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I have evaluated the Accelerometer offset occurring due to placement of Accelerometer away from the centre of rotation of body. In the below evaluation I am trying to calculate Accelerometer's reading away from the centre of rotation of the body. It is made sure that the Accelerometer is placed rigidly inside the vehicle.

This calculation is done because I need to calculate pure translational accelerations recorded by the vehicle, however when the Accelerometer is not placed at centre of rotation of body it will measure rotational + translational accelerations of the body.

Kindly look at my evaluation and let me know is my evaluation correct. Also I have a few questions which I have posted in the end of my evaluation which I have added as an Image file enter image description here enter image description here enter image description here enter image description here

  1. Is my evaluation correct? Is this the accelerometer's reading at the centre of rotation of the body?
  2. If we replace units of angular velocity and angular acceleration from rad/sec and rad/s2 to degree/sec and degree/s2 the output values for a_x,a_y a_z change, Is this normal or do we have to use only one kind of unit in this formula? i.e., Either rad/sec or deg/sec
  3. If it is made possible that the body rotates on it's own axis(i.e., No translational velocity in the body) the accelerometer would read pure rotational accelerations of the body. In this case if we use the above formula the accelerometer readings should be 0 ? right as in the center of rotation of body we should get 0 value if the body is in pure rotational motion? Will this condition be satisfied with this formula?

Update

  1. Rotation specification of device & Accelerometer specification includes Forward motion as motion in x axis, z axis is upwards, and y axis is corresponding to x axis. The three axis of rotation are coincident with the linear acceleration axis. Positive rotation is a counter-clockwise rotation about an axis enter image description here

References

  1. https://physics.stackexchange.com/questions/222947/calculating-acceleration-offset-by-center-of-gravity-c-g
  2. https://www.nxp.com/company/blog/accelerometer-placement-where-and-why:BL-ACCELEROMETER-PLACEMENT
  3. https://www.basicairdata.eu/knowledge-center/compensation/inertial-measurement-unit-placement/
Akash Sagar
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  • This is properly a physics question, not a mathematics question. While there are many people in MathExchange with the expertise to answer the question, you will find far more expertise on the matter there. I will say on your third question: an ideal single point accelerometer would indeed measure $0$ in that case. But an actual physical accelerometer cannot lie entirely on the axis of rotation, and thus may be affected by rotation without translational acceleration. – Paul Sinclair Jan 14 '23 at 17:59
  • Hi Paul, Thanks for your response, as for your response on question 3, You are right even if I transform the acceleration values at centre of rotation of the body there may be certain error in those values, however they should be very close to zero is my assumption right ? – Akash Sagar Jan 16 '23 at 06:48
  • Also, Should I remove this question from this community? As I posted this question here to verify my vector representation of the formula and verify the calculation. – Akash Sagar Jan 16 '23 at 06:49
  • For my comment on (3), I just intended to draw your attention to this difference between reality and theory, not to disagree with your theoretical calculations themselves. It may seem obvious, but I've seen it overlooked many, many times. As for removing the question, maybe you should, but at this point I don't think it likely you'll get an answer here anyway. Your question is definitely better asked in the physics forum. All physicists must have a strong understanding of the basics of mathematics. But mathematicians need not understand even simple physics. – Paul Sinclair Jan 16 '23 at 12:53

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