Biomedical Engineering Reference
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COM of foot
=
0 . 50
×
0 . 195
=
0 . 098 m between ankle
and metatarsal markers
COM of leg
=
0 . 433
×
0 . 435
=
0 . 188 m below femoral
condyle marker
COM of thigh
=
0 . 433
×
0 . 410
=
0 . 178 m below greater
trochanter marker
COM of HAT
=
1 . 142
×
0 . 295
=
0 . 337 m above greater
trochanter marker
where COM stands for center of mass.
4.1.7.2 Calculation of Total-Body Center of Mass. The calculation of the
center of mass of the total body is a special case of Equations (4.6) and (4.7).
For an n -segment body system, the center of mass in the X direction is:
m 1 x 1 +
m 2 x 2 +···+
m n x n
x =
(4.11)
m 1 +
m 2 +···+
m n
where m 1 + m 2 +···+ m n = M , the total body mass.
It is quite normal to know the values of m 1 =
f 1 M , m 2 =
f 2 M , and so on.
Therefore,
f 1 Mx 1 +
f 2 Mx 2 +···+
f n Mx n
x
=
=
f 1 x 1 +
f 2 x 2 +···+
f n x n
(4.12)
M
This equation is easier to use because all we require is knowledge of the
fraction of total body mass and the coordinates of each segment's center of
mass. These fractions are given in Table 4.1.
It is not always possible to measure the center of mass of every segment,
especially if it is not in full view of the camera. In the sample data that
follows, we have the kinematics of the right side of HAT and the right limb
TABLE 4.2
Coordinates for Body Segments, Example 4.5
X (meters)
Y (meters)
Segment
Right
Left
Right
Left
Foot
0.791
1 . 353
0 . 707
=
0 . 646
0.101
0.067
Leg
0.814
1 . 355
0 . 707
=
0 . 648
0.374
0.334
Thigh
0.787
1 . 402
0 . 707
=
0 . 695
0.708
0.691
1 / 2 HAT
0.721
1 . 424
0 . 707
=
0 . 717
1.124
1.122
x
=
0 . 0145 ( 0 . 791
+
0 . 645 )
+
0 . 0465 ( 0 . 814
+
0 . 648 )
+
0 . 1 ( 0 . 787
+
0 . 695 )
+ 0 . 339 ( 0 . 721 + 0 . 717 ) = 0 . 724 m
y = 0 . 0145 ( 0 . 101 + 0 . 067 ) + 0 . 0465 ( 0 . 374 + 0 . 334 ) + 0 . 1 ( 0 . 708 + 0 . 691 )
+ 0 . 339 ( 1 . 124 + 1 . 122 ) = 0 . 937 m
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