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 Post subject: Helical Hysteresis MazePosted: Fri Jun 21, 2013 4:47 pm

Joined: Sun Mar 11, 2007 3:11 am
Location: Oregon, USA
This is a spin-off of Carl's discussion of alternative-shapes of hysteresis mazes from the Eight Inch Bolt thread. Here's a recap of the original discussion, edited solely to preserve the image link and remove duplication where any quote contained a quote of another quote.

Carl's first comment:
wwwmwww wrote:
I personally really like puzzles that make use of hysteresis. I typically think of them as multi-state mazes which this is... just wrapped around a cylinder.

I'm curious... could this be made to look much more like an actual nut and bolt.

The nut could be threaded and the maze cut deeper then the threads. And instead of just sliding the nut up and down you actually turned the bolt to get it to go up and down on the threads. The ring which enganged the maze would still be free to turn on its own inside the bolt. If this would work I think it would take the dexterity element out of the solution as the solution could be written in the form of turn x-degree clockwise, then y-degrees counter clockwise, then z-degrees clockwise, etc. I think it would make a much more "family friendly" puzzle and you could even used it as a locking nut and bolt if you wanted to. Only thing I'm not sure about is if there would be enough of the threads left after the maze was added for the nut to actually function as a nut.

Carl

Here's my first comment on the side topic
VeryWetPaint wrote:
It's getting off the topic, but it's interesting because I've separately mused with the idea of 1) a threaded-bolt puzzle with some sort of state mechanism inside the nut, and 2) a helical hysteresis maze themed like a lipstick. But those were separate ideas, I didn't think of combining them into a single puzzle.

But I would prescribe inverting your idea: put the continuous thread at the bottom and put the maze onto the peaks of the threads. Here's a proof-of-concept model that demonstrates that information can be encoded (or rather modulated) into the peaks of threads without disturbing the underlying thread structure. In this instance the 'information' is simply a guide to make the nut go the wrong way, a bit like Jerry Slocum's Its' Nuts exchange puzzle but using a totally different premise.

If you think it's worth exploring these ideas I'll take it to a new thread.

And Carl's reaction, for which this thread was spawned:
wwwmwww wrote:
Yes, please do. I actually have an Its' Nuts puzzle. However I don't see how the maze could be encoded into the top of the threads in this case. Wouldn't the ring which engages the maze be free to turn on its own when ever the point where it contacted the maze was between threads?

Carl

I'm working on some diagrams to clarify the discussion, but for the sake of clarity and help organize this thread I will post my followup in a separate comment. (That means I might double-post if there are no other comments in the meantime, but I think that will be better than lumping it all into the thread's Opening Post.)

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 Post subject: Re: Helical Hysteresis MazePosted: Fri Jun 21, 2013 5:40 pm

Joined: Sun Mar 11, 2007 3:11 am
Location: Oregon, USA
wwwmwww wrote:
I actually have an Its' Nuts puzzle. However I don't see how the maze could be encoded into the top of the threads in this case. Wouldn't the ring which engages the maze be free to turn on its own when ever the point where it contacted the maze was between threads?

Sorry, I inadvertently misled you.

I didn't mean to suggest Its' Nuts was, itself, relevant. I meant to suggest that the maze could be modulated into the peaks and the guides into the valleys of the threads. That's not much like Its' Nuts.

The Mk3 bolt uses this modulated peaks-and-valleys scheme to arbitrarily imitate the way Its' Nuts behaves. That is to say, on the Mk3 the visible threads turn in one direction while the peaks contain a so-called modulated signal to turn in the other direction. The nut could be tuned to follow the visible threads, in which case it would turn normally. Or the nut could be tuned to lock onto the "signal" modulated into the peaks of the threads, in which case the nut would be forced to always go the other way because it's following the encoded signal to go that way--as shown in the video.

The Mk3 model in the video was just a proof-of-concept, to verify that this modulated peaks-and-valleys scheme could actually work in a mechanical toy. It definitely worked!

