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 Post subject: Linear versus Binary style for super high NxNxN
PostPosted: Tue Dec 29, 2009 3:48 pm 
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Hi Twisty Puzzle fans,

Several of our twisty puzzle friends have been pushing the limits of high order twisty puzzles. With this post, I wish to share some ideas on these and start discussion how we can get even higher. Not that that this will result in any interesting puzzles, but because of the challenges in the mechanical design. Because we can.

So far, most high order twisty puzzles have a linear design style. That is, the number of shells is linear with the order of the puzzle. Verdes style is a well-know example of a linear style.

In my explorations, I found that a binary design style might be a working alternative to the linear style for super high order twisty puzzles. The rather awkward Pagoda style is an example of a binary style. The number of layers is proportional to the logarithm of the order, which may make a big difference at super high orders.

Here is a preliminary analysis.

Linear style …
• … is a proven style for high order twisty puzzles
• … has robust pieces
• … results in stable puzzles
• … is easy to design in 3D
• … becomes rather massive for super high order twisty puzzles
• … has a linear tolerance problem
• … may even be unstable when going super high

Binary style …
• … has rather flimsy pieces
• … is complex to design in 3D
• … has far less layers than linear style
• … may have less tolerance problems than linear
• … is less massive than linear
• … looks promising for super high order twisty puzzles
• … has yet to be proven

Work in progress. The jury is still out …

Enjoy the animated sketches below!

Oskar

P.S. These four are all GIF animations. You have to click them to get them started.
Attachment:
File comment: Linear Style
Linear Style.gif
Linear Style.gif [ 122.69 KiB | Viewed 10605 times ]

Attachment:
File comment: Binary Style
Binary Style.gif
Binary Style.gif [ 92.83 KiB | Viewed 10582 times ]

Attachment:
File comment: Example of a Linear 17x17x17
Over The Top Linear.gif
Over The Top Linear.gif [ 62.06 KiB | Viewed 10605 times ]

Attachment:
File comment: Example of a Binary 17x17x17
Over The Top Binary.gif
Over The Top Binary.gif [ 62 KiB | Viewed 10605 times ]

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Last edited by Oskar on Tue Dec 29, 2009 4:16 pm, edited 3 times in total.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Dec 29, 2009 3:54 pm 
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This makes a lot of sense, the pictures were great! :D

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Dec 29, 2009 7:37 pm 
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maybe a binary puzzle of a lower order than 17x17x17 should be made, so that quality can be tested without extreme prices?
How about another 7x7x7 is made with this new mechanism?
That way it can be compared in quality to the existing Verdes design, prove itself as a concept and will be fairly high order while still being cheap enough to print in shapeways...

Edit: Also, is there any way this binary style idea could be expanded to beyond nxnxn into cuboids? Maybe not, since it seems to be based on the fact that the level of the surface of the puzzle doesn't change.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Dec 29, 2009 7:53 pm 
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Nice and straightforward, and probably better quality than a lot of other mechanisms due to its simplicity. :D

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Wed Dec 30, 2009 4:25 am 
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elijah wrote:
maybe a binary puzzle of a lower order than 17x17x17 should be made, so that quality can be tested without extreme prices?
How about another 7x7x7 is made with this new mechanism?

I think better will be to embody the 9x9x9 - this mechanizm is more stable than 7s.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Wed Dec 30, 2009 4:36 pm 
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Here is a third style, Flat Style, just for completeness sake. I don't believe it will work for high NxNxN, as it results in even more flimsy pieces than Binary Style. The good thing is its minimal number of layers.

Oskar

Note: click the .gif file to see the animation.
Attachment:
File comment: Flat Style
Flat Style.gif
Flat Style.gif [ 66.62 KiB | Viewed 10394 times ]

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Last edited by Oskar on Sun Jan 03, 2010 9:00 am, edited 1 time in total.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Wed Dec 30, 2009 4:43 pm 
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I noticed some issues on tolerances you placed on the pieces oskar, and as you liked my feedback in PM I am offering it to the forum.

