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The Mobius Strip

Author Photo
By Staff

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221 North End Road Westport, Maine 04578

I have always been fascinated by a geometric oddity called the
‘Mobius Strip.’ It is also called a ‘Unilateral
Surface’ because it has only one side.

The last time my wife, my son and I sawed firewood it occurred
to me, as I was putting belt dressing on the belt, that a mobius
strip might prove useful.

We had the old 6 HP Fairbanks-Morse belted up to the saw table
and using belt dressing involved reaching inside the belt. If there
is a loose wire in the belt lacing it could snag your hand or arm
and gash you or pull you into the machinery. Neither prospect is
very attractive, and even though I’ve been doing this same job
for many years without a mishap, it’s always an uneasy
feeling.

So this time, we unlaced the belt and put a twist in it before
putting the lacing pin back. Now at the lacing we apparently had
the top of the belt on one side and the bottom on the other. The
beauty of the arrangement is that now the belt has only one side!
If you put the belt dressing on what appears to be the
‘outside,’ it gets to where it belongs on the pulley side
of the belt (inside).

To demonstrate the principle, take a long, narrow strip of paper
and tape it together like a belt, but put a 180 inch twist in one
end before you tape it. Now draw a line down the center of the
strip. You’ll find as you proceed down the strip that
you’ll draw a single line that meets itself and will have
covered ‘both sides’ of any single segment of the paper.
Truly you have a ‘belt’ with only one side!

In practice, with a real belt, always put the ‘straight’
length of the belt on the tension side (the bottom for my rig) and
the twist on the slack side. If you have to twist the belt to
reverse the direction of rotation of the saw blade, that makes this
a Mobius Strip that does not alter the direction of rotation at
all. It just provides for twice the belt life and for easier belt
dressing application.

Check the picture, the performance is the same as for a
conventional flat belt. It just looks kind of funny. If the belt is
rather long to start with, this twist does not make any noticeable
difference in belt tension. With a very short belt you might have
to adjust the engine and saw to be a bit closer together.

If you want to play with this concept a bit, make a paper Mobius
Strip and cut it right down the middle. Then, watch what happens,
cut it again, right down the middle. You’ll get some
surprisingly weird results! Have fun!

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