Let an orthogonal coordinate system B be defined by the intersection of the three principal planes of the body passing through the center of gravity in the standing position as shown in Fig. A.2.1. The location of the center of mass (gravity) of the body is measured along the b3 axis from top of the head (L3), along the b1 axis from the back plane (L1), and along the b2 axis from the anterior superior spine of the ilium (L2) as shown in Fig. A.2.2. The body positions identified with symbols 1, 2, 3, and 4 are illustrated in Fig. A.2.3. The parameters I1, I2, and I3 denote the mass moment of inertia elements along the b1, b2, and b3, respectively.
Position L1 |
L2 L3 |
Ii |
I2 |
I3 |
Subject 1: Age, 29; height, 72.2 1 3.62 |
in.; weight 173.5 lb 5.31 32.2 |
132 |
119 |
13.1 |
2 3.52 |
5.31 29.9 |
174 |
159 |
12.5 |
3 3.34 |
5.31 29.5 |
172 |
135 |
41.9 |
4 7.70 |
5.31 23.9 |
41.4 |
37.3 |
29.9 |
Subject 2: Age, 23; height, 67.4 1 3.50 |
in.; weight, 147.3 lb 4.25 29.8 |
95.6 |
81.9 |
10.3 |
2 3.49 |
4.25 27.5 |
126 |
110 |
10.2 |
3 3.18 |
4.25 27.2 |
125 |
90.3 |
30.0 |
4 7.03 |
4.25 21.7 |
32.9 |
30.4 |
21.5 |
Subject 3: Age, 33; height, 73.3 1 3.81 |
in.; weight, 203 lb 5.61 31.8 |
144 |
129 |
14.2 |
2 3.67 |
5.61 29.4 |
188 |
172 |
13.8 |
3 3.56 |
5.61 29.5 |
187 |
142 |
51.2 |
4 7.75 |
5.61 23.4 |
48.9 |
41.9 |
36.7 |
Note: AH lengths (Li, L2, L3) are inches (in.; multiply by 2.54 to convert to centimeters, cm) and moment of inertia (I1, I2, I3) in lb-in.-s2 (multiply by 0.11298 to convert to kg-m2).
frontal sagittal plane posterior right frontal b
posterior right
sagittal plane
Figure A.2.1. Body coordinate system.
Figure A.2.1. Body coordinate system.
Figure A.2.2. Reference landmarks for the location of center of gravity.
Figure A.2.2. Reference landmarks for the location of center of gravity.
Matsuo et al. (1995) proposed the following equations for relating the moment of inertia I1 and I2 of adolescent boys to their height H (in m) and weight W (kg). These equations may provide reasonably accurate results for other subpopulations.
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The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.
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