User guide
Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 4
CX1 USER GUIDE - COMPLETE.doc 26/04/04
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SEGMENTAL ANALYSIS - Inverse Dynamics
The lower body is to be considered as an arrangement of individual limb segments
connected at the joints. In order to obtain moments and powers in respect of each joint
the limb segments are treated mechanically as free bodies to which we can apply three
dimensional Newtonian mechanics relating motions and forces. The analysis is simplified
by modeling each limb segment as a fixed, uniform distribution of mass around the
longitudinal axis connecting the joint centres, thereby simplifying its inertial properties and
rendering the location of its centre of mass on this axis at a fixed proportion of the
segment length from the proximal end.
We then define, for each segment, an embedded (orthogonal) vector basis (EVB), or
co-ordinate system with its origin situated at the centre of mass (labelled G) and whose
axes are coincident with the principal axes of the segment, thereby nullifying the products
of inertia.
The EVB for a given segment is deduced from three significant marker positions using a
Gramm-Schmidt process to deliver three new orthogonal unit vectors whose directions
represent the orientation of the limb segment with respect to laboratory (Coda)
co-ordinates. An EVB for the foot, for example, would consist of the following set of
vectors:
foot
e
0
=
e
e
e
0
0
0
x
y
z
,
foot
e
1
=
e
e
e
1
1
1
x
y
z
,
foot
e
2
=
e
e
e
2
2
2
x
y
z
These point “along” and perpendicular to the foot.
Having obtained segmental EVBs, we transform vector quantities such as torque,
angular velocity and acceleration, into vectors localized with respect to the limb-
embedded co-ordinate systems.
For each limb segment we must specify the following:
segment mass m (kg) (as a proportion of body mass)
principal moments of inertia I
0,1,2
(kg m
2
) (derived from radii of gyration)
G location parameter µ (a proportion of segment length)
absolute angular velocity ω
ωω
ω (rad/s)
angular acceleration α
αα
α (rad/s
2
)
linear acceleration a (m/s
2
)
various position vectors H, K, A, T, etc. (derived from marker positions)
We must also use the force plate reaction vector F and its location P (centre of pressure).
Vector quantities are labeled as bold characters and will have 3 orthogonal components:
for example α =
α
α
α
x
y
z
, ω =
ω
ω
ω
x
y
z
= [
ω
x
,
ω
y
,
ω
z
]
T
,