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 Post subject: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 8:40 am 
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Hi Twisty Puzzles fans,

Dumbbell Cube is a revisit of the failed Barbell Cube, posted earlier at the Twisty Puzzles Forum. I have designed new, strong center pieces, tightly connected to the gear train. I have also added a lot of silicone lubricant. The result is a puzzle that turns convincingly, as shown on this new YouTube video.

Dumbbell Cube is a challenge for intellectual weight lifters. This puzzle has two Rubik's Cubes that are connected through an intricate gear system. If you turn a face on one cube, a face at the other cube will follow. However, the connections between the two cubes have no symmetry. This makes solving this puzzle extremely difficult. Let's say Rubik's Cube squared. Unfortunately, the prototype has failed.

A lot of work has gone into the design of the gear train. The connecting rod has seven layers in total. The inner layer connects the two spherical cores. The outer layer connects the two opposite white faces of the two cubes. The other five layers have gears to connect specific faces. For logistical reasons, I dyed the five sets of gears red, orange, yellow, green and blue, matching with the colors of the faces. This way, I could keep track which gear drives which face.

The gears are so-called "double chevron gears", as invented by car maker Andre Citro├źn. This gear design has the advantage that the gears do not slip sideways and that they can handle a lot of force. They also generate less noise than regular spur gears because of their continuous meshing.
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The gear trains work really well. They never jam or touch adjacent gears.

One remaining problem is the slack of the gear train due to the flexibility of the nylon connecting rods. One solution would be to make the whole gear train out of (3D-printed) steel. However, there would be a lot of cost involved in this, so I am opening this project up for sponsors. Please contact me if you are willing and able to risk to $2000 for the potential to own the first working prototype of this design.

Watch theYouTube video.
Watch the internal mechanism.
Buy the puzzle from my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below, copied from the Barbell Cube post.

Enjoy!

Oskar
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Last edited by Oskar on Sun Jun 19, 2011 8:46 am, edited 1 time in total.

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 8:45 am 
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Very nice, its good that you got it working properly :D

Robert

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 10:13 am 
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Beautiful piece of design and engineering Oskar. And a monstrously difficult puzzle to solve.

I see that it costs over $590 on your Shapeways shop, so I guess Claus already has three :lol:

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 10:16 am 
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Nice puzzle :P ,great work.

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 10:17 am 
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"Chevron gears.... Like a rock"

It's great to see this puzzle turn so well! I hope you find a sponsor for the metal-geared version!

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 10:40 am 
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I really like this puzzle! I'm really glad you got it working! I find it interesting that sometimes the two faces turn in the same direction and sometimes they turn in opposite directions.

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 11:29 am 
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I have to verify the number of permutations.
I expet it to be even higher than RubiksCube squared.

Meanwhile: Well made.


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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 12:06 pm 
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Oskar wrote:
I have designed new, strong center pieces, tightly connected to the gear train. I have also added a lot of silicone lubricant. The result is a puzzle that turns convincingly

Can you comment of the design changes which made the center pieces stronger? Visually they look the same as they did before. And silicone lubricant is great stuff isn't it?

Glad to see this working. Great job.
Andreas Nortmann wrote:
I have to verify the number of permutations.
I expet it to be even higher than RubiksCube squared.

I've been wondering about the number of permutations as well. Assuming one cube can reach any of the normal states of a Rubik's cube while the other cube is solved then I would think the max possible number of permutations is the number of permutations of the Rubik's cube squared. However to me the question seems to be is the reachable states of one cube really independant of the other? If not wouldn't the number of permutations have to be less then the number of permutations of the Rubik's cube squared?

Carl

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 12:17 pm 
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Oskar wrote:
This puzzle has two Rubik's Cubes that are connected through an intricate gear system. If you turn a face on one cube, a face at the other cube will follow. However, the connections between the two cubes have no symmetry.

Hmmm... this gives me an idea. I've long wanted a working Multi5x5x5. Here is one of my shots at a design...

http://twistypuzzles.com/forum/viewtopic.php?f=1&t=19622

However this dumbbell idea may be a better approach.

Oskar,

How hard would it be to put the symmetry back in this design and have a 5x5x5 on one side of the dumbbell and a 3x3x3 on the other? Face turns on the 5x5x5 should have no effect on the 3x3x3 but if a layer below a face of the 5x5x5 is turned the corresponding face on the 3x3x3 turns with it. Really curious if you think something like that is doable?

Carl

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 1:01 pm 
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Wow, great to see that it turns so well! I think it would be really nice to have the 3x3x3 parts printed in a somewhat more transparent material, so that the gearing mechanism can be seen more clearly- those colors are beautiful, it's a shame to hide them underneath black-dyed parts. Too bad Shapeways' transparent material isn't exactly that clear, but it's better than nothing. :wink:

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 3:14 pm 
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Really good work Oskar. Glad to see this one is a success. Who wants to start a puzzle solving theory thread for this puzzle? :wink:

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 7:04 pm 
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wwwmwww wrote:
How hard would it be to put the symmetry back in this design and have a 5x5x5 on one side of the dumbbell and a 3x3x3 on the other? Face turns on the 5x5x5 should have no effect on the 3x3x3 but if a layer below a face of the 5x5x5 is turned the corresponding face on the 3x3x3 turns with it. Really curious if you think something like that is doable?
Cool idea. Would probably be easier to understand than your current representation of the multi-5x5x5 (even though I would like one of yours too).


