## Finding Joint Angle from Motion Capture

### Mary (view profile)

on 12 Dec 2012
Latest activity Edited by TAEYUN

on 30 Oct 2014

### Roger Stafford (view profile)

Hi!

I'm working right now with data from a motion capture device, essentially picking up data for three markers placed on the head neck and shoulder in an x y z plane.

My difficulty trying to develop a code to calculate the joint angles between these three markers. I am able to animate the three coordinates to play as an animation, but I'm more interested in the calculation of the angles between these points changing over time.

Thanks

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### Roger Stafford (view profile)

on 12 Dec 2012

```At any time, let H = [x,y,z], N = [x,y,z], S = [x,y,z] be coordinate vectors of the head, neck, and shoulder markers at that time.  Then the three respective inner angles within the triangle HNS then are:
```
``` h = atan2(norm(cross(N-H,S-H)),dot(N-H,S-H));
n = atan2(norm(cross(S-N,H-N)),dot(S-N,H-N));
s = atan2(norm(cross(H-S,N-S)),dot(H-S,N-S));```

(The sum of these should always be pi to within round-off accuracy.)

Roger Stafford

Mary

### Mary (view profile)

on 12 Dec 2012

Thank you again for the response! I managed to get that aspect of my motion capture data working. Most of the trouble I had was conceptually figuring out how to break down my data into each [x,y,z] coordinate.

Would you happen to know how I can take these same data sets of three points in separate x, y, and z columns and figure out the velocity and acceleration of these moving joints? I'm hoping to compare different data sets of the moving head neck and shoulder to identify which is cause the most stress internally, so looking at the motion capture data is becoming somewhat more difficult than working with my empirical biomechanical model!

Thank you (I hope I'm not asking too much!!!)

George Vendo

### George Vendo (view profile)

on 6 May 2014

Hi, Thank you for the answer. Could you please explain why the sum should always be pi?

With 3D coordinates how can we specify the position in space, by the angles? thank you

TAEYUN

### TAEYUN (view profile)

on 30 Oct 2014

u r a awesome dude!!!! i luv u!!!

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