Biomedical Engineering Reference
In-Depth Information
Figure 4.5 Radius of gyration of a limb segment relative to the location of the center
of mass of the original system.
Consider the moment of inertia I 0 about the center of mass. In Figure 4.5
the mass has been broken into two equal point masses. The location of these
two equal components is at a distance ρ 0 from the center such that:
I 0 = 0
(4.9)
ρ 0 is the radius of gyration and is such that the two equal masses shown in
Figure 4.5 have the same moment of inertia in the plane of rotation about the
center of mass as the original distributed segment did. Note that the center
of mass of these two equal point masses is still the same as the original
single mass.
4.1.6 Parallel-Axis Theorem
Most body segments do not rotate about their mass center but rather about
the joint at either end. In vivo measures of the moment of inertia can only be
taken about a joint center. The relationship between this moment of inertia
and that about the center of mass is given by the parallel-axis theorem. A
short proof is now given.
m
2
m
2
ρ 0 ) 2
ρ 0 ) 2
I
=
(x
+
(x
+
0 +
mx 2
=
mx 2
=
I 0 +
(4.10)
where I 0
=
moment of inertia about center of mass
x
=
distance between center of mass and center of rotation
m
=
mass of segment
Actually, x can be any distance in either direction from the center of mass
as long as it lies along the same axis as I 0 was calculated on.
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