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 Post subject: Hex Barrel Mechanism Design HelpPosted: Sun Apr 13, 2014 1:55 pm

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Hey Everyone,

I've been trying to come up with a way to implement this puzzle concept for some time now, but have been unable to figure out a reasonable way to do it short of magnets, or an incredibly complicated shells mechanism that would probably result in internal jumbling. The idea is a hexagonal prism (barrel shaped) with three vertical slice planes through the origin, resulting in a simple pattern of six triangles on the top and bottom hexagonal faces of the puzzle. These slice planes define the only axes available for turning.

The vertical (rectangular) faces of the puzzle would have stored cuts on them. Each face has a center triangle surrounded above and below by a half triangle, and a rectangle above and below that. These stored cuts only become available for use after a 90 degree turn.

The basic concept is probably familiar by now if you know my "fracture-cut" series of puzzles. When starting, only 180 degree turns are possible. However, when two of the vertical faces separated by 120 degrees have their triangular centers pointing away from each other, the axis in between them can be turned in 90 degree increments. This puzzle is to Fracture-12 what RotoPrism 2 (prismatic) is to Fracture-6.

Since I'm sure my description on it's own is inadequate, I've made some images of the solved puzzle, and of four possible turns. First is the solved puzzle. The bottom color (not visible here) is light blue. The colors around the edges follow the rainbow (red, orange, yellow, green, dark blue, purple).
Attachment:

hex barrel solved.jpg [ 27 KiB | Viewed 1236 times ]
The first 180 degree turn is made:
Attachment:

hex barrel one turn.jpg [ 27.75 KiB | Viewed 1236 times ]
Then a 90 degree turn can be made:
Attachment:

hex barrel two turns.jpg [ 16.76 KiB | Viewed 1236 times ]
Followed by another 180 degree turn:
Attachment:

hex barrel three turns.jpg [ 16.27 KiB | Viewed 1236 times ]
And then another 90 degree turn:
Attachment:

hex barrel four turns.jpg [ 16.62 KiB | Viewed 1236 times ]

Hopefully that's enough information to properly explain the concept, but please let me know if you have any questions. I'd love to see this concept implemented, and I'm looking forward to seeing any ideas you can come up with!

Many thanks,
Dave

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 Post subject: Re: Hex Barrel Mechanism Design HelpPosted: Sun Apr 13, 2014 2:26 pm

Joined: Fri Dec 28, 2012 1:50 pm
Location: Near Las Vegas, NV
I don't have SW running for me right now but I can suggest some things.
Have you tried to use only 3 axes for the inner mechanism rather than 6? I know a face-turning hexagonal prism has a self-dual geometry that could allow this, but I don't know if it works with stored cuts...

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 Post subject: Re: Hex Barrel Mechanism Design HelpPosted: Mon Apr 14, 2014 1:08 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
Awesome, a fracture-cheese! I've wondered for a long time if some sort of "unbandaged cheese" could be done, but it never occurred to me that the 90-degree fracture style would work. (Is a 60-degree version possible?)

If it's not too much trouble, could you make up some renders of a cylindrical version?

You might talk to Jason about adapting his rails mechanism that he's used for so many awesome things.

I wonder if it's possible to solve the puzzle into alternate configurations where the triangles are pointing in different patterns (for example, alternating left-right-left-right).

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 Post subject: Re: Hex Barrel Mechanism Design HelpPosted: Mon Apr 14, 2014 8:25 am

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
benpuzzles wrote:
Have you tried to use only 3 axes for the inner mechanism rather than 6?
I've looked at using only three axes, but what it does is fix three of the triangular face centers to the core. This prevents those faces from changing position relative to each other, and limits the possible movements of the puzzle.
Jared wrote:
(Is a 60-degree version possible?)
Interesting idea! I'll have to play with the geometry a little to see what happens.
Jared wrote:
If it's not too much trouble, could you make up some renders of a cylindrical version?
Already done. I've also looked at an alternative stickering scheme to make sure that the right colors go next to each other, and an edge turning version to accomplish the same thing. I decided to stick with the version presented first since I like the simplicity of the sticker pattern, and I'd be curious as to whether the colors can change places.
Jared wrote:
I wonder if it's possible to solve the puzzle into alternate configurations where the triangles are pointing in different patterns (for example, alternating left-right-left-right).
This is another interesting idea along with the possibility of color swapping.

Here are some images of the alternative models:
Attachment:

hex barrel round model.jpg [ 25.76 KiB | Viewed 1064 times ]
Attachment:

hex barrel alternate stickering.jpg [ 28.59 KiB | Viewed 1064 times ]
Attachment:

hex barrel edge turning.jpg [ 29.06 KiB | Viewed 1064 times ]
Jared wrote:
You might talk to Jason about adapting his rails mechanism that he's used for so many awesome things.
Jason and I have looked at this already, and we weren't able to find a way to use the skirting rails. Jason also did an analysis showing the potential for a shells mechanism using 6 shell layers and somewhere around 700 parts, but we didn't pursue the model further due to the high complexity, cost, and probable internal jumbling.

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 Post subject: Re: Hex Barrel Mechanism Design HelpPosted: Mon Apr 14, 2014 10:25 pm

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
David Pitcher wrote:
Interesting idea! I'll have to play with the geometry a little to see what happens.

Well, maybe start with a 60-degree Fracture-12 first.

Actually, on that note, can Fracture-12 be altered to allow 30-degree turns with split edge pieces, similar to Spiral Fracture?

