Some years ago, I think I remember reading (in Douglas Hofstadter's
second (?) "major" book, as I think of them) that someone had designed a
mechanism for a 7^3. When I started this message, I thought I'd offer a
description of such a mechanism to the members of this list, but then
realized that the problem is even harder than I thought. I hope these
thoughts are not a waste of bitspace; let me know if so!

Evidently, the design Hofstadter (probably) alluded to is not generally
known to this List's members. Perhaps he could enlighten us.

Also, one wonders whether Erno Rubik has contemplated the mechanical
design for a 7^3.

Edge cubies could be retained by schemes such as are now used, but only
until they are moved out "into midair"; then they have one or two rubbing
surfaces completely exposed, so to speak. The mechanism for retaining them
is probably closely related to that for retaining corner cubies when out
of alignment. Once the scheme for retaining corners is worked out, then a
minor variant might be what's needed for the edges. (Or possibly
conversely...)

(Ideally, one would not want to prohibit an inner slice from being
rotated all by itself; less-clever locking schemes might require that
no more than one plane in the whole Cube be sheared at once.)

For a first try, the corners would be retained by three locking pins to
hold them in alignment with their neighbors. However, the problem is to
retract one of the three pins before shearing an outside layer with
respect to its neighbor. Until the pin is retracted, you can't shear the
layer by much! Furthermore, that surface has to be locked once more when
the corner is realigned, and this must happen automatically, reliably,
and quickly. IMHO, it takes someone like Mr. Rubik to invent such a
mechanism, and it might be one of the most difficult to invent yet.

In the next few paragraphs, I get into speculative electronic/mechanical
engineering, but try not to presume specialized knowledge any more than
necessary.

If one allows an electronic/mechanical scheme, cost balloons, and one has
the disgusting thought of a battery to power things. Sliding contacts to
distribute power from one central battery are bound to be unreliable
unless carefully maintained; they would be a pain.

They also would constitute an interesting problem in their own right: Can
power be distributed without short circuits caused 1) by intermediate
physical relative positions, and 2) by any possible configuration of a
Cube? Keep in mind that two paths for current are needed, and they must
never intersect. This is an interesting problem in topology, if I'm
thinking correctly. A related problem is to ask whether every cubie could
always have power connected to it.

The thought of a small battery inside each corner and each edge cubie
(or every other one) is even more painful.

But, if there were power inside, here's what could be done. The locking
pins would have a certain amount of "give", to permit limited shear
movement. They could be mounted so they could tilt slightly (say, 10
degrees max.) against spring tension, and their mating sockets could be
narrow "funnels", wide end at the surface.

Some sort of sensor would detect misalignment well before the limit of
"give" was reached. Misalignment would cause internal electronics to apply
a pulse to a coil to retract the locking pin. (The pin should have minimal
friction; a polished surface and a Teflon-lined mating hole should do.)
Once the pin was retracted, the electronics would ignore other
misalignments. (Otherwise, one could simply push against a cubie in
"midair" and detach it!)

The pin would be kept both extended and retracted magnetically, by a
remanent alloy that stays magnetized, but which can have its
magnetization reversed by the flux from a coil. Extending the pin would
be done by pulsing the coil with the opposite polarity. (The principle is
closely-related to pulsed magnetic latching relays, which do not require
continuous coil power in either of their states.)

As has been implied, once the cubie is realigned, a second
(reverse-polarity) pulse re-extends the locking pin.

Pulsed operation should give acceptable battery life; the misalignment
sensor might be somewhat of a challenge to engineer, but not a major
problem. One could consider mechanical contacts; with electronics, they
wouldn't need to be kept scrupulously clean, only clean enough to permit
a milliampere or so to flow. (Contamination becomes a factor if you make
the electronics too sensitive.)

The electronics seems quite straightforward, and by today's standards,
quite simple and entirely practical. The locking-pin mechanism would be
the most costly, more than likely; it would have to be custom-built, and
might cost $2 US apiece in 10,000 lots, perhaps more. I can imagine many
people-weeks of development to create a decently-reliable locking-pin
design. It's essentially a miniature solenoid.

Battery access would be via a screw-threaded cover with a slot that fits
the edge of a coin; the Cube would look distinctive.

The clicking sound of the retaining pins would be interesting!

It's not immediately obvious (to me) how the pins and mating sockets
should be arrayed; their number must be minimal. Edge cubies would need
four locks apiece, while corners would need three apiece.

The mind wants sleep, so I think I'll give this mad message a quick
proofread and post it.

---------------------
On Thu, 30 May 1996, der Mouse wrote:

{Snips}

that locking pins (or the equivalent) would be necessary. I really

{Snips}

On the other hand, a straightforward locking mechanism could probably
be put together by a good watchmaking shop at no more than the price of

mouse@collatz.mcrcim.mcgill.edu

Best regards to all,

NB   Nicholas Bodley   Autodidact & Polymath  |*| Keep smiling! It makes |
      Waltham, Mass.   Electronic Technician  |*|   people wonder what   |
     nbodley@tiac.net    Amateur musician     |*|  you have been up to.  |
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