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# Accelerometer Limitations

There are various types of accelerometers but the force balance pendulous accelerometer and piezoelectric accelerometer are the most common. The pendulous accelerometer has excellent performance but unfortunately is relatively large and expensive. The piezoelectric accelerometer is less expensive and can fit on one's hand but cannot measure either static accelerations or ones occurring at the low frequencies commonly found in human motion.

All of these linear accelerometers measure, of course, the acceleration which represents the actual dynamics of a moving body, but may also be contaminated by components of earth's gravity which may also be sensed.

An accelerometer sitting stationary on the Earth with its sensitive axis pointing vertically will give an output signal equivalent to one g, or 32.2 ft/sec squared (9.8 m/sec squared), assuming that it responds to static acceleration inputs. If this accelerometer is rotated 90 degrees and left stationary with its sensitive axis pointing parallel to the surface of the Earth, it will produce an output signal equivalent to zero g's.

If one orients this accelerometer so that its sensitive axis is pointing down, it will yield a minus one g signal and so on. In each of these cases, the accelerometer has not been moving but is yielding an output suggesting that there have been some dynamic motions.

Of course, if one rotated the sensitive axis of the accelerometer to a new position only a few degrees (theta) from the horizontal, it would produce a small indicated acceleration (mathematically: g(sine theta)). Note that its output now would be entirely position dependent.

If one slowly moved the sensitive axis of the accelerometer to a new position only a few degrees above and to a few degrees below the horizontal plane one would see an oscillating acceleration output no matter how slowly you rotated the accelerometer. Again, the magnitude of the output would be completely dependent on the angular position. Often, this varying output is interpreted as a measure of the dynamics of a hand tremor when it is actually the error contributed by Earth's gravity.

One cannot filter out low frequency accelerometer signals and expect to eliminate the gravitational component since that component will most often occur at the frequency of the movement, the tremor frequency for example.

When the motion of the accelerometer is random, it will measure the linear sum of true dynamic accelerations and those due to Earth's gravity. It cannot differentiate or distinguish one from the other, and there is no way of filtering its output to eliminate the signal due to Earth's gravity.

Only in the unlikely situation that the measured motion was in a perfect straight line would it be possible to eliminate the gravity "noise" component since it would be a constant. In this unusual circumstance one could be left with the true dynamic acceleration (the rate of change of velocity). If the direction on movement is not precisely known, the contribution of Earth's gravity cannot be removed unless numerous other sensors are utilized in addition to the one accelerometer; even a triaxis accelerometer package would not be sufficient.

With relatively small dynamic motions such as in human tremors, the magnitude of the accelerations due to dynamics may be of the same relative size as those due to small changes in the orientation of the sensitive axis, by coupling to Earth's gravity.

Unless a tremor is restricted to a perfect straight line, the orientation input for just a few degrees of rotation will mask the true dynamics of the tremor. For example, a tremor of plus and minus 0.1 g would easily be in error by as much as 100% due to a rotation of just plus and minus 5.7 degrees.

Only a large inertial measurement system containing more accelerometers and gyros can separate the dynamic motions from the errors due to angular position. Such a system would be significantly larger than most hands, arms, legs, etc. that it was to measure.

In conclusion:

It is technically impossible to quantify typical tremors with a simple accelerometer since the best such a sensor could do is to occasionally capture the high frequency components (not the magnitude) of a tremor.

Since human skeletal components are basically hinged together, their relative motions are primarily rotational. A gyroscope that measures angular rotation rates is thus fundamentally superior and hence the sensor of choice.

The choice is clear:  Motus

The miniature Motus gyro is insensitive to linear accelerations and also insensitive to Earth's gravitation. It measures the true dynamics (angular rotation rates) of an object and is not confused by orientation changes.

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