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unknown user
05-16-2001, 02:46 AM
For the convenience of our subscribers I placed in this email all messages
which I received during the last half hour. Enjoy!

Krystyna Gielo-Perczak, Co-moderator of Biomch-L
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From: Chuck Pell

Mammals all. Think of the rest of the chordates (one phylum).
Think of the other 35 or so phyla, or look them up. Then you'll
see why they called it "Loco" motion!

Do you mean a three-legged creature, or a five-legged creature?
Go check out Bob Full's Polypedal lab site at UC Berkeley...
# of legs matters little. Or go check out E. Muybridge...
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From: "Edmund Cramp"

Dear List members,

I would think (as a non-scientist) that the basic reason for the
dominance of bi-lateral symmetry is that at a very early stage of
evolution the neural wiring for symmetry was simpler and more
"efficient" than that of an asymmetrical body plan. Thus we, and our
biological relatives, are bi-pedal because we are symmetrical. Even the
oddest of the Burgess Shale critters eventually turned out to be
symmetrical so it looks as if "dumb luck" was something's lunch at a
very early stage in evolution.

Regards,
Edmund Cramp,
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From: Thomas Burkholder

>But to draw the further conclusion that therefore bi-laterally symmetric
>architecture always yields faster locomotion does not follow. One can
>imagine a rabbit-like animal which possesses a single front limb instead of
>two (a three legged rabbit!).

Certainly an interesting image...

When I try to imagine the kinematics of tripod running, with at most
one leg on the ground at all times, it seems out of balance. eg: let's
say it strikes first the left leg-the reaction gives it a push forward and
a push right. In a bilaterally symetric beast, the right push is nicely
countered by the right leg, and a more-or-less straight path is generated.
In a tripod, the center leg must follow either the left or right leg, and
that lateral push is not countered.

When I try to imagine the kinematics of a tripod walking (which non-bipeds
do by switching from 3-point stance to 3-point stance) I find that it
lacks a "walk". Maybe the 5 legged bug: normal bugs use their 6 legs as
two pair of tripods and are thereby stably supported throughout gait. In
order for the 5-legged bug to maintain support, one leg would have to be
a member of both tripods (or perhaps all legs be members of a set of 5
rotating tripods). In either case, the efficiency of locomotion is
compromised. (see Full & Koditschek, 1999;
http://www.biologists.com/JEB/202/23/jeb2375.html )
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From: Dhelenberg@aol.com

In a lighthearted take on this discussion, how does one reconcile the Riddle

of the Sphinx with this? If I recall correctly, the riddle goes something
like this:
What animal walks on four legs in the morning, two legs at midday, and three

in the evening?
The answer is the human animal --> Four "legs" as a baby (crawling), two
legs
as an adult, and three when older, counting the use of cane.

My serious point with this is would the use of a cane be classified as a leg

in this discussion?

Happy pondering,

Derek Helenberger
Product Development Engineer
Becker Orthopedic
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From: Chuck Pell

"Jenkyn, Thomas" wrote:

> I will state up front that I fall into the "dumb luck" camp on this
> discussion.

Mix the two. Luck acts, physics rules.

> In this discussion we need to be careful to distinguish between what
> architectures of animals actually exist and what architectures are
possible.
> There is a big difference between the two and by no means are all the
> possible modes of locomotion represented in the fauna of this planet.

I've looked at that issue, and there are several modes that we've seen
no evidence for as of yet.

> Therefore making the conclusion that bi-laterally symmetrical animals are
> faster than assymetric and radially symmetric animals because that is what
> we see in the animal kingdom is valid (with perhaps the exception of the
> squid).

Not enough data, except for squid, dragonfly larvae, damselfly larvae, etc.,
etc.

> But to draw the further conclusion that therefore bi-laterally symmetric
> architecture always yields faster locomotion does not follow.

Right, right, just the point, exactly.

> One can
> imagine a rabbit-like animal which possesses a single front limb instead
of
> two (a three legged rabbit!). This front limb may be placed along the
> midline of the animal and the locomotion would be much the same as the
> common four-legged rabbit. With the same maneouvrability.

No data.

> One could also image an scorpion-like animal with 3 legs on one side and 2
> on the other. The timing of the legs would be somewhat different perhaps,
> but no biomechanical restrictions would stop this animal from being as
fast
> or maneouvrable as its 6 legged cousin.

No data.

> These thought experiement animals aren't even particularly different from
> the existing fauna. And I would suggest that there are plenty of other
> odd-legged schemes that the bioengineer could dream up that would hold
their
> own just fine in a foot race with even-legged competitors.
>
> Therefore, as unsatisfying as it is to an engineer, it is probably just
dumb
> luck that the even-legged animals on this planet are the fastest.

Ah, but the data do not exist to say so. Or do they? Let's look
at ghost crabs. Decapods often have to run with legs missing, and
I have seen a ghost crab with 5 legs (2R/3L) that was chugging
along. Does anyone have data on any arthropods that could illuminate
the issue? UCB Full lab, ever run any 9-legged or 8-legged crabs?
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From: DSmith

An interesting discussion but as a mere physicist I am surprised that =
the question of lateral stability whilst in motion has not been =
mentioned. Try hopping on one leg over rough terrain as compared with =
running with two feet.
The odd-footed animals e.g.snails and starfish, and the squid all use =
suction adhesion to prevent themselves falling over or off the surfaces =
which they are traversing. The jet propulsion of the squid does not =
apply to walking/running on a surface under the influence of gravity.
The three legged rabbit* would have to have a different kind of joint on =
the mid line of travel for the odd leg, and that leg, foot and joint =
would have to be symmetrical either side of the line of travel to =
maintain stability. I suggest that the five legged rabbit would always =
run with one foot off the ground to avoid tripping itself up. The simple =
optimum for heavy surface dwelling animals is 4; a leg at each corner of =
a rectangle with the line of action due to gravity passing roughly =
through the crossing point of the diagonals.
(*Rumour has it that these are to be found on the Isle of Man along with =
the tail-less cats)
PS Have you looked at the number of feet or castors on your office chair =
lately. Once you could rock back comfortably on two legs out of four, =
now they have five?
Denis Smith
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