Just click to view the animation


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Binary.gif
Binary.gif [ 19.63 KiB | Viewed 10386 times ]

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Thu Dec 31, 2009 12:25 am 
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I think a question that needs to be asked in order to properly answer the question of which mechanism is best is as follows: What is the area of contact between layers for each style of mechanism? As puzzles grow into higher orders, no matter what mechanism they use, the amount of surface area during contact will increase. But I think it is important to include this factor in the debate. With puzzles, like the 17x17x17 that Oskar has designed, the amount of friction between the layers will be a large roadblock to overcome. To my knowledge a puzzle implementing the linear, or Verdes style mechanism, would be the best at reducing the contact area between layers. This is due to the fact that the mechanism utilizes a straight line for each cut (with a few others to shape the pieces). As many of you know, the shortest distance between two points is a straight line; and when this mostly straight line (formed by the cuts in a Verdes style mechanism) is rotated around the turning axis is will result in the smallest possible contact area.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Thu Dec 31, 2009 1:26 am 
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gingervergo wrote:
I think a question that needs to be asked in order to properly answer the question of which mechanism is best is as follows: What is the area of contact between layers for each style of mechanism? As puzzles grow into higher orders, no matter what mechanism they use, the amount of surface area during contact will increase. But I think it is important to include this factor in the debate. With puzzles, like the 17x17x17 that Oskar has designed, the amount of friction between the layers will be a large roadblock to overcome. To my knowledge a puzzle implementing the linear, or Verdes style mechanism, would be the best at reducing the contact area between layers. This is due to the fact that the mechanism utilizes a straight line for each cut (with a few others to shape the pieces). As many of you know, the shortest distance between two points is a straight line; and when this mostly straight line (formed by the cuts in a Verdes style mechanism) is rotated around the turning axis is will result in the smallest possible contact area.


Nice point to bring the amount face contact into consideration of an optimal design.

Theoretically, the V-mech and Oskar's approaches are all suffering from this issue when going above 10 layers. However, by careful settings of assembly tolerance and suitable linearizations of spherical/conical characteristics while keeping precise configurations, face contact can be reduced significantly. The problem is: when we come too close to this limit, the assembly is likely to pop. A straight V9/V11/V13 will pop very easily. So i suggest consider popping issue together with tolerance/amount of face intact.

Leslie


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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Thu Dec 31, 2009 1:38 pm 
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I agree with Leslie Le
- the crown of precise configurations will give us the best result without poping and with great clutch,
- huge friction of surface areas can be eliminated by lubricating, believe it works good enough.

Also, I think, third question is count of big size elemets, which will be fundamental pieces for holding smaller pieces. In this sense: V-mechanism is worst - where only middle center piece keep weight of all other elements. But Oskar`s pagoda style has best solution - where a half of elements get load of other half elements. The stipulated question means the total strong of construction for extra big cubes.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Fri Jan 01, 2010 2:35 pm 
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I have some questions:

2 Drewseph - About tolerances. Are you sure of right values proposed for tolerances? 0.04mm is ve-ery small value... Any garbage or filings may lock of this span.
Second question: why in such gaps need to improve only? not for all slits of the cube? If You afraid of unfolding cube like fir-tree, for binary slyte (like as it is in linear style), - you don`t have to worry! The effect of blossom on binary style will be less appreciable.

