Acceleration at the center of the triangle

I am trying to calculate the acceleration at the node between the three points, photo attached. The points (1,2,3) measured accelerance via tri-axial acceleromter and now with the help of that info I want to calculate the acceleration at the center point. How can I proceed with this problem? Is there any function available to calculate the acceleration in matlab?

[Sam Chak]

There are 4 faces. Which face of the triangle?

Are you using the correct term in Geometry? Perhaps, consider a Tetrahedron.

Are you referring to the triangle in X–Z plane?

Once you have clarified, then we can proceed properly.

[Abhikaran Amitkumar Bhatia]

I am attaching the photo of the actual case, maybe this might explain my point more clearly. With the help of accelerance data collected from 3 tri-axial sensor I want to calculate the acceleration at the screw.

[James Tursa]

What is the ultimate goal here? Is the device you built translating and rotating? Are you ultimately looking to calculate integrated position? What about gravity and any reaction force if the device is on the ground? Can you give us more details?

[Abhikaran Amitkumar Bhatia]

Yes, the goal here is to calculate the acceleration at the screw with the help of the accelerance data collected by those three sensors. There is no rotating motion. Not the position and the sensors are not collecting data considering the gravity so they are only capturing the motion.

[James Tursa]

"... the sensors are not collecting data considering the gravity ..."

Not sure what this means. If your device is in contact with the ground then the sensors are certainly sensing the reaction force to gravity, even if the device is perfectly still on the ground. What do you mean "they are only capturing the motion"? Are you only considering the horizontal component of the acceleration? Or ...?

Answer 1

[John D'Errico]

If you have some known parameter at the three corners of a triangle, then the best estimator of that parameter at the center of the triangle is the average of the three values. This assumes the relation varies linearly over the triangle, and since you provide no reason to assume anything else, that is the best possible estimator.

In fact, you you have some uncertainties in the three parameter estimates at the corners, the mean should also be the minimum variance estimator.

And that means your answer is simple, just take the mean. And that is trivial.

acc_center = (a1 + a2 + a3)/3;

There is no explicit "function" necessary. Just one line of code.

[Abhikaran Amitkumar Bhatia]

Okay I understand. What if take the co-ordinates and the distance as a parameters? because the accelerometer/points are measured from a fixed co-ordinate system. I also came across interpolation to calculate the acceleration.

[Matt J]

Because the instantaneous position of the centroid is a linear function of the position of the corners, the instantaneous acceleration of the centroid will be a linear function of the acceleration at the corners.

The only think that might complicate matters is if the sensor data from the 3 corners are not simultnaeous. Some sensors will timestamp the data so that that can be handled.

[Torsten]

I think the center of gravity of the triangle is the center of the circumcircle - thus the distance to the three points is the same and we again are at John's formula.

[Abhikaran Amitkumar Bhatia]

I attached one more photo of the actual case.Maybe that might make my explaination more clear.