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 Post subject: Pentultimate mechanism ideas using Jaap's Sphere appletPosted: Thu Oct 21, 2004 10:17 am

Joined: Mon Oct 18, 2004 11:06 pm
Location: Portland, ME
Go to the following URL:

http://www.geocities.com/jaapsch/puzzles/sphere.htm

This applet is great because it lets us visualize the geometries involved in the mechanism components.

Set all four shapes to dodecahedron, then try these settings:

RED: 0
GREEN: 140
BLUE: 133
YELLOW: 119

This mechanism concept uses a central sphere with grooved tracks (similar to the original 4x4x4, but with differences).

In this scenario, the red lines show the outer pieces (i.e. pentagon and triangle pieces). The green and blue lines show the outer edges of the grooved "track" that the pieces would move in. The yellow shows the position of the recessed "lip" under the edges of the track.

Each pentagonal face would have a "foot" in its center that moves along the track. The foot would have a rounded flange that fits under the lip (yellow lines). The triangle faces would be held in place by the pentagons via some type of tongue and groove arrangement.

To prevent misalignment of the central sphere, one of the 12 pentagons would be fixed to the sphere. Any rotation that included that piece would rotate the sphere with it along the direction of the move. Rotating the other half would leave the sphere in place. If it were machined well enough, you would not be able to tell which of the 12 pieces was fixed.

The big problem I see is that when the puzzle is at rest, the pentagons' feet would have a tendency to fall right out of the intersection of the 5 tracks. I'm hoping that would be offset by the collective tension of the triangles tongue-and-groove mechanism, plus the fixed piece.

Chris

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 Post subject: Posted: Thu Oct 21, 2004 1:05 pm

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Chris, you can click on the bottom of that applet to get a url to cut and paste which includes the current applet position. For example, people can get the slice depths you described just by clicking on this link.

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 Post subject: Re: Pentultimate mechanism ideas using Jaap's Sphere appletPosted: Thu Oct 21, 2004 2:14 pm

Joined: Thu Jan 24, 2002 1:10 am
pelley wrote:
The big problem I see is that when the puzzle is at rest, the pentagons' feet would have a tendency to fall right out of the intersection of the 5 tracks. I'm hoping that would be offset by the collective tension of the triangles tongue-and-groove mechanism, plus the fixed piece.

Maybe I'm missing something from another thread, but isn't the real problem the mech inside? I don't see how the six slices would work at all.

Your plan certainly seems like it would work to keep the pentagons attached. I can't see any reason why the "foot" would only extend one direction under a lip (maybe you just ran out of lines on Jaap's app). The foot could be more mush-room shaped, and you could certainly make it reach deeper than the opening that would occur at the vertex of five grooves. In any case, that might not matter once all the pieces are in place and are pushing up against each other for stability.

Consider the centers on the 4x4x4 as a perfect example. A single center cubie can wiggle out of the opening as long as the other three are not in the way. When all four are in place, there is no way one can wiggle out.

Sandy

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 Post subject: Re: Pentultimate mechanism ideas using Jaap's Sphere appletPosted: Thu Oct 21, 2004 4:41 pm

Joined: Mon Oct 18, 2004 11:06 pm
Location: Portland, ME
Sandy wrote:
Maybe I'm missing something from another thread, but isn't the real problem the mech inside? I don't see how the six slices would work at all.

In this version, the central sphere is fixed (similar to the old Rubik's Revenge mech.) The external pieces are "plates" that slide around in tracks on the sphere. Every twist moves exactly half the plates. The one plate that is fixed to the sphere must be able to rotate in place, but it cannot travel on the tracks.

Sandy wrote:
Your plan certainly seems like it would work to keep the pentagons attached. I can't see any reason why the "foot" would only extend one direction under a lip (maybe you just ran out of lines on Jaap's app). The foot could be more mush-room shaped, and you could certainly make it reach deeper than the opening that would occur at the vertex of five grooves.

Yes, I'm visualizing large feet (think Impossi-Ball mech.) I did run out of lines. The yellow lines show the lip under the triangular sections of the sphere. The narrow petal-shaped sections would have the same lip, which isn't shown in the Sphere applet as configured.

Sandy wrote:
Consider the centers on the 4x4x4 as a perfect example. A single center cubie can wiggle out of the opening as long as the other three are not in the way. When all four are in place, there is no way one can wiggle out.

But it gets more complicated with 5 intersecting tracks. The 4x4x4 only has two intersecting tracks. The depth of the lip and the size of the "mushroom" would need to be tuned for smooth operation.

Chris

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 Post subject: Re: Pentultimate mechanism ideas using Jaap's Sphere appletPosted: Thu Oct 21, 2004 4:43 pm

Joined: Mon Oct 18, 2004 11:06 pm
Location: Portland, ME
pelley wrote:
The one plate that is fixed to the sphere must be able to rotate in place, but it cannot travel on the tracks.

Scratch that! It must be fixed, and cannot rotate. Its job is to hold the sphere in place so the external plates can never misalign with the internal sphere once a twist is completed.

