You are only dealing with one body segment (the trunk), so some of the equations you wrote are not relevant.

Also you did not refer to translations, only rotations. Translations are important here.

I assume you have at least three markers on the trunk so you can track its position and orientation through time.

Here is how I would do it:

1. Define a trunk coordinate system. You can do this with markers at anatomical sites, or simply by defining the local (trunk) coordinate system to coincide with the global (lab) coordinate system during a reproducible reference pose such as standing.

2. Determine the local coordinates of your trunk markers.

3. At any time point during the movement activity, use the global coordinates of the markers to determine the position and orientation of the trunk coordinate system.

4. Transform the global coordinates of your breast marker to the local trunk coordinate system.

5. Repeat 3 and 4 for the entire movement, plot the local x,y,z obtained from step 4 vs. time. This is the motion of your breast marker relative to the trunk.

If you use Matlab, look up the Kinemat and soder.m codes on isbweb.org:


These codes are 25 years old but still work. If needed I can write some lines of code here to clarify things.

Ton van den Bogert