Coda AMPLIFIER 15.0 Betriebsanweisung PDF herunterladen (Seite 94)

Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 1

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

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To relocate M

‘out-of-plane’ one has only to specify the appropriate 2

offset, X, (ignore

the first!).

The direction of offset X is determined by the ‘cross-product’ of vectors derived from

marker position vectors and its positive sense (vertically up or down in the above

example) depends on the spatial ordering (clockwise or anti-clockwise) of M

, M

and M

Again it is important to note the requirement of non-colinearity for these markers.

To summarise: three markers (a ‘triad’) are necessary and sufficient to construct a virtual

marker whose location is 3 dimensionally fixed relative to the triad. One may choose to

specify either two weights and two offsets, or three weights and just the second offset.

The same relative virtual marker location may be arrived at using a less intuitively obvious

construction involving a fourth, non-coplanar, weighted marker, thereby dispensing with

offsets altogether. Such an approach to rigid segment modelling is unlikely given the

usual economies of marker placement (and the requirement that all must remain in view),

yet it is entirely reasonable to construct a virtual marker from the weighted mean position

of any number of markers (up to 20). Indeed this is exactly how we approach the non-

rigid modelling of centres of mass.

Centres of mass

The equivalence of virtual marker to centre of mass (centre of gravity) provides a useful

clinical tool. Where a body consists of a number of segments of masses m

, m

, ...

, whose centres of mass are located at points P

, P

, ... P

, the centre of gravity of

the entire body is given by

= (m

+ m

+ ... + m

) / 





which is identical to the definition of virtual marker.

The points of centres of mass, P

, may themselves be defined as vitual markers (but

these virtual markers cannot include virtual markers in their definitions in the current

version of Motion Analysis.)

To serve as an illustration of this method we consider the task of identifying the centre of

mass of the human body. This centre is in no way fixed relative to any single segment of

the body and need not even be located within the body.

(out of plane)

offset

intermediate

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