But it was designed for a different purpose, so it wouldn't be useful for your suggestion as it is. It would entail some adaptations, but it should be straightforward. Simpler than you might expect. I'll try to develop a schematic example, and post it as I go.

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 Post subject: Re: Helical Hysteresis MazePosted: Sat Jun 22, 2013 2:12 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
I guess I'm not sure what is different between the Mk3 Bolt and Its' Nuts. Both appear to do the same thing. If they are pulling off the same stunt with different methods I don't understand the method employed in the Mk3 Bolt.

Carl

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 Post subject: Re: Helical Hysteresis MazePosted: Sun Jun 23, 2013 2:18 pm

Joined: Sun Mar 11, 2007 3:11 am
Location: Oregon, USA
wwwmwww wrote:
I guess I'm not sure what is different between the Mk3 Bolt and Its' Nuts. Both appear to do the same thing. If they are pulling off the same stunt with different methods I don't understand the method employed in the Mk3 Bolt.

Carl

Okay, I'll explain how the modulated-peaks scheme works and how it was applied to build the Mk3.

I started with a simple thread profile (green) that has an unconventional shape so the 'peaks' have parallel walls at their tops (blue). A nut (yellow) reaches all the way down to the bottom of these deep grooves--this nut will follow the threads like an ordinary nut on an ordinary bolt.
Attachment:
File comment: Unmodulated thread profile, showing bolt (green) and conventional-behaving nut (yellow), and parallel walls (blue).

unmodulated thread profile.png [ 15.32 KiB | Viewed 1151 times ]

Despite its unconventional thread profile, the threads look pretty standard because the eye is drawn to the details at the bottom of the groove. (This is already very different from Its' Nuts where the normal-acting nut doesn't go deep into the bolt's threads, it rides the peaks of the threads, and it actually has twice as many grooves as the bolt.)
Attachment:
File comment: 3D Rendering of unmodulated threads

unmodulated thread render.png [ 113.57 KiB | Viewed 1151 times ]

Because of the thread walls are parallel at their peaks, the top section (blue) can be varied in height without causing the threads to vary in width. The original conventional-acting nut (yellow) is totally unaffected by the height variations modulated onto the peaks because the nut rides on the base threads--it hardly even touches those peaks.
Attachment:
File comment: Thread profile where peaks vary in height (blue zone) without affecting nut (yellow) which still follows baseline threads.

Modulted thread profile.png [ 14.6 KiB | Viewed 1151 times ]

Even after modulating an arbitrary pattern into the peaks, the bolt's threads still look conventional. It's feasible to encode an arbitrary information into the peaks--it could be a maze or some sort of guides. Sure you can detect there's something slightly odd in this 3D rendering, it's not obvious that there's an entire second channel of information encoded into it. At most, the threads just look a bit uneven at the edges.
Attachment:
File comment: A second "channel" of information is modulated into the peaks, but it's mostly hidden by the baseline threads.

Modulted thread render.png [ 155.72 KiB | Viewed 1151 times ]

To confirm whether this modulation scheme would actually work, I developed the Mk3 with an arbitrary goal of imitating the behavior of Its' Nuts while trying to remedy several unfortunate limitations of Its' Nuts:
1. The trick thread on Its' Nuts created fine details that are too easy to see under examination. To disguise those details I built Its' Nuts in transparent material, applied a shiny reflective finish, and gave it a sinusoidal thread shape to ensure there would always be reflections and glare. This hugely restricted my material choices.
2. The trick thread on Its' Nuts is really delicate because I was trying to keep the details tiny to help hide them. Consquently the trick thread isn't very robust, it can be stripped with moderate force, and it's sensitive to small imperfections.
3. The trick thread on Its' Nuts can be cross-threaded too easily, causing the trick nut to go onto the bolt crookedly and potentially harming the threads. The trick nut has three parallel threads, but that unavoidably interacts with the conventional thread to create six starting points at the end of the bolt so the nut has plenty of opportunities to catch a bad combination of starting points.

