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 Post subject: Geary Master Pentultimate
PostPosted: Wed Nov 21, 2012 4:16 pm 
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As the title implies, this puzzle is basically a geared Master Pentultimate. On the outside, it looks no different than a normal Master Pentultimate.
Attachment:
1.JPG
1.JPG [ 1.59 MiB | Viewed 2781 times ]

Opposite sides turn in opposite directions.
Attachment:
2.JPG
2.JPG [ 1.83 MiB | Viewed 2781 times ]

The puzzle can scramble quickly. This is what it looks like after just three turns.
Attachment:
3.JPG
3.JPG [ 1.74 MiB | Viewed 2781 times ]

The puzzle measures 40mm to an edge. Because the puzzle has so many screws, it feels quite heavy, weighing about 250 grams. I'm amazed how smooth the turning is, considering the number of parts moving on a given turn.

I'd like to thank Timur for making his excellent guide on designing geared twisty puzzles, and also Oskar for giving me a bit of advice designing gears.

VIDEO

This puzzle is available for sale from my Shapeways shop in three parts for $315:

Part 1
Part 2
Part 3

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Wed Nov 21, 2012 4:23 pm 
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Fantastic! A geared master pent has been discussed a lot in the IRC channel I know there was another designer working on it too.

EDIT: It's hard to tell from your video what the gear ratio is. Per our IRC conversation the outer part is 2/5th of a turn for 1/5th of a slice turn.

I can't wait to play with this :D

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Wed Nov 21, 2012 4:41 pm 
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Nice work, Will.
As Brandon said, this has been a long discussed topic in IRC. It is nice to see this finally made, even if it is not by who we expected :lol:

-Doug

P.S. I am thrilled to have another geared puzzle designer!

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Wed Nov 21, 2012 5:02 pm 
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WOW!! That looks nice and it turns even better. Great Job!

Carl

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Wed Nov 21, 2012 5:28 pm 
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Great idea, superbly executed. How on earth did you cram the gear mechanism inside a Master Pentultimate?

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Wed Nov 21, 2012 5:32 pm 
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@Gus: You might get an answer earlier, but you might also get one in february.

Good job will !! :D

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Wed Nov 21, 2012 5:37 pm 
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Gus wrote:
How on earth did you cram the gear mechanism inside a Master Pentultimate?

The gears only add one shell to the mechanism. Also, the gears are pretty small. They measure less than 12mm in diameter.

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Wed Nov 21, 2012 11:39 pm 
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After carefully watching your video, I'd call this gearing 4:3. Because this is happening modulo 5 this is the same as -1:-2 (which is basically the same as 1:2). What I mean by this is that if you hold one face completely stationary in space and turn the opposite face, then you need to turn it 4/5th of a turn and when you do this you get a 3/5ths of a turn in the slice (same direction).

EDIT:
If I follow the 4:3 rule above then if you label two opposite faces U and D, then if you do U4 while holding D stationary and then D'4 holding U stationary, then U4 again, you'll end up with U turned 1/5th of a turn.

If this isn't correct then I'm seriously confused. If it is correct then this puzzle is equivalent to a Master Pentultimate.

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Thu Nov 22, 2012 12:26 am 
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bmenrigh wrote:
If you hold one face completely stationary in space and turn the opposite face, then you need to turn it 4/5th of a turn and when you do this you get a 3/5ths of a turn in the slice (same direction).

I'm assuming that by a whole "turn" you mean a 360 degree rotation of one face relative to the opposite, stationary face. If that's the case, then no, you do not get 3/5 of a turn on the slice, you get 2/5 of a turn, or rather -3/5 of a turn, if you prefer.

bmenrigh wrote:
If I follow the 4:3 rule above then if you label two opposite faces U and D, then if you do U4 while holding D stationary and then D'4 holding U stationary, then U4 again, you'll end up with U turned 1/5th of a turn.

No combination of only U and D turns will result in just the U face being rotated by 1/5 of a turn.

Anyways, I don't see why you insist on looking at this puzzle as having a stationary bottom layer and two layers above it that are geared. I think it makes much more sense to look at it as having a stationary middle layer with two opposite faces than rotate equal amounts in opposite directions for any given turn, especially since this is how it works mechanically.

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Thu Nov 22, 2012 2:25 am 
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This puzzle doesn't even allow for mixup moves!


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 Post subject: Re: Geary Master Pentultimate
PostPosted: Thu Nov 22, 2012 2:51 am 
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Great! It turns so smoothly!
Can you show us the geared layer?

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Thu Nov 22, 2012 2:55 am 
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will_57 wrote:
bmenrigh wrote:
If I follow the 4:3 rule above then if you label two opposite faces U and D, then if you do U4 while holding D stationary and then D'4 holding U stationary, then U4 again, you'll end up with U turned 1/5th of a turn.

No combination of only U and D turns will result in just the U face being rotated by 1/5 of a turn.