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 Post subject: Re: Hex Barrel Mechanism Design HelpPosted: Tue Apr 15, 2014 12:43 pm

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Jared wrote:
Well, maybe start with a 60-degree Fracture-12 first.
With a dipyramid base geometry, you're really limited to the four-way symmetry of the equatorial vertices. In order to allow 60 degree turns, you need to go to a different base geometry, and you end up with either the Fractured Tetrahedron, or the Fractured Cube. If you want 72 degree turns, then QuadStar is the puzzle.

Jared wrote:
Actually, on that note, can Fracture-12 be altered to allow 30-degree turns with split edge pieces, similar to Spiral Fracture?
Yes, you can use curved cuts to allow 45 degree moves, in a similar manner to Spiral Fracture. However, the curves end up going the other way, bulging towards the center of the puzzle. This means that there are actually less "filler" pieces needed in between parts. Note how Spiral fracture has three of the spacers on each face, and a Spiral Fracture-12 would only have two. Here's a picture showing a model I made a while back:
Attachment:

spiral fracture-12.jpg [ 72.46 KiB | Viewed 947 times ]
I wasn't planning to make this puzzle, but if anyone is interested I could be persuaded.

Back on topic though, any thoughts on how the hex barrel puzzle could be made? I'm really curious to see if anyone on the forum can find a way to make the hex barrel a reality.

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 Post subject: Re: Hex Barrel Mechanism Design HelpPosted: Sat Apr 19, 2014 6:23 pm

Joined: Sat Apr 21, 2007 11:21 pm
Location: Marin, CA
If anyone would like to play with this on Jaap's sphere, there's a modified version here with this puzzle included:

http://www.puzzleforge.com/sphere/spher ... gle=0,90,0

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 Post subject: Re: Hex Barrel Mechanism Design HelpPosted: Sat Apr 19, 2014 7:45 pm

Joined: Fri Dec 28, 2012 1:50 pm
Location: Near Las Vegas, NV
I'd like to throw a couple of ideas out there, even though they may not work.
Have you tried every possible shell mech? I just had an idea (although it might not be very stable) and that is to have a very inner Rubik's cheese shell, and then from that build shells with continually deeper and deeper stored cuts on top, until you reach the puzzle. That way there aren't as many cuts that will be changing depths at one time and that might simplify things. Although the more I think about it, the less stable it would be...
EDIT: I just realized something. Correct me if I'm wrong but it looks like the stored cuts have the same geometry as my Gemstone I. Would it be possible to overlay the mechanism of that puzzle on top of a cheese as well? It could be a potential solution too.
EDIT 2: Sorry but I just realized that the stored cuts and the cheese part of the puzzle have separate self-dual geometries. Could you try using only 3 axes rather than 6 for the stored cuts only and then try a shell buildup? If so would that enable those other movements that would normally be blocked if both geometries were made self-dual?
Just some ideas to experiment with...

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 Post subject: Re: Hex Barrel Mechanism Design HelpPosted: Sun Apr 27, 2014 10:20 pm

Joined: Sat Apr 21, 2007 11:21 pm
Location: Marin, CA
I'm going to place some of the notes here that were generated during my investigation of this puzzle with David.

Shells Mech:

Use this modified Jaap Sphere to evaluate this discussion.

*snip*
You can drag the top slider to see different depths of shells for this puzzle. If you drag it to 0 (all the way left) you see the deep cut version. As you drag the slider you can see parts created and destroyed. I think these shells would be needed:

184
161
131
112
96
35-this layer can be bandaged

Because of the complex jumbling, I don't think it would be good to bandage on one of the inner layers instead of the outside.

Seeing the complexity here, I think again that this might be about on par with the Radio Chop, which would make it a pretty expensive print. Around \$700-\$1300 I think. I don't think I have the appetite for that cost, so I'm shying away from completing a design.

*snip*

I think other shells approaches (like a cheese core) also hit similar complexity, and due to the severe jumbling, they may even unintentionally bandage the puzzle later after jumbling.

Skirting Rails

Skirting rails was investigated, but couldn't be used because of the complex jumbling.

3 axis version

Before giving up entirely, I examined the relationship between this puzzle and fracture 6, and found they are equivalent when unbandaged:

Of course the bandaging to get a Hex Barrel is where we deviate from the Fracture 6. Here's Hex Barrel bandaging:

If we view from above, we can see the six vertical axes around the sides of the Hex Barrel:

If we take the duality of the axes into account, we can consider each point rotatable, by 90 or 100 degrees. Looking at it this way it starts to appear a lot simpler, because it doesn't even shape shift, and each point can be fixed to a core.

So think of these three black tips (black only to point them out for you) as fixed to the core:

Let's look at some turns and get more and more excited that fixed tips can work:

This is all fine as long as the off axis slices are never usable without first lining up with the vertical slices. Here's what I mean by off axis slices:

If those slices are stored only, and only come into play when aligned vertically, then we're fine. If not, then we can break our three black tips off the core.

You see where this is going. After more investigation, back on hex barrel geometry, I was able to break the three black tips (shown here as black triangles) using a valid off axis slice:

So the real Hex Barrel can't be made with the three axis simplification.

However, there could be a version made that does not shapeshift in fracture 6 shape, and only allows vertical slices, treating the off axis slices as stored cuts. David and I discussed this, and he may pursue it. But it's not THE Hex Barrel.

I'm now pretty convinced designing this would be about on par with designing a working, jumbling Big Chop.

Good luck to anyone who wants to pick this up!

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Jason Smith posted here as 'io' through 2012.
Visit Jason Smith's PuzzleForge on Shapeways!
Jason Smith's Puzzles - YouTube Channel.

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