2 Oskar - Why you deside to insert next layer in exact positions, you display in presentstion (Binary_Style.gif)? I understand that mathematical point of view offers the simplest way to fill next level layer by insertion from the beginning to the end (from left to right in presentation). But I have a doubt of is there optimal way to fill on real practice?.. Will be it best solution for avoid popping? May be better will be insert from the right side,.. or from the middle to both of directions, in really big sizes?
Attachment:
File comment: see here example below: such piece inserted for 11`s level of binary style
Binary_11.png
Binary_11.png [ 360 Bytes | Viewed 10092 times ]

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 8:21 am 
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Tesseract750 wrote:
I have some questions:

2 Drewseph - About tolerances. Are you sure of right values proposed for tolerances? 0.04mm is ve-ery small value... Any garbage or filings may lock of this span.
Second question: why in such gaps need to improve only? not for all slits of the cube? If You afraid of unfolding cube like fir-tree, for binary slyte (like as it is in linear style), - you don`t have to worry! The effect of blossom on binary style will be less appreciable.




i was told that local factories providing 3d printing services always use positive tolerance unless specified. e.g., the default SLA precision +/- .05mm will result in .1mm thicker than STL data. What's worse is that, error doesn't distribute evenly. in this case, a void gap of .04 doesn't help much.

It can be seen from V7 that the gap is much larger than .1 and it works smoothly, however it pops.
R5 is even more generous in this situation and it has a more stable structure which is the binary structure in Oskar's sense, however it has a bad displacement tolerance.

Leslie


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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 8:59 am 
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Here are some more sketches. The colors are only for illustration purpose. Following Drew's advice, clearances are minimal (0.04 mm) everywhere, except where pieces are clamped within another piece (0.15 mm), around the "mushrooms" (0.30mm) and near the surface (0.00 mm). The caps are for coloring Mini Gigaminx style.

Oskar

Attachment:
Over The Top v13 - view 5.jpg
Over The Top v13 - view 5.jpg [ 109.02 KiB | Viewed 10032 times ]

Attachment:
Over The Top v13 - view 6.jpg
Over The Top v13 - view 6.jpg [ 83.58 KiB | Viewed 10032 times ]

Attachment:
Over The Top v13 - view 11.jpg
Over The Top v13 - view 11.jpg [ 44.75 KiB | Viewed 10032 times ]

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 10:15 am 
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Leslie Le wrote:
gingervergo wrote:
I think a question that needs to be asked in order to properly answer the question of which mechanism is best is as follows: What is the area of contact between layers for each style of mechanism? As puzzles grow into higher orders, no matter what mechanism they use, the amount of surface area during contact will increase. But I think it is important to include this factor in the debate. With puzzles, like the 17x17x17 that Oskar has designed, the amount of friction between the layers will be a large roadblock to overcome. To my knowledge a puzzle implementing the linear, or Verdes style mechanism, would be the best at reducing the contact area between layers. This is due to the fact that the mechanism utilizes a straight line for each cut (with a few others to shape the pieces). As many of you know, the shortest distance between two points is a straight line; and when this mostly straight line (formed by the cuts in a Verdes style mechanism) is rotated around the turning axis is will result in the smallest possible contact area.


Nice point to bring the amount face contact into consideration of an optimal design.

Theoretically, the V-mech and Oskar's approaches are all suffering from this issue when going above 10 layers. However, by careful settings of assembly tolerance and suitable linearizations of spherical/conical characteristics while keeping precise configurations, face contact can be reduced significantly. The problem is: when we come too close to this limit, the assembly is likely to pop. A straight V9/V11/V13 will pop very easily. So i suggest consider popping issue together with tolerance/amount of face intact.

Leslie


Yes I agree.
It is important to consider the physical act of turning such a puzzle. The design might theoretically be fine but when a fumbling human hand tries to turn it they are applying pressures in all sorts of different unpredictable ways. Things that lined up before are now slightly off and the puzzle needs to cope with that.
My gut feeling is that the binary style would have massive popping issues and one slight misalignment would result in a new multi coloured carpet.
With the exponential advancement in 'home' puzzle making I assume by the end of the year we will be seeing some of these in the flesh (plastic?).
Thank you for the beautiful illustrations Oskar.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 12:18 pm 
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How would you put these together?
It seems the only way to down such a thing is unscrewing a side before assembling, but with super-high order cubes, it could be extremely difficult to put one together this way.
Just wondering if you've thought the putting together part of the design through.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 12:28 pm 
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Oskar wrote:
Here are some more sketches. The colors are only for illustration purpose. Following Drew's advice, clearances are minimal (0.04 mm) everywhere, except where pieces are clamped within another piece (0.15 mm), around the "mushrooms" (0.30mm) and near the surface (0.00 mm). The caps are for coloring Mini Gigaminx style.