For the Mk3 I modulated this simple, low-frequency reverse-helix onto the peaks of the threads.
Attachment:
File comment: For the Mk3 trick bolt, I modulated this backward helix onto the threads.

overlay thread render.png [ 101.38 KiB | Viewed 1151 times ]

The resulting Mk3 bolt resolved all three of the aforementioned objections:
1. The encoded information is low-detail, so it's naturally hidden among the highly-detailed baseline thread--so the Mk3 didn't need any special material properties. As an acid test I built one in cast-brass, a material whose surface tends to reveal fine details, but the trickery was still well-disguised.
2. The details of Mk3's trick thread are relatively coarse, so they're much more robust than the fine details of Its' Nuts. Thanks to the relaxed material restrictions above, I could choose stronger materials too.
3. The trick thread on Mk3 is completely immune to cross-threading thanks to the aforementioned coarser details and availability of rigid materials.

Attachment:
File comment: You can just barely detect the trickery in the Mk3 threads if you know what you're looking for, and hold it just right under the right lighting conditions.

IMG_7061.JPG [ 151.94 KiB | Viewed 1151 times ]

Attachment:
File comment: But under ambient light and a different angle, the modulated-peaks scheme is visually undetectable.

IMG_7056.JPG [ 191.51 KiB | Viewed 1151 times ]

(EDIT: If you want to see how Its' Nuts was implemented for comparison, an early version of it can be downloaded from Thingiverse here. The trickery is obvious even in the default renderings.)

So even though the Mk3 bolt was designed to behave much like Its' Nuts, it is a totally different beast. Does this make sense?

But the goal of the Mk3 was disguise. The goals would be different if this modulated-peaks scheme is adapted to a helical hysteresis maze. I've got a concept model in mind, so I will explain the adaptations in a followup post.

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 Post subject: Re: Helical Hysteresis MazePosted: Sun Jun 23, 2013 5:08 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
VeryWetPaint wrote:
The goals would be different if this modulated-peaks scheme is adapted to a helical hysteresis maze. I've got a concept model in mind, so I will explain the adaptations in a followup post.
Very interesting and informative... thanks for posting all that. I think I'm starting to see how you can encode a maze in there. If I'm correct I think you may just need a one part nut... Correct? By that I mean there wouldn't be a second ring which was free to turn inside the nut. I'm really curious to see more.

Thanks,
Carl

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 Post subject: Re: Helical Hysteresis MazePosted: Mon Jun 24, 2013 12:54 am

Joined: Thu Dec 21, 2006 5:32 pm
Location: Bay Area, CA
Great explanation Scott, I had been reading this thread and understood some of the idea but your post really clarifies it.

Dave

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 Post subject: Re: Helical Hysteresis MazePosted: Mon Jun 24, 2013 10:12 am

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
I tried showing the video to a few people and they thought you just had the threads going opposite the normal way. Apparently, most people can't read threads to figure out how to turn a screw so it's not that impressive.

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 Post subject: Re: Helical Hysteresis MazePosted: Tue Jun 25, 2013 9:48 pm

Joined: Sun Mar 11, 2007 3:11 am
Location: Oregon, USA
wwwmwww wrote:
Very interesting and informative... thanks for posting all that. I think I'm starting to see how you can encode a maze in there. If I'm correct I think you may just need a one part nut... Correct? By that I mean there wouldn't be a second ring which was free to turn inside the nut. I'm really curious to see more.

I envisioned a two-piece design, with the pin mounted on a ring concealed inside a larger collar (which could be "nut" shaped for thematic reasons).

For the purpose of demonstration, I sketched a simple hysteresis maze about 12x12 in size. The user controls up-down movements, the maze controls left-right movements. It would be self-resetting, like Oskar's mechanical mazes, so that the pin will return to the start any time the user moves to the bottom. This maze will be mapped onto the bolt-like cylinder.

