## Normalized Segment Coordinate System

Hello,

I have recorded some movement data with Vicon and would like to know the relative movement of certain markers (i.e. breast markers) in their respective segment coordinate system (i.e . trunk coordinate system).
For this, I would like to normalize the segment orientation to the calibration pose.
I followed the description in 'Research Methods in Biomechanics' 2nd ed. in constructing the orientation/rotation matrix (pg. 40).

According to the book: "the rotation matrix that defines the relative orientation of a segment, Rseg, with reference segment Rref, can be expressed as" (pg. 57)

R = Rseg * transpose(Rref)

To my understanding, if I want to apply it to my case, Rseg would be the rotation matrix i.e. of the trunk at each instant and the reference segment, Rref, the rotation matrix of the trunk of the static trial.

However, the book further states that "for a normalized joint angle, the rotation matrix must include the orientation of the segments in the calibration pose Rcalseg and Rcalref and is expressed as follows:

R = (transpose(Rcalseg)*Rseg) * transpose(transpose(Rcalref)*Rref)

As I am only interested in the normalized rotation matrix without referencing it to a further segment, I am now confused if I have to calculate my rotation matrix either

a) R = R_trunk_dynamic * transpose(R_trunk_static)
or
b) R = transpose(R_trunk_static) * R_trunk_dynamic

Also, as the rotation matrix is made up of the unit vectors of the local or segment coordinate system (LCS) I would now like to have a normalized LCS with reference to the static trial.

Therefore, I assumed that R has now the unit vectors of my normalized LCS. However, I am wondering if now the columns or the rows of R will be the unit vectors in x, y and z direction? Assuming Rseg and Rref originally had their unit vectors as rows.