Today, flexible origami and paper bags. The
University of Houston's College of Engineering presents this series about the
machines that make our civilization run, and the people whose ingenuity created them.
The paper bag is a remarkable contrivance. It serves us
constantly and inconspicuously. It folds flat, yet opens into a structure that
can stand open upon the table while we eat our sandwiches from it and chat with
friends.
If we take the bag apart, we find it's made from a single paper cylinder. One
end of the cylinder has been folded into a complex 3-dimensional pattern and
finished off with a bit of paste. It would be, and once was, costly to make,
because each fragile cylinder had to be folded manually into that hardy sack.
Robotics engineers have come up against another strange feature of paper bag
folding. They've been looking at the origami art of paper
folding in their attempt to make industrial robots more effective. They've
built robots that can fold paper, and, though they've mastered much, the paper bag
poses a peculiar problem.
They find two kinds of origami: rigid and flexible. The surfaces and edges of
flexible origami can be bent as the objects are folded. The fancy folded napkins
you find in some restaurants might be done in flexible origami. Rigid origami
forms can only be folded, not bent. Imagine working with hinged metal plates
instead of creased paper. Robotics engineers are doing remarkable things with a
class of robots that does only rigid origami.
However, as we fold and unfold our paper bag, we have to bend the paper. And we've
had paper-bag-making machines -- in effect, flexible-origami robots -- for almost
a century and a half. And therein hangs the tale of Margaret Knight.
Margaret Knight was born in Maine in 1838. She went to work in the Amoskeag cotton
mills at nine. When, at the age of twelve, she saw a fellow worker badly injured,
she invented a device to quickly stop the machinery; and the owner put it to use.
After the Civil War, she moved to Springfield, Massachusetts where she worked for the
Columbia Paper mill. She studied machinery by day, and developed drawings for a
bag-making machine at night. Margaret Knight hired a machinist to build a patent model,
and she finally received a patent in 1871. But that was only after narrowly averting
theft of the idea by an early industrial spy.
Knight went on to form the Eastern Paper Bag Company in Hartford, and she kept inventing.
By the time she died at the age of 76, she held 27 patents in all. And she'd probably
invented twice that number of devices with no patent protection.
Those bags are called S.O.S. for stand-on-shelf or self-opening-sacks.
Some seven thousand bag-making machines operate around the world, while Margaret Knight's
original machine rests in the Smithsonian Institution. And, next time I idly fold a
paper swan, I'll remind myself that I haven't really come to grips with origami until
I've mastered something far more beautiful -- the lovely, delicate, ever-present, brown
paper sack.
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.
(Theme music)
For a general discussion of paper bag folding see:
http://www.maa.org/mathland/mathtrek_07_25_05.html
For movies showing a rigid-origami robot at work, see:
http://www.cs.dartmouth.edu/~robotics/origami.html
This site treats the mathematics of rigid-origami folding:
http://theory.lcs.mit.edu/classes/6.885/fall04/erik_notes/anydpi/L19_slides.pdf
These two sites provide information about Margaret Knight:
http://www.paperhall.org/inductees/bios/2006/margaret_knight.php
http://members.aol.com/KiteCD/inventw.htm
All photos by JHL. This one is a view looking down into the bottom of an open bag illuminated
from below; it shows details of folding and pasting.
The patent office drawing for Knight's bag-making machine:
The Engines of Our Ingenuity is
Copyright © 1988-2006 by John H.
Lienhard.
