles at home. Here's one where I needed to support my downward-pointing test-tower autocollimating flat mirror. Boundary conditions were that I had to be able to rotate the fiducialized flat about its center, without differentially-distorting it, or otherwise compromising its alignment to the ~test article~ (big telescope or Newt PM). Note that the final interface to the mirror itself is a circular hose filled with a fluid. It works magnificently!    Tom

 

~ click on ~ >>>

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Edited by TOMDEY, 14 December 2019 - 09:22 PM.

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#24 brave_ulysses

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Posted 14 December 2019 - 11:10 PM

freecad uses calculix for fea. some instructions here with a money-back guarantee:

https://www.cloudyni...0/#entry9089468

 

 

I'm not a good FEA person or even much of a mechanical engineer.  I'm an electrical engineer. Took statics and dynamic force classes too long ago.  It seems to me that it might not provide an even force at each point of contact to the mirror.  Which a correctly made whiffel-tree does.  That is because now the torsion spring nature of the bars start to work instead of just a gravity load by the mirror.  

 

Fusion360 can do FEA and it is free to people like us.  However there is a learning curve that some may not want to tackle.  Me included.  I use it to make 3D printed parts but have never tried the FEA feature.

 

Dale



#25 Pinbout

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Posted 14 December 2019 - 11:40 PM

 

that I envisioned as 3D-printed and replacing a single pivoting triangle pair in a conventional 18-point support.

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