Oskar

Attachment:
Over The Top v13 - view 5.jpg

Attachment:
Over The Top v13 - view 6.jpg

Attachment:
Over The Top v13 - view 11.jpg

How would the middle layers turn? They appear to be thicker with variable (tapering) thickness, unless it's just the perspective of the projection?

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 12:56 pm 
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elijah wrote:
How would you put these together?
It seems the only way to down such a thing is unscrewing a side before assembling, but with super-high order cubes, it could be extremely difficult to put one together this way.
Just wondering if you've thought the putting together part of the design through.


My best guess would be to use a similar tactic the Drew used to assemble his teraminx(and I'm guessing a lot of his other higher order puzzles): teraminx assembly No matter what method is used to assemble a super high order puzzle, it will be very tedious and time consuming.

Kelvin Stott wrote:
How would the middle layers turn? They appear to be thicker with variable (tapering) thickness, unless it's just the perspective of the projection?


It appears that its just the perspective that it is being viewed at.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 1:15 pm 
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gingervergo wrote:
Kelvin Stott wrote:
How would the middle layers turn? They appear to be thicker with variable (tapering) thickness, unless it's just the perspective of the projection?

It appears that its just the perspective that it is being viewed at.
Hmm, I'm not so sure, because the degree of tapering is way out of line from adjacent layers. Even the effect of pillowing could not account for this... :?

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 1:24 pm 
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The tapering is on purpose. Otherwise there would not be enough room for the screw to fit under the central cap.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 1:29 pm 
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Oskar wrote:
The tapering is on purpose. Otherwise there would not be enough room for the screw to fit under the central cap.

This makes sense, thanks for confirming, but then how could you rotate/slice the tapered middle layers without creating gaps (and therefore potential pops) at mid/45 degree rotation?

Did you try to model a 45 degree rotation/slice of the middle layer? Perhaps that might give more clues about required tolerances...

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 4:28 pm 
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There is my first attempt to design 11x11x11 of pagoda style. In current process it is not totaly fillets and tolerances. See below...

I deside to make 11x11 because it is more difficult - it is not simple pagoda. 17x17 and 9x9 are completly described by Oskar - there are clear binary designs.

Attachment:
File comment: click to enlarge actual resolution 1280x994 px
Pagoda11_v01_source.png
Pagoda11_v01_source.png [ 156.69 KiB | Viewed 9809 times ]

Attachment:
File comment: click to enlarge actual resolution 1280x994 px
Pagoda11_v01_source-sketch.png
Pagoda11_v01_source-sketch.png [ 67.13 KiB | Viewed 9809 times ]

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Last edited by Tesseract750 on Mon Jan 11, 2010 6:04 am, edited 2 times in total.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 03, 2010 7:02 pm 
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Perhaps it would be best to use a mixed approach. A single split followed by linear in both halves would cut down on the amount of material a lot with only small amount of the binary approach's disadvantages.


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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Jan 05, 2010 4:15 am 
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One more thing have to be improved...

... I think all of you saw Tony Fisher`s 11x11x11 and Leslie Le`s 12x12x12 videos. One general thing terrible to me - for super high order cubes, every time you rotate layer, you have to line up whole parallel layers for next moving any of perpendicular layer. It`s very tedious, and may spend a seconds... (for one move only)!