Anyways, I don't see why you insist on looking at this puzzle as having a stationary bottom layer and two layers above it that are geared. I think it makes much more sense to look at it as having a stationary middle layer with two opposite faces than rotate equal amounts in opposite directions for any given turn, especially since this is how it works mechanically.

Sorry for being a pain. There are a few reasons why I want to think of this as one face staying stationary and then the opposite face and slice moving. For one, that's how you actually hold it. For two, since I'm not holding the puzzle, my limited mental model works much better when I turn a face and slice without re-orienting the puzzle. Three, I want to simulate it on GB using only two moves and not worrying about the notation changing after a re-orientation.

I'm trying to reconcile your video with a normal Master Pentultimate. Before you do a turn:
Attachment:
geary_mp_start.png
geary_mp_start.png [ 192.38 KiB | Viewed 2465 times ]

After the turn:
Attachment:
geary_mp_end.png
geary_mp_end.png [ 215.53 KiB | Viewed 2465 times ]


Here it is on GB:
Attachment:
geary_mp_gb.png
geary_mp_gb.png [ 18.04 KiB | Viewed 2465 times ]


Let us call the yellow face Y and the slice yS. You can either view that effect as Y4 and yS3 or as Y' and yS'2. Since [Y', yS'2] is easier to enter that's what I'll use.

The white face is opposite the yellow so we'll call the white face W and the white slice wS (yes it's the same slice as yS, just the direction is defined relative to W instead of Y).

If you perform [Y' yS'2] then [W wS2] and then [Y' yS'2] then the net effect is a W' turn:
Attachment:
geary_mp_gb_simulate_turn.png
geary_mp_gb_simulate_turn.png [ 17.99 KiB | Viewed 2465 times ]

In Gelatinbrain's notation this is: [F', F'2&2, G, G2&2, F', F'2&2]

I wouldn't be surprised if my analysis is wrong but if it is I'd like to understand where it's failing if possible.

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Thu Nov 22, 2012 9:22 am 
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bmenrigh wrote:
After the turn:
Attachment:
geary_mp_end.png


Here it is on GB:
Attachment:
geary_mp_gb.png
You've probably studied the video harder then I but I believe if the bottom layer is held stationary then the slice layer will turn 1 degree in the same direction that the top layer turns 2 degrees. Your GB picture appears to have the slice layer turning 2 degrees in the same direction that the top layer has turned 1 degree. I don't think this is a valid picture . The first picture you have posted I believe was taken after one layer was turned 432 degrees relative to the opposite layer. So the slice layer should be rotated by 216 degrees or a negative 144 degrees. I think its just stickers appearing to be similar colors in that picture that is throwing you off. Maybe I need to watch the video a few more times myself.

Carl

P.S. Ok... just watched the video a few more times. And I'm pretty sure I'm correct. Look at the very first picture in the thread. Notice the orange and red faces are next to each other and in the photo they look very similar. I believe this is what is confusing you.

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Thu Nov 22, 2012 9:43 am 
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will_57 wrote:
No combination of only U and D turns will result in just the U face being rotated by 1/5 of a turn.
I agree. But my question would be... is there a combination of turns (not limiting yourself to just U and D turns) that would result in just the U face being rotated by 1/5 of a turn? I honestly don't have a clue. Counting the states might answer that question but I don't even know if anyone has yet counted the sates of a normal Master Pentultimate.

Doesn't it just seem like yesterday that even a well working Pentultimate (not even a Master one) was outside of reach? Now we have this with little gears inside and it turns like butter. Stuff like this really makes me wonder what crazy stuff we'll see in a few years that no one have even yet thought of.

Carl

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Thu Nov 22, 2012 11:28 am 
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bmenrigh wrote:
There are a few reasons why I want to think of this as one face staying stationary and then the opposite face and slice moving. For one, that's how you actually hold it.

I guess I hold it differently? When I turn it, I turn both sides with both hands and keep the middle layer more or less in the same place. I can see how it might make the puzzle easier in GB, though.

bmenrigh wrote:
I'm trying to reconcile your video with a normal Master Pentultimate. Before you do a turn:
Attachment:
geary_mp_start.png

After the turn:
Attachment:
geary_mp_end.png

Where you're mistaken is that after the turn, that is not a red sticker between the blue center and the pink corner. It's an orange sticker.

Timur wrote:
Can you show us the geared layer?

Sure:
Image
Image
I get the feeling that there might be some unnecessary layers in there, but having never designed a gear puzzle before, I wanted to be sure that it would be stable.

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Thu Nov 22, 2012 3:20 pm 
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Fantastic, Will. It turns so well!

-Eitan

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 Post subject: Re: Geary Master Pentultimate
PostPosted: Fri Nov 23, 2012 3:00 pm 
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Indeed, very impressive. The addition of the gears must have been a difficult process.

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