Topological Conrundrum

[Tunnelcat]

How would you build a square four-walled room and make all the walls move inwards evenly, without bending anything, resulting in the internal space shrinking smaller and smaller, which would then crush any contents located inside? I saw this recently and it's a cool solution, although I can't figure out a mechanical way to get it to work right in practicality.

[Spidey]

Way too easy...

[Foil]

The pure mathematician in me just cringed a bit at the reference to topology (my favorite subject, a highly abstract branch of mathematics) with such pragmatic terms as \"mechanical\" and \"practicality\".

In all seriousness, that's a pretty good question. Reminds me of one of those questions I've heard of people getting in a job interview.

[snoopy]

I'll also throw in the fun fact that it's the only way you can make a square from four identical walls, when the walls have a finite thickness.

[Tunnelcat]

Spidey got it, yea! Sorry Foil, I loosely used the word 'topology' to describe this 'changing space' problem.

Where I saw this recently was in a Spanish 'math horror' movie called 'Fermat's Room' or 'La Habitacion de Fermat'. You'd love it Foil, it involves 4 mathematicians trapped in a room under the control of a crazed math genius. He controls the mechanism that slowly shrinks the room bit by bit if they can't solve mathematical puzzles in fixed time periods. That shape Spidey drew is shown on the wallpaper in the movie's diabolical room. A surprisingly entertaining movie.

http://www.imdb.com/title/tt1016301/



However, what intrigued me is HOW would you make a mechanism to move these 4 walls the way Spidey showed above and have enough force to crush things inside the room? The movie had this elaborate set of 4 hydraulic presses set at an angle mounted on sliding rails, but it still didn't look like the setup would have enough force to crush things in the room. Everything's at a weird angle. Any ideas?

[Foil]

... 'Fermat's Room' or 'La Habitacion de Fermat'. You'd love it Foil, it involves 4 mathematicians trapped in a room under the control of a crazed math genius.

Interesting!

Not available on NetFlix yet, but it's now on my "Save" list.

[Spidey]

Yes hydraulic presses, and slide joints, but not at an angle. If you wish I can show you a diagram.

[Tunnelcat]

If you can dream one up.

[Spidey]

After I posted last night, I was thinking …how would this work, and this is the “first thing” I came up with.

I would use 4 Presses for stability, and two slip joints. Probably controlled by computer via some sort of position sensors.

I know if I actually had to build this thing, it would probably have to be tweaked, if not redesigned completely.

The four “walls” sit on a plate suspended only by the presses. The presses provide the compression, and the slip joints allow the walls to move at the 90 degrees needed. Exact position on the walls would have to be determined. The slip joints (slide rail) would probably be the key to the system, and would have to do the job very well.

Final “cube” compression could be accomplished with a top and bottom plate with a square cutout , and more presses, that activate at the right time.

As far as not being able to provide the pressure needed…heh, not a problem.



You would probably also want to put some sort of compression “springs” on the leading edge of each wall.

[snoopy]

I think you can also do it with just linkages and pivots, if you get the geometry right.

[Isaac]

Do it with legos!

[Spidey]

I think you can also do it with just linkages and pivots, if you get the geometry right.

Could you demonstrate that? My first gut instincts are…

1. Need for longer press throws.
2. Loss of forward pressure.
3. Tricky job of maintaining “square”.

[snoopy]

I'll take a look at it over lunch on Monday. I'd work it out in autocad, and don't have it installed here at home.

[Tunnelcat]

That looks similar to the setup in the movie, Spidey. I'm just wondering about torque loads on the press arms at their ends, the sliding rails and the walls themselves. Since the walls are sliding sideways AND moving forward linearly, I'd think that there would be a lot of pressure on the room side of the walls, causing a severe assymetric loading, that would drastically increase as the pressure built inside the room. It would have to be built like a battleship to even have a chance of working. Would the walls have to be in some type of track as well? Think of an iris mechanism. Lets see what snoopy comes up with with his autocad.

Also for Foil, this movie was shown on the Sundance Channel recently, but it's not listed in the 2 week ahead schedule. I'll keep an eye out for it. It really was an interesting little find of a movie. It's subtitled, but a well done little suspense flick.

