# Calculate the Angular Velocity of an Arm from a Data Set

Hi, a newbie to the site and hoping someone can help. Its been a long time since I studied physics or math at school.

I am having some difficulty calculating the angular velocity of the arm trhough a partial movement (phase). The data set I have separates the angular velocity into the three axes, X, Y and Z.

If I use the following method I get 1.3977 radians per second which seems close to what I need:
• Find the total of each axis
• Find the average of these values
• Find the square root of the squared average values
• Divide this value by the change in time
If I use the next method which I actually thought would be correct, I get 0.1201 radians per second which seems very low:
• Find the square root of the squared average values for the angles at the start of the phase
• Find the square root of the squared average values for the angles at the end of the phase
• Subtract the final angle from initial angle
• Divide this value by the change in time
I have tried to find if anyone else has at least an estimate of the angular velocity of the arm during motion to give me a rough idea of what the speed would be close to but haven’t been able to unfortunately.

I can take a rough estimate if my thinking is clear. If the phase of the arm motion moves roughly through 90 (degrees) and it takes on average about 0.7 seconds then that would equal to approximately 128 (degrees) per second or 2.2 radians per second.

The data set does have the angular velocity for each of the axes, however if I take the square root of squared value of the average of total sum of each axis I get around 55 radians per second which seems excessively high.

Do you know which method would be best to use or if I am looking at this problem completely wrong?

Thank you in advance to anyone who can help and if any further information or clarification is required I can try to explain further.

Dale
Mentor
2021 Award
Have you read your sensor’s documentation? It may be that they are using different units than you expect. The documentation may also give recommendations on algorithms for processing the data.

Hi Dale, thank you for your reply and help. Yes I had checked the documentation but was unable to find the units that the angular velocity were measured in, however, the angles are measured in radians so was hoping I could calculate the angular velocity from them and the time.

I take it from your reply that those values do seem incorrect?

Thanks again for your help Dale, it is appreciated.

Dale
Mentor
2021 Award
Without clear documentation on the units I would contact the manufacturer directly. They need to tell you the specifications of the data. Trying to guess it or reverse engineer it is a bad idea in my opinion.

I have heard that Kalman filters are frequently used for this purpose, but I do not know the details.

MAV
Ah OK Dale, I didn't think of that at all, I had read something about Kalman filters regarding the sensor, that could be affecting the results. That's fantastic Dale, honestly I thought I was going a bit loopy. I probably need to go back to school and redo some physics!

Thanks again, you have been a great help.

Dale