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linear motion encoder



Hi --

I was thinking that air tracks ought to have a _built in_ motion
encoder. Does somebody make such a thing? (I didn't see it in the obvious
catalogs.) If not, why not? It seems obvious that air tracks are used for
kinematics experiments, and that a motion encoder might be useful....

In particular I was thinking that you could attach a linear encoder pattern
right to the track.

The proper encoder pattern is not a picket fence. The problem with a
picket fence is that it is insensitive to direction. A lot of kinematics
experiments involve a change in direction. A picket fence can be
considered a one-bit Grey code:

mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..
mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..

but what you need is a two-bit Grey code, i.e. two picket fences staggered
by 1/4 cycle:

mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..
mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..
y..yy..yy..yy..yy..yy..yy..yy..yy..yy..yy..y
y..yy..yy..yy..yy..yy..yy..yy..yy..yy..yy..y

and if you use colored inks you can overlay the two patterns on top of each
other:

mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..mm..
rm.yrm.yrm.yrm.yrm.yrm.yrm.yrm.yrm.yrm.yrm.y
y..yy..yy..yy..yy..yy..yy..yy..yy..yy..yy..y

where m is magenta, y is yellow, and r is red.

Notice that the middle row is not a palindrome, while the outer rows
are. The middle row is sensitive to direction of motion.

The advantage of overlaying them is that you can focus a light source and
detector at a _single_ point; there's no danger that wobble or skew will
mess up the results.

The most elegant thing might be to silkscreen the pattern directly onto the
metal of the track, but it might be easier to pre-print a bunch of tape and
stick it on the track.

With such a pattern on the track, and some simple optics and electronics,
the motion of a cart could easily be tracked within a fraction of a millimeter.