This annoyance is hard in both of cases:
- weak cube, like Tony`s done - lining up doing hard because of layers feeling like jelly;
- strong cube, like Leslie Le`s done, where tolerances are as small as possible, and rotations are embarrassed - layers cling each other, so lining up have to be more scrupulous.
Excuse me, dear Tony and Leslie Le, for criticism - but we have to take into account all possible disadvantages or mistakes of construction. In super high order`s cubes - this little discomfort may increase to big problem.

:idea: But I think we have solution!.. It implemented for some different cases, heh) but can be apply to our question. It is... clicking mechanism! Yes, the same as in V-cube-6. With this one - lining up of layers will be automatically done!!!

---
P.S. "lining up" - means "alignment".
sorry for my quite bad english )

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Last edited by Tesseract750 on Mon Jan 11, 2010 1:11 am, edited 1 time in total.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Jan 05, 2010 1:06 pm 
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Tesseract750 wrote:
One more thing have to be improved...

... I think all of you saw Tony Fisher`s 11x11x11 and Leslie Le`s 12x12x12 videos. One general thing terrible to me - for super high order cubes, every time you rotate layer, you have to line up whole parallel layers for next moving any of perpendicular layer. It`s very tedious, and may spend a seconds... (for one move only)!

This annoyance is hard in both of cases:
- weak cube, like Tony`s done - lining up doing hard because of layers feeling like jelly;
- strong cube, like Leslie Le`s done, where tolerances are as small as possible, and rotations are embarrassed - layers cling each other, so lining up have to be more scrupulous.
Excuse me, dear Tony and Leslie Le, for criticism - but we have to take into account all possible disadvantages or mistakes of construction. In super high order`s cubes - this little discomfort may increase to big problem.

:idea: But I think we have solution!.. It implemented for some different cases, heh) but can be apply to our question. It is... clicking mechanism! Yes, the same as in V-cube-6. With this one - lining up of layers will be automatically done!!!


I cannot speak for Leslie and his 12x12x12 but the main reason "my" 11x11x11 moves so poorly is because during the moulding process I inadvertently introduced several inaccuracies. Or to put it another way I screwed it up a bit. Accurately made I think it would be fine.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Jan 05, 2010 2:06 pm 
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so, question to you, Tony: how do you think - improving by clicking mechanism, for avoid tedious lining up, will give good result? Is it a good idea?

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Jan 05, 2010 8:44 pm 
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Tesseract750 wrote:
One more thing have to be improved...

... I think all of you saw Tony Fisher`s 11x11x11 and Leslie Le`s 12x12x12 videos. One general thing terrible to me - for super high order cubes, every time you rotate layer, you have to line up whole parallel layers for next moving any of perpendicular layer. It`s very tedious, and may spend a seconds... (for one move only)!

This annoyance is hard in both of cases:
- weak cube, like Tony`s done - lining up doing hard because of layers feeling like jelly;
- strong cube, like Leslie Le`s done, where tolerances are as small as possible, and rotations are embarrassed - layers cling each other, so lining up have to be more scrupulous.
Excuse me, dear Tony and Leslie Le, for criticism - but we have to take into account all possible disadvantages or mistakes of construction. In super high order`s cubes - this little discomfort may increase to big problem.

:idea: But I think we have solution!.. It implemented for some different cases, heh) but can be apply to our question. It is... clicking mechanism! Yes, the same as in V-cube-6. With this one - lining up of layers will be automatically done!!!


Nice point to consider alignment issue as I've addressed in my test version. There are so many problems to be considered for a physical advance in puzzle design. Try a misalignment of about 30% of the size of facelet of V6/V7, you'll probably see its mech during rotation. Shift more and it is likely to explode or jam-up. The misalignment tolerance of 2mm out of 6.7mm in my 12th cube is fair enough though.

The hidden layer mech is applicable in high order cubes but it will be more challenging to have a stable build to which I believe Tony and his friends had made essential improvements.

And I think Bram has picked up a good idea.

Leslie


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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 4:59 pm 
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If you think allignment is a big issue, don't go about it by making a mech like the v-6, but use magnets instead.
I think this will not be as much of an issue with more precisely made cubes, however, like tony said.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 5:31 pm 
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But with magnets wouldn't it get extremely expensive?

