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In 3-D kinematic analysis of movement, we typically track the motion of three or more markers on a rigid body segment. Here are various methods to extract a 3-D position vector and rotation (or attitude) matrix from marker coordinates.

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An Excel spreadsheet that converts Euler X-Y-Z rotation angles to the other 5 possible rotation sequences as well as to the tilt-twist angles. Instructions are included in the spreadsheet.

Ron Jacobs, Ton van den Bogert

A Matlab function using singular value decomposition. Includes references.

Joe Sommer

FORTRAN subroutines and test data for finite helical axis (FHA) and instant screw axis (ISA).

H.J. Woltring.

A Fortran subroutine, using the eigenvalue decomposition method described in: Veldpaus et al., J. Biomech. 21,45-54 (1988).