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When using a gyro chip to measure angular velocity, does it matter whether it is located at the center of rotation?

I've seen it mentioned online without much explanation that it should be placed at the center, but in my introductory physics courses I learned that the angular velocity is the same at every point on a rigid body. Wikipedia seems to confirm this in the last section of Angular velocity, but I'm not sure I'm interpreting it correctly.

I expect that there is normally some non-ideal coupling of the acceleration terms into the gyro measurement -- is that the main problem?

Is there something obvious that I am missing?

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I wonder if the rigid body theory says the same for the accelerometer...? – Stefan K. Aug 21 '12 at 15:39
    
@Stefan - Accelerometers will generally be different, for both of these cases: ① If the object is rotating, even if the angular velocity is constant, each point will see a centripetal acceleration of \$\omega^2\cdot r\$ pointing toward the center of rotation, where $r$ is the distance from the center. ② If the angular velocity is changing (non-zero angular acceleration), the tangential acceleration is also proportional to the distance from the center. – Justin Aug 21 '12 at 17:23
2  
From what I've seen in RC helicopters, almost always the gyro is not in the center of rotation and they work fine. – AndrejaKo Aug 21 '12 at 17:38
    
Thx Justin, thats totally correct. The difference is exacly when rotating. The distance from the rotation center will differ for some points and these will move in different speeds, therefore the acceleration must be different. – Stefan K. Aug 21 '12 at 17:38
up vote 2 down vote accepted

I just checked this by "thinking" about that and noticed, that for an ideal rigid body (!) it doesn't matter where you place it.

I just imagined that like this:

  • You have a gyro at each side of a stick (axes of the gyros parallel to each other).
  • You rotated the stick about one end (e.g. x axis by 90°).
  • Observation: the other axes is also rotated 90° about the same axes, same direction, seen from center of the other gyro.

Theory vs. Practical "Rigid Body":

  1. You won't have an ideal rigid body. Your material is at least slightly flexible...
  2. If you want to combine data from 2 sensors, e.g. accelerometer / gyro the axis of the two sensors should be pointing in the same direction (or you need even more sophisticated math). And this coupling should be very tight, e.g. not flexible or swinging (else you'll measure a lot of garbage); Rule: the longer the distance the more influence of those effects.

You possibly want to measure the orientation/position of something (e.g. wings of a plane or the "body" of quad copter). So the gyro should be fixed to exactly that.

PS: Thank's for pointing me at this issue. This helps me a lot (need those sensors for research).

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