Chris

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 Post subject: Posted: Fri Oct 22, 2004 9:20 am

Joined: Thu Jan 24, 2002 1:10 am
Ah, I get you now. I can't think of anything else wrong with it, other than the concern over the size of the mushrooms and the ability to smoothly twist it.

Maybe you can slap one together this weekend!!!

Sandy

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 Post subject: Posted: Fri Oct 22, 2004 9:57 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Chris, I've looked over your design now, and there are a number of problems. For starters, there's nothing holding down the triangles. In addition, the depth you've put the blue and green cuts at (I'm not sure why you've got two, but this problem applies to both) there's no room whatsoever for the connector between a pentagonal piece and its foot.

As a general approach, umbrellas on a pentultimate wind up being very fragile.

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 Post subject: Posted: Fri Oct 22, 2004 10:35 am

Joined: Mon Oct 18, 2004 11:06 pm
Location: Portland, ME
Bram wrote:
For starters, there's nothing holding down the triangles.

For the triangles, I envision them being held in by the pentagons. This would occur closer to the surface of the puzzle, with a tongue and groove arrangement. (Tongue on the triangle, grooves around the pentagons).

Bram wrote:
In addition, the depth you've put the blue and green cuts at (I'm not sure why you've got two, but this problem applies to both) there's no room whatsoever for the connector between a pentagonal piece and its foot.

I used blue and green to depict the left and right sides of the track. The narrow space between the blue and green lines represents the width at the surface of the track. Deeper into the sphere, the track would widen to hold the base of the pentagon's foot, which would also be wider at that depth. The yellow line depicts a possible depth on the "blue" side of the track. I ran out of lines to depict the lip under the "green" side, but it would be correspondingly the same.

Bram wrote:
As a general approach, umbrellas on a pentultimate wind up being very fragile.

Yeah, this is what I am afraid of. I guess the trick is to vary the thichness of the various parts (foot depth, foot width, track width, lip width, lip depth, etc.) until you find a satisfactory strength and smoothness balance.

Chris

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 Post subject: Posted: Fri Oct 22, 2004 6:51 pm

Joined: Sat Sep 18, 2004 1:24 pm
pelley wrote:
For the triangles, I envision them being held in by the pentagons. This would occur closer to the surface of the puzzle, with a tongue and groove arrangement. (Tongue on the triangle, grooves around the pentagons).

But wouldn't the tongues get locked up on each other? Because, during a partial turn, it is possible to have two triangles next to each other. Am I correct in this?

_________________
aka: insanity_cubed

I've gone off the idea of progress. It's overrated. - Arthur Dent

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 Post subject: Posted: Sat Oct 23, 2004 5:28 am

Joined: Thu Oct 07, 2004 8:47 am
pelley: You know you can use four lines for every color? Maybe that might create a better visual appearance.

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 Post subject: Posted: Mon Oct 25, 2004 8:31 am

Joined: Mon Oct 18, 2004 11:06 pm
Location: Portland, ME
Okay, here's another revision:

http://www.geocities.com/jaapsch/puzzle ... le=38,95,5

In this one, the blue represent the track for the pentagons (with yellow showing the lip under the track). The green represents a parallel track for the triangle pieces. This avoids the problem of the tongues blocking each other, but I wonder if the puzzle could hold together with so many overlapping tracks?

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 Post subject: Posted: Mon Oct 25, 2004 8:38 am

Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
pelley wrote:
The green represents a parallel track for the triangle pieces. This avoids the problem of the tongues blocking each other, but I wonder if the puzzle could hold together with so many overlapping tracks?

It may be worse than you think since you forgot some tracks - the large circle for the triangles right next to the cutting plane about which you are twisting the pentultimate.

_________________
Jaap

Jaap's Puzzle Page:
http://www.jaapsch.net/puzzles/

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 Post subject: Posted: Mon Oct 25, 2004 11:58 am

Joined: Thu Jan 24, 2002 1:10 am
jaap wrote:
It may be worse than you think since you forgot some tracks - the large circle for the triangles right next to the cutting plane about which you are twisting the pentultimate.

That's a lot of tracks:

http://www.geocities.com/jaapsch/puzzle ... le=37,94,4

Maybe we shouldn't give up so quick on finding a way to get the triangles to hold onto the pentagons!

Sandy

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 Post subject: Posted: Mon Oct 25, 2004 12:30 pm

Joined: Thu Jan 24, 2002 1:10 am
Here's an idea that might keep the triangles in.

The black lines make up the outline of a triangle piece. The red line is a groove that runs around all triangles and all pentagons. The blue lines are "springy" tongues (plastic, wires, or whatever works) held in place so they can't move from side to side. As the puzzle is turned, they reach into the neighboring piece tracks to hold the triangles in place. When a tongue encounters a tongue from another triangle, one or both of the tongues retracts to let the other piece past. Having two or three of these tongues per triangle edge would ensure the triangle pieces are holding very strongly onto the neighboring pentagons when the tongue/groove system on the third side is compromized during a twist.

As an added bonus, having these included in the puzzle would mean you could easily implement a nice little "locked in" feel whenever the cuts are all lined up again after a twist.

Sandy

 Attachments: Pentultimate Triangles.gif [ 7.37 KiB | Viewed 2104 times ]
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