View Full Version : Matrix order of multiplication - ISB standard

Ben Stansfield
07-03-2003, 12:56 AM
Dear All,
I am reading the 'ISB recommendations for standardisation in the reporting
of kinematic data' (Wu and Cavanagh, Journal of Biomechanics, vol.28, No 10
pp1257-1261) and am finding it difficult to get the matrix product as given
in the paper (T1g).
>From my reading of the paper the order of rotations that is suggested to get
from one system to another is rotations about Z then Y then X. However, it
appears that the matrix given does the reverse order.

Am I correct in saying that to get from a local reference system to a global
one a rotation about the Z (Rz) followed by one about the Y (Ry) followed by
one about the X (Rx) would be calculated:


[L] is the local co-ordinate system location
[G] is the global co-ordinate system location
[Rx],[Ry] and [Rz] are the rotation matrices representing rotations about
the relevant axis.

(note no translation in this example)

The matrix as given in the paper is calculated as:


Would this not mean that the first rotation was about the x-axis?

Your's in hope of clarification.

Ben Stansfield

PhD, CEng, MIMechE
Bioengineering Unit
University of Strathclyde, Wolfson Centre
106 Rottenrow, Glasgow, G4 0NW
Tel: ++44 (0)141 548 3031
Fax: ++44 (0)141 552 6098
MSc in Applied Biomechanics by Distance Learning:

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