Does a gyro need to be placed at the center of rotation?
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":


You won't have an ideal rigid body. Your material is at least slightly flexible...
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).