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 6:00 pm 
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I guess you are probably right.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 6:05 pm 
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http://kjmagnetics.com/proddetail.asp?prod=D101%2DN50 10,000 for $400.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 6:08 pm 
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But if you are making, say a 17x17x17, you would need $400(of magnets) for an already $3500 puzzle

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 6:34 pm 
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you'd need the same number of magnets for a given puzzle as you'd need stickers. I believe that means you'd be able to make at least 2-4 17x17s with 10000 magnets.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 7:31 pm 
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TBH, to help alignment you wouldn't magnets on every piece.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 8:16 pm 
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what pieces would you put magnets on then? I'd say you'd need at least the cornermost pieces on each layer.
Maybe all edges and corner pieces would have magnets then?

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Sun Jan 10, 2010 10:27 pm 
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Loving this thread! I don't really have much to add other than some questions...

Oskar - First I hadn't said this before, but welcome to the forums. Love your work! I see Tesseract750 is using Solidworks - what do you use? Just curious.

And then a question for Tesseract750: Any chance of some insight into your work flow with Solidworks? Something similar to the video Drew did, or can you just send me one of your files to review?? :) :) Just kidding, but I really would like to see your work flow since I'm learning Solidworks myself...

Oh - and I think the pagoda style is just beautiful, regardless of how it works... It makes me want to own a half finished puzzle, just to admire the mechanism!

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Jan 11, 2010 6:13 am 
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2 jabeck:
Thanks for enjoying of hi-order cubes :)

Yes, I used SolidWorks; and yes, I`m respect Drew`s tutorial video. I a lot improve his 3D-building way for modelling hi-order puzzles.

By the way, there you can see my current results:
viewtopic.php?f=9&t=15929

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Sep 06, 2010 7:47 am 
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Hi Twisty Puzzles fans,

The quest for super-high NxNxN is still on. My binary-style 17x17x17 design has been an interesting learning experience. Prototype builder Claus has identified at least two major problems.
1) Friction
2) Popping
Problem 1) may be intrinsic to the binary style, as many pieces move through each other. Problem 2) would also occur in extensions of the linear-style Verdes design, as it has also small pieces around the center.

Here is a hypothesis: all these problems occur due to tilting.
1) Friction: "Buckling" is what happens if you try to push a rope through a long tube. Due to tilting of the rope sections, they press to the sides of the tube and friction prevents pushing further. I believe a similar phenomenon occurs when you want to push a row of 64 small pieces around a 17x17x17.
2) Popping: If I understand Claus correctly, the problem of the 17x17x17 prototype was with the small pieces, which would tilt and pop out.

So how can we prevent tilting?

My idea to prevent tilting is by elongating all pieces inward. The sketches below illustrate the idea. It is a linear style which one could call "twisty/slidey style". The base of the new design is a rugged 3x3x3 frame. All other pieces hang inside the frame by some sliding-piece-type tongs and grooves. As the pieces are very long, they cannot tilt. I hope this will work to prevent popping and reduce buckling-induced friction.

Enjoy!

Oskar
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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Sep 06, 2010 8:06 am 
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Hmm, I would love to experiment with something like this. So instead of layers of nested spherical shells, you use concentric conical cuts under each face. This would result in a much simpler assembly of a large puzzle too :D

It may reduce buckling but how stable do you think it would be?

EDIT: Another plus of this, is that with pillowing, since there aren't so many layers of shells underneath, the inner 3x3x3 made by the corners and middle edges can be made very large in relation to the entire puzzle. This way all the other pieces' tails that extend down into the puzzle can be reduced dramatically in length.
EDIT 2: Seems I was wrong about that last point :lol: see Oskar's post below.