(I'm treating this as a dry run, so I won't slow down to fix mistakes as I go; I'll just make note of them for future reference.)

So here's the maze I'll use for this test design...
Attachment:
File comment: A hastily-designed hysteresis maze, just for demo purposes.

IMG_7476.JPG [ 208.36 KiB | Viewed 977 times ]

The next step is to map this maze onto a bolt-like cylinder. Unlike the Mk3 I want the features of the maze to be visible so I chose to adapt the modulated-peaks technique by making the peaks flat and wide to make room for very distinct maze elements.

My next adaptation is to increase it to 12 threads, so each peak represents one entire column in the sketched hysteresis maze. The grooves of the threads will act as guides for the nuts, and also mark the boundaries between the column positions in the maze.

(At this point I discovered my first mistake: my maze sketch didn't allow any space for wall thickness. That is to say the lines in the maze are just lines, not solid walls. For now I arbitrarily thickened the features where possible, and omitted any that would have overlapped others.)

The "bolt" would look something like this...
Attachment:
File comment: Bolt-like hysteresis maze

Skewed shaft.png [ 100.73 KiB | Viewed 977 times ]

(My second mistake, the 'maze' features have the wrong angles so they won't guide the pin smoothly from one position to the next. There are step-like jumps in places that ought to be aligned.)

The "nut" isn't nut-shaped at this point. It has 12 helical teeth-like threads that ride in the 12 threads on the bolt, with sufficient space to ensure it won't collide with the raised features of the maze.

Inside the nut there's a separate ring with a raised pin that's guided left-right by the maze. It needs some sort of mechanism to make it stop only at the 12 positions corresponding to the 12 columns in the maze. On my physical "nut" model I had used magnets, but there I just put 12 detents on the ring (not shown in this view). The sides of the pin are skewed so all sides will meet the skewed features of the maze at the same tangent.
Attachment:
File comment: Although it's not nut-shaped, this is the "nut" with a floating ring whose pin traverses the maze.

Skewed ring and pin.png [ 56.02 KiB | Viewed 977 times ]

When the collar ("nut") is installed on the maze, the user can move it up or down by screwing the whole collar left or right. The movements of the collar are synchronized with the threads, so the pin inside the collar will only move left or right relative to the 'maze' when it encounters features of the maze that push it sideways onto adjacent peaks.
Attachment:
File comment: Collar (nut) installed on cylinder (bolt)

Skewed shaft and collar.png [ 82.85 KiB | Viewed 977 times ]

This particular model has several faults that would prevent it from fully working, but it illustrates the basic idea...warts and all!

For reference, I've attached a 3-dimensional PDF of the bolt-like maze cylinder.

 Attachments: File comment: 3D PDF of the cylinder 12trak_core.pdf [525.07 KiB] Downloaded 24 times

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 Post subject: Re: Helical Hysteresis MazePosted: Sat Jun 29, 2013 8:13 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Nice... and sorry for the slow reply. Its been a crazy week and I missed this post until just now.
VeryWetPaint wrote:
It needs some sort of mechanism to make it stop only at the 12 positions corresponding to the 12 columns in the maze.
This part sounds like it could pose problems mechanically and if the maze was deeper then the threads I don't think it'd be needed. It also appears that due to the steepness of the threads a small turn on the nut would result in much more vertical movement then one would typically expect from a nut on a bolt. You have proven that in principle the maze can be shallower then the threads... but for this type of maze (both from a function stand point as well as trying to maintain an appearance as similar as possible to that of a typical nut and bolt) I still think having the maze deeper cut then the threads may be the better option.

In principle I even think one could start with a large bolt and nut and with the right milling tools cut the maze into the bolt and also cut a ring out of the inside of the nut. Then all you would need would be a SW&F ring that you could print on Shapeways which should be flexible enough to allow being popped into the space made for it inside the nut. Though finding the right milling tool(s) I think may be harder (and more expensive) then simply printing the entire puzzle on Shapeways.

Carl

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