# Center of Gravity (COG)

### Segmental Method for Determining Center of Gravity

Once center of gravity (COG), or center of mass, is determined for the body or group of segments moving as a unit, you can treat the COG as a single mass resting on that point. Since the subject's segmental stats are not known, an average of these stats (see Body Segment Data) may be used. Knowing the actual weight of the subject or the segments is unnecessary since percentages are used.

X = Distance of Center of Gravity from fulcrum or arbitrary axis
W= Weight (Percentage)

since...

Xtotal x Wtotal = X1W1 + X2W2 + X3W3...XnWn

therefore...

Xtotal = X1W1 / Wtotal + X2W2 / Wtotal + X3W3 / Wtotal...XnWn / Wtotal

or... Xtotal = Σ (Wseg x Xseg) / Wtotal

### Entire Body

When determining the center of gravity for the total body (2 dimensions only):

1. Begin with traced or printed photo of the subject in the exact position to be analyzed
1. A larger image may help reduce measurement error
2. Draw dots on joints representing proximal and distal points
3. Connect dots with straight lines
4. Distinctly mark