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Last edited by dannyb21892 on Mon Sep 06, 2010 9:49 am, edited 1 time in total.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Sep 06, 2010 8:47 am 
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dannyb21892 wrote:
It may reduce buckling but how stable do you think it would be?
I give it a 25% chance of success ...
dannyb21892 wrote:
all the other pieces' tails that extend down into the puzzle can be reduced dramatically in length.
Such reduction would also reduce its chance of success. Those long tails are there for a reason, viz. to prevent tilting.

Oskar

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Sep 06, 2010 2:30 pm 
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Oskar, I think you're on the right track here, but there's still room for improvement. It looks like the biggest potential issue is with the pieces which diagonally touch the very centers. Just a little bit of slop and they might slide straight out. Also, there's potential weakness issues with the groove you had to put in all the pieces to nominally stop that from happening.

My thought is that you could widen the centers under the surface dramatically so that the those pieces next to the centers have to reach backwards to get to the right positions on the surface. That way they're implicitly held in place by the kink, and also all the other pieces could be simplified to have one kink instead of two, essentially straightening out over what's currently the first kink. That would make the whole thing be held in place somewhat holistically, which might result in it feeling a little loose, but I don't think it would fall apart, and the pieces would individually be held in well by the ones around them and the overall amount of friction should be very under control.


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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Sep 06, 2010 2:39 pm 
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Bram wrote:
My thought is that you could widen the centers under the surface dramatically so that the those pieces next to the centers have to reach backwards to get to the right positions on the surface. That way they're implicitly held in place by the kink, and also all the other pieces could be simplified to have one kink instead of two, essentially straightening out over what's currently the first kink. That would make the whole thing be held in place somewhat holistically, which might result in it feeling a little loose, but I don't think it would fall apart, and the pieces would individually be held in well by the ones around them and the overall amount of friction should be very under control.


Actually, I got that a little wrong - while it's true that ideally the very outermost non-actual-corner pieces should be almost straight before the outer kink, all the ones before that should have a kink which gets increasingly prominent all the way up to the centers, which goes in the opposite direction as the inner kink does right now. That should be able to hold everything in and prevent the pieces from rotating in place.


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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Sep 06, 2010 5:39 pm 
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I like Oskar's twisting/buckling hypothesis and rope analogy, the logic makes sense. But this would actually suggest designing interlocking parts that PULL (drag) each other along in a chain, rather than PUSH each other, which is still the case and potential problem with Oskar's latest design above. So just like the rope analogy, the pieces must be connected so that they are pulled along in a chain to prevent the buckling, which should reduce friction as well as popping.

I'd like to call this the "pull vs push principle" to solve the mechanism of higher order cubes. This principle could be applied and work equally well in both linear and binary style mechs.
Attachment:
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Last edited by KelvinS on Tue Sep 07, 2010 2:57 am, edited 1 time in total.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Sep 06, 2010 6:39 pm 
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Personally I wonder why no one has ever (publically) thought of extending the hidden centre extension in the V cube design, it seems plausible, it also seems to be less likely for pieces to twist in their place compared to the V cube 11 design.

I made a quick sketch which would become an 11x11x11
Note that I don't really know how all parts will look, as Solidworks isn't that great a program for many part files, meaning it locks up my computer when I try to split the cube.


Attachments:
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11x11x11.png [ 45.92 KiB | Viewed 8436 times ]

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Mon Sep 06, 2010 10:58 pm 
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Namegoesnowhere, not sure if you were responding to what I just said, but that's approximately the suggestion I just gave, although your design does a much better job of holding everything in than what I suggested.


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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Sep 07, 2010 3:12 am 
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Bram wrote:
Namegoesnowhere, not sure if you were responding to what I just said, but that's approximately the suggestion I just gave, although your design does a much better job of holding everything in than what I suggested.

Only after looking at my sketch again, and then your responce do I now realize what you meant was what I sketched :lol:
The way I made it still is rather flawed though, it is only a 10 minute sketch.
Maybe I'll throw this into NX 5 soon, it is not as intuitive of a CAD program but handles high numbers of parts much better.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Sep 07, 2010 6:37 am 
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Tesseract750 wrote:
One more thing have to be improved...

