User guide

Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 3
CX1 USER GUIDE - COMPLETE.doc 26/04/04 107/162
Note that the order in which the decomposition is solved is NOT the same as the Euler
sequence of rotations. In fact the mid-sequence angle is solved first.
Closer scrutiny of the equations for φ and ψ reveals that these angles would remain
undefined in the event cosθ = 0 (division by zero isn’t allowed). This only happens when θ
= +/- 90
o
, i.e. when ad/abduction reaches 90
o
, a condition known as ‘gimbal-lock’
10
and is
unlikely in the context of lower limb movements. (This may, of course, be taken as one of
the constraints upon the choice of Euler sequence - the chosen scheme must avoid a
mid-sequence rotation of 90
o
.)
Neutral alignments
The Euler angles described here are taken to be measured relative to a hypothetical
position of neutral alignment, i.e. all distal segment axes aligned exactly with proximal
axes. In clinical applications these hypothetical alignments may not even be possible, let
alone considered neutral. In normal stance, for example, one would expect to be able to
claim neutral positions for the segments but the alignments are clearly never perfectly
square and will therefore register non-zero Euler angles. Thus, the extent to which ‘real’
neutral positions are offset from hypothetical alignment is a matter for the clinician to
judge. Unreasonably large offsets between segments in neutral position may lead to
slight crosstalk in the angular coupling patterns observed.
Coda implementation
Codamotion segmental analysis software automatically calculates the Euler Angles for
lower limbs (from the pelvis down) according to the schemes outlined above. With the
exception of the foot, which uses u
x
for the longitudinal axis, limb- segment longitudinal
axes are represented by u
z
in the EVB. In any case u
Y
is always medio-lateral. With this
arrangement the usual clinical angle descriptions correspond to the aforementioned
notions of pitch, yaw and roll for the moving distal segment.
In so far as distal segment Euler Angles relate to a ‘proximal’ reference frame the
following relations apply:
Hip joint angles - Thigh EVB (distal) relative to Pelvis EVB (proximal);
Knee joint angles - Shank EVB relative to Thigh EVB;
Ankle joint angles - Foot EVB relative to Shank EVB;
Pelvic rotations - Pelvis EVB (distal) relative to global ‘laboratory’ frame (proximal);
Foot rotations - Foot EVB relative to ‘laboratory’ frame.
Notes and References
1
Consultation group: Computer Aided Movement in A Rehabilitation Context
2
See, for example: Fowles, G. R., Analytical Mechanics (1962; Saunders College
Publishing). or: Goldstein, Classical Mechanics.
3
See Coda User documentation.