Properties include:
-- Small, light, powerful, and cheap. Or to say it in more
professional terms, huge power-to-weight ratio, huge power-to-cost
ratio, et cetera.
-- Typical reduction ratio of 100:1. This stands in contrast to
planetary systems, which rarely exceed 10:1.
-- Precise motion. Usually touted as "zero" backlash. Certainly
very much less backlash compared to a comparable conventional gear
train.
It was invented about 50 years ago, which makes it quite a bit younger
than other simple machines, such differential pulleys ... not to mention
inclined planes et cetera. This is somewhat important, because it makes
the point that physics is not a "dead" subject.
You may be wondering, where's the physics angle in this. Well, for
starters, I take a rather expansive view of "what is physics". Anything
this nifty has got to have some good physics in it. More specific
angles include:
*) There is always the completely practical aspect, namely that you
might want to know about this, because some day you might need to
design one into a piece of laboratory apparatus.
*) Simple machines have always been part of physics.
*) It's certainly not going to be covered in any other class (math,
chemistry, biology, English, home ec, ...) so if it's going to be
done, it has to be done in physics.
*) There is some interesting scaling involved in the fact that the
spline needs to be flexible in one direction, but must greatly
resist torsion in another direction. The principle involved here
shows up again and again in physics and engineering, for instance
when you use masking tape to create geodesics: http://www.av8n.com/physics/geodesics.htm
*) Usually a "small difference between large numbers" is a curse ...
but if you can harness such a thing and put it to good use, you
can create huge mechanical advantage. There are obvious analogies
between the harmonic drive and the differential pulley.
From there you can segue to other systems that have near-infinite
mechanical advantage, such as lateral push on a taut cable....
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The principle of operation is not easy for everyone to grasp. As a
warm-up exercise, to lay some groundwork, it helps to look at some
partially-analogous systems, such as a 20" diameter bicycle wheel
rolling against the inside of a 22" diameter drum. Emphasize that
in the absence of slip, circumferential /length/ controls what's
going on. (For gears, counting teeth is the same as measuring length,
since the pitch is necessarily the same everywhere, but for tires on
wheels you need to stick with length.)