... I think all of you saw Tony Fisher`s 11x11x11 and Leslie Le`s 12x12x12 videos. One general thing terrible to me - for super high order cubes, every time you rotate layer, you have to line up whole parallel layers for next moving any of perpendicular layer. It`s very tedious, and may spend a seconds... (for one move only)!

This annoyance is hard in both of cases:
- weak cube, like Tony`s done - lining up doing hard because of layers feeling like jelly;
- strong cube, like Leslie Le`s done, where tolerances are as small as possible, and rotations are embarrassed - layers cling each other, so lining up have to be more scrupulous.
Excuse me, dear Tony and Leslie Le, for criticism - but we have to take into account all possible disadvantages or mistakes of construction. In super high order`s cubes - this little discomfort may increase to big problem.

:idea: But I think we have solution!.. It implemented for some different cases, heh) but can be apply to our question. It is... clicking mechanism! Yes, the same as in V-cube-6. With this one - lining up of layers will be automatically done!!!

---
P.S. "lining up" - means "alignment".
sorry for my quite bad english )


Excuse me, but do you own an original unmodified V6? The clicking is annoying and leads to major misalignment isues. That is because sometimes the clicking does not happen as it should.

Sorr to bump old thread. Browsing brought me here rather randomly ..

Per

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Sep 07, 2010 6:40 am 
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perfredlund wrote:
Sorr to bump old thread. Browsing brought me here rather randomly ..

You're forgiven: 3.5 hours is not too much of a bump. :wink:

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Sep 07, 2010 9:31 am 
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Oskar wrote:
...
Over The Top v14 - view 4.jpg

I think such design will failed, like a matchs in cupped hand attempt to push them through the imaginary layer... It`s my opinion.

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Sep 07, 2010 2:19 pm 
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Thank you all for many suggestions. Super high NxNxN are truly a quest. Here are some responses, which I hope will stimulate discussion and stir up more even ideas.
Kelvin Stott wrote:
suggest designing interlocking parts that PULL (drag) each other along in a chain, rather than PUSH each other
Your sketch has identified a potential flaw of the design. My long "fins" prevent the pieces from tilting, but they don't prevents the skewing that you show. I like your "pull suggestion". However, where do I find the "meat" for that in those small pieces?
Namegoeswhere wrote:
extending the hidden centre extension in the V cube design
Nice idea. What problem does it solve?
Bram wrote:
issue is with the pieces which diagonally touch the very centers. Just a little bit of slop and they might slide straight out.
Those pieces are contained from four sides. Why should they slide straight out?
Bram wrote:
held in place by the kink
I do not believe the kink alone can hold pieces in place.
Bram wrote:
the other pieces could be simplified to have one kink instead of two
The two kinks follow from the cross-section design, one from the N-S cut and the other from the E-W cut. The purpose of the kinks is to entend the pieces to the surface. Why remove them, and how?
Tesseract750 wrote:
I think such design will failed, like a matchs in cupped hand attempt to push them through the imaginary layer
Ouch, that makes much sense. How can I make the long pieces remain vertical after a turn, such that they don't get criss-cross and block subsequent turns in another direction?

More ideas are very welcome! Thank you.

Oskar

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 Post subject: Re: Linear versus Binary style for super high NxNxN
PostPosted: Tue Sep 07, 2010 3:37 pm 
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Oskar wrote:
Namegoeswhere wrote:
extending the hidden centre extension in the V cube design
Nice idea. What problem does it solve?

Quote:
1) Friction
2) Popping
Problem 1) may be intrinsic to the binary style, as many pieces move through each other. Problem 2) would also occur in extensions of the linear-style Verdes design, as it has also small pieces around the center.

Those pieces now have a much larger scoop beneath which they are held in, simply put, it will pop less.

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