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Knots are used widely in our
every day life. All the way from
rock-climbing to sailing to
surgery. And empirically over
the many centuries of us tying
knots we have learned how to
relate how some knots are better
than others for specific
applications. But what we lack
is a predictive understanding,
so models that are able to
relate a particular knot
configuration with its
mechanical response, which is
what our study is able to
provide. When you tie your
shoelaces if you do a left-handed
knot followed by another left-
handed knot the result is not
as secure than if you do a left-
handed (knot) followed by a
right-handed knot. Now, the
question is: Why? To address
this question we started with
the simplest possible knot,
which is called the treffle knot
which looks like this, and
change the topology by adding
subsequent turns to the knot.
And then we asked, how much
force does it take to pull the
knot shut? And I can keep
increasing the number of turns
and so as we increase the
number of turns what we are
doing is we are increasing the
force that it takes to close the
knot; that is essentially making
the knot more secure. And we
show that by varying the number
of turns from one to ten, say,
we can increase the pulling
force by a factor of a thousand.
So we can divide this problem
into two parts. We have to be
able to deal with what's
happening in this braid, and
what is happening in this loop.
And the braid is particularly
difficult because we have to
deal with the bending energies
of the rope, the tension, as
well as the friction that comes
from the fact that we have
self-contact in between the rod.
And putting all of this together
into a predictive framework was
the challenge. So in our
experiments we didn't actually
use standard rope we used
nitinol rods and we tied our
treffle knots, changed the
topology by increasing the
number of turns and at some
point the pulling force becomes
so high that I can't actually
close the knot. Because we can
so dramatically change the force
that it takes to slip this knot
we might be able to control
how heavy an object we might be
able to sustain by changing the
topology.
Of course to start somewhere
we had to start with a very
simple example first but what
I believe we have done is set
up the foundations from which
more complex knots configurations
can be studied.