[Foil]

Unfortunately, we don't have the Sundance Channel. My wife and I often enjoy indie films, but we generally get 'em via NetFlix.

[Spidey]

Well tc, it depends on what you have in mind to crush…

Something that needs a great deal of pressure, would never be designed like this. IE: car crusher

People and furniture would not be a problem…

No you couldn’t use a track. And as I pointed out the Slip Joints would be the key component. A system using roller bearings could probably take a lot of pressure. Then again, you might just have to give up the forward pressure advantage, and go with the pivots. Problem there is, the forces would no longer be pushing straight against the presses, and bending could be a problem. Of course you could put the presses on rails, but then you would be back to the original problem.

DISCLAIMER: Spidey does not advocate crushing people.

[snoopy]

I completely forgot to look at this. Hopefully I remember tomorrow.

[snoopy]

Okay. Here's my resolution: I'm not sure if it is possible in a geometrically perfect way. I couldn't figure out how to find the geometry other than empirically. I *think* the geometrically perfect way to do it would require an infinitely long pivot arm, and thus would be impractical. If you make the pivot arms ~double the length of the walls, a small gap opens between the walls in transition, but not all the big of one.

Summary: The sliding method is probably the best way to practically build something like this.

[Tunnelcat]

Well tc, it depends on what you have in mind to crush…

Something that needs a great deal of pressure, would never be designed like this. IE: car crusher

People and furniture would not be a problem…

No you couldn’t use a track. And as I pointed out the Slip Joints would be the key component. A system using roller bearings could probably take a lot of pressure. Then again, you might just have to give up the forward pressure advantage, and go with the pivots. Problem there is, the forces would no longer be pushing straight against the presses, and bending could be a problem. Of course you could put the presses on rails, but then you would be back to the original problem.

DISCLAIMER: Spidey does not advocate crushing people.

Well, in the movie, the characters laid some bookshelves loaded with books on the floor flatwise and packed the books in tight. I would think that the books would be very hard to compress into a small enough area to actually do the job of crushing your victims. Like I said, a twisted way to kill people, but with no good practical engineering solutions to do it.

Yes Spidey, we know you don't advocate squishing people.

[Spidey]

Heh…

Well tc, the problem here is simple, no one in their right mind would create a room to crush people, and no engineer would use this design to crush things. So the only solution is to “overbuilt” the system, and any evil madman worth his starch, would have plenty of money to do the job.

[Foil]

<bump>
Well, I finally saw \"Fermat's Room\" over the weekend, and definitely enjoyed it.

As far as the film goes, it was much more character-driven than mechanically/mathematically accurate. The puzzles were really secondary to the discoveries of the reasons why they were there, and the personal revelations that came from their dire situation. Without giving away the end, I was a bit surprised by the final plot twist.

One thing that I found amusing was that the questions the characters were given to solve were all 'classic' logic-puzzles that most math folk know, but none of the genius-types in the room were familiar with them. That is, except for one puzzle I've never heard, which was quickly dismissed by a character saying, \"Oh, that one's a classic\".

Anyway, I'd second tc's recommendation. It's an enjoyable little film, not pointlessly gory like some of the well-known American films in the genre.

[Tunnelcat]

Thought you'd like it Foil. Where did you finally see the movie? I liked the character-driven plot too, even though I had to read subtitles constantly to understand what they were saying.

Speaking of gory, I happened to tune in the movie 'Hostel' when I was bored one night and curious. What a mindless, sadistic gore fest. No wonder it was said to be one of the most violent, over-the-top carnal house of horror movies ever made. It makes little offbeat horror/suspense flicks like 'Fermat's Room' look like Oscar material. I also like the Hitchcock classic, 'Rear Window', another good suspense/scare flick with NO gore but plenty of character-driven interest.

[Foil]

Where did you finally see the movie?

It finally showed up as available through NetFlix.

I also like the Hitchcock classic, 'Rear Window', another good suspense/scare flick with NO gore but plenty of character-driven interest.

Agreed! There are a number of good suspense/thriller films from that era; one of my favorites in that genre is Orson Welles' "The Third Man".