At 08:18 AM 12/5/97 -0500, you wrote:
>My (vague) understanding of accelerometers is that they can only measure
>inertial force, not orientation.  Is there a formula to extract angular
>rate information from an accelerometer reading over time? Sure would
>save a lot of money on tiny little gyroscopes!  I'm trying to come up
>with a fairly accurate (and relatively cheap) way to track position over
>time in 2-axis.
>
>- Jeff Cesnik
>

The problem with using accelerometers to measure position information is
that it requires integrating twice (accel = 2nd deriv of position) and this
means that any little offset error in the output of the accelerometer gets
accumulated over time. So, the setup would be accurate for a little  while
but after a few minutes (a guess abt exact length of time), the whole setup
would need recalabration to be accurate.

If you place an accelerometer at the end of a rod that is in the plane of
roataion which you are trying to sense, the formula for angular
acceleration from the accelerometer output is:

ang. accel. = R * accel. output

where R is the distance along the rod from the axis of rotation to the
accelerometer.

This formula is assuming that the whole setup has no linear acceleration,
ie. it is only rotating, not moving otherwise. If it is also moving, you
can correct for this by placing another accelerometer on the other end of
the rod, such that you now have a rod, the midpoint of which which passes
through the axis of rotation, which lies in the plane of rotation, and has
an accelerometer on each end. Now, the formula becomes:

ang. accel = R/4 * ( accel#1 - accel#2)

where R is the TOTAL length of the rod
and accel#1 and accel#2 are the accelerometer outputs.



Now, you can integrate ang. accel. with respect to time and get an
approximate answer.

IMHO, a gyro would be much more accurate and maybe even not as expensive
(if you end up needing two accelerometers). There is one consideration with
the gyro, though. Due to friction in the gyro bearings and other factors,
the gyro will begin to precess and re-align its axis after a while. So, it
is difficult in general to sense angle by inertial means.

I think that you probably just want to use a plumb weight and an optical
encoder wheel! :-)


Good Luck

Sean




+--------------------------------+
| Sean Breheny                   |
| Amateur Radio Callsign: KA3YXM |
| Electrical Engineering Student |
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