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Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 3

CX1 USER GUIDE - COMPLETE.doc 26/04/04

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Two key points of this methodology arise from consideration of segment-joint physical

characteristics:

(1) Segment-joint geometries tend to suggest a local plane of symmetry (usually mid-

sagittal) on either side of which we might expect to find similar angular deviations.

(2) Medio-lateral ‘bending’ and antero-posterior flexion/extension are both similar and

complementary in their nature (‘bending’ which is not medio-lateral must be flexion/

extension and vice versa) and are quite different from the torsional nature of internal/

external axial rotation. To illustrate this let us consider, for example, knee rotations.

The tibia may be allowed to rotate varus/valgus, as well as axially, on either side of the

femoral mid-sagittal (XZ) plane. To visualise these rotations in planar views we would

choose to project the tibial Z and X axes (from the tibial mid-sagittal plane) onto the local

frontal and transverse planes respectively. Having committed the tibial Z axis frontal

projection to represent ‘lateral bending’ we are bound by the notion of complementarity to

further use the Z axis to depict flexion/extension, projected, this time, as a sagittal view.

Thus, for the tibia in relation to the femur, we have chosen to project u

transversely and

both frontally and sagittally; a projection angle set (

X-Y

X-Z

Y-Z

) which, according

to Crawford et al., corresponds to the Euler axis sequence: Z => X => Y, or in other

words:

zxy

Similar reasonings justify the same choice for all segment joints throughout the lower body

and it is worth reminding ourselves that the ZXY Euler sequence corresponds to rotations

of the distal segment, about proximal segment axes, in the order (i) internal/ external axial

rotation, followed by (ii) medio-lateral bending, followed by (iii) flexion/ extension.

Furthermore, being last in the sequence, the Euler flexion angle will be identical to the

projection angle on a (local) sagittal view and, if the angles are small, the Z and X rotation

angles will be comparable to corresponding projections.

Yaw, Pitch and Roll

(but not necessarily in that order)

Seafaring terminology often finds its way into the discussion thanks to the generality of the

terms ‘yaw’, ‘pitch’, ‘roll’ in respect of a ship’s motion. This is all very well but for the

potential confusion over frames of reference. The inference from these terms is of

rotations measured against the ship’s own co-ordinate frame immediately prior to its re-

orientation. This is analagous to describing re-orientation of the distal segment in the

absence of the proximal segment, which is perfectly acceptable - some texts on

biomechanics proceed exactly in this fashion on the subject of Euler Angles.

It is vitally important to realise that a sequence of Euler angles given with respect to the

moving co-ordinate frame of a (distal) segment is different to the sequence which

describes the same re-orientation with respect to the proximal segment. Fortunately it is

only the sequence which differs: the magnitudes of the angles and the types of rotations

they measure are the same, but the order is reversed (Paul, 1982).

The chosen ‘ZXY’ sequence in respect of proximal segment axes would be reversed to Y-

X-Z with respect to (moving) distal segment axes, corresponding to the nautical sequence:

pitch, followed by yaw, followed by roll (for most segments).

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