How many possible dumbbell cubes are there? I'm thinking it can't be more than 4! once you remove symmetries. You could theoretically tie a bunch of these together right? Though I'm sure that would exaggerate the problems with the gear train just like with the Connected Cubes.

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Sun Jun 19, 2011 9:10 pm 
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Excelent Puzzle! Oscar super Genius :)

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Mon Jun 20, 2011 10:04 am 
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Andreas Nortmann wrote:
I have to verify the number of permutations.
GAP says: Size(Dumbbell) = Size(Rubiks cube)^2 /2
Don't ask me for an explanation


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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Mon Jun 20, 2011 10:35 am 
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Andreas Nortmann wrote:
Andreas Nortmann wrote:
I have to verify the number of permutations.
GAP says: Size(Dumbbell) = Size(Rubiks cube)^2 /2
Don't ask me for an explanation


So you used all six permutations? (each with 20+20 elements - excluding the centers).
That is some number!

:)


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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Mon Jun 20, 2011 11:10 am 
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Andreas Nortmann wrote:
GAP says: Size(Dumbbell) = Size(Rubiks cube)^2 /2
Don't ask me for an explanation

Actually I think that makes perfect sense. On a rubik's cube all the states can be divided into two groups. Those being the one reachable with an odd number of face quarter turns from the solved state and those reachable with an even number of face quarter turns from the solved state. Correct? Since one turn on one cube ALWAYS turns a face on the other cube then both cubes must always be either in the odd state or the even state. This means when one side is solved you can only reach half of the other states on the other cube, the even half. In other words, if one cube is solved and the other cube has a quarter face turn on one of its faces then its in an unreachable state and needs to be taken apart to be solved.

At least that is what I think is going on here,
Carl

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Mon Jun 20, 2011 1:59 pm 
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wwwmwww wrote:
Can you comment of the design changes which made the center pieces stronger?
Previously, a gear had a square hole connecting it to the stem under its center piece. However, the forces are so high that the square hole breaks open and moves can be forced. Now, the gears are printed with the stem, and the center is placed on top of the stem, see sketch below. Much stronger ...

Oskar
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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Mon Jun 20, 2011 2:04 pm 
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I was wondering whether this idea could be expanded on further using gears. By this I mean using a gear mechanism to control the whole turn. For example, performing an L on one cube could do a U2 on the other one. I think that would make the puzzle all the more challenging.

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Tue Jun 21, 2011 10:30 pm 
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This reminds me of a puzzle idea I had a while ago. There are several things resembling puck puzzles next to each other, the one all the way on the left having 12 pieces. When you rotate the one all the way on the left clockwise one unit, the one next to it rotates two units, the one after that three, etc. When you do a slice move the right half of all the pucks flips on a vertical line. Solving this one would be an interesting experience, but I don't know of an elegant mechanism.


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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Tue Jun 21, 2011 11:50 pm 
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Luke wrote:
I was wondering whether this idea could be expanded on further using gears. By this I mean using a gear mechanism to control the whole turn. For example, performing an L on one cube could do a U2 on the other one. I think that would make the puzzle all the more challenging.


Yes, I can actually answer this one (though I don't know how well it would fit given 3d printing parameters). If one were to build one face at a 2:1 ratio, which *should* be simple enough to accomplish, then for each turn of one face on one cube, a specific face on the second would turn twice.

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Wed Jun 22, 2011 7:53 am 
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Luke wrote:
I was wondering whether this idea could be expanded on further using gears. By this I mean using a gear mechanism to control the whole turn. For example, performing an L on one cube could do a U2 on the other one. I think that would make the puzzle all the more challenging.

Interesting... two things to note but lets look at a simplier picture first.

Lets say a U turn on the left cube does a U2 turn on the right cube.
Lets also say a D turn on the left cube does a R turn on the right cube.

(1) This puzzle jumbles. We can do a U turn on the right cube at which time the U face on the left cube is only turned by 45 degrees. At this time we can then do a R turn on the right cube before doing another U turn on the right cube to complete the U turn on the left cube. You've turned the puzzle between doctrinaire states so this is considered jumbling.

(2) You've also broken the requirement that both cubes must be in either an odd or even state so I suspect this puzzle would indeed have the number of permutations of the Rubiks cube squared.

Carl

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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Wed Jun 22, 2011 8:08 am 
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Looks like an interesting puzzle to solve. The best strategy I can think of is to perform some non-trivial identity on one cube, and observe what happens to the other, and try and find some which are useful.

wwwmwww wrote:
(1) This puzzle jumbles. We can do a U turn on the right cube at which time the U face on the left cube is only turned by 45 degrees. At this time we can then do a R turn on the right cube before doing another U turn on the right cube to complete the U turn on the left cube. You've turned the puzzle between doctrinaire states so this is considered jumbling.
l


Not necessarily. An alternative scenario is that they are both regular 3x3x3s, so performing a U turn on the right cube will stop some twists on the left cube being possible (since the U layer is misaligned), probably with the result that you will need to do another U twist on the right cube in order to make further twists. The jumbling idea certainly sounds fun though :D.


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 Post subject: Re: Dumbbell Cube by OSKAR
PostPosted: Wed Jun 22, 2011 9:14 am 
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bobthegiraffemonkey wrote:
Not necessarily.

Agreed... not saying all dumbbell cubes jumble. Just those with mappings similiar to this...
wwwmwww wrote:
Lets say a U turn on the left cube does a U2 turn on the right cube.
Lets also say a D turn on the left cube does a R turn on the right cube.

Carl

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