# Calculating acceleration of an object using $x$, $y$ and $z$ coordinates

I have x, y and z coordinates for a test I had carried out for a tool. I had an accelerometer installed on the tool and I used two types of motion to move the tool, rotation and translation. Right now I have x, y and z coordinates of the object as it moved and they are recorded with respect to a certain time interval of approximately 0.037s and I need to calculate its acceleration. do you know if this is possible? please let me know if you have any ideas.

• Out of interest, why do you need to calculate the acceleration if you had an accelerometer installed on it? I think I must be picturing the situation wrong. – jacob1729 May 28 '19 at 12:49

I need to calculate its acceleration. do you know if this is possible?

No, it is probably not possible.

Since you allowed some rotation, and probably did not strictly rotate about the center of the accelerometer the rotating motion about a different point probably induced some additional signal to the accelerometers.

Imagine mounting an accelerometer to the edge of a wheel and spinning the wheel. Even if you don't translate the wheel's center, your sensor will still report a strong acceleration along the line which is normal to the rotation axis passing through the accelerometer.

If you want to do a better job, here are two things you might try:

1. Only do careful rotations of your object around the center of your accelerometer. The problem here is that you don't know where it is exactly and the X, Y, and Z accelerometers are in slightly different positions.
2. Use a six-axis device; three acceleration axes (proper accelerometer) and three rotation axes (gyroscope). Know the vector distance between the accelerometer and the gyroscope and then go through some math to predict and subtract the induced acceleration due to rotation to recover the linear acceleration.
3. Mount two 3D accelerometers opposite each other, equidistant from the object's center, and *only rotate the object around this center.
4. Read further for other strategies on how to use accelerometers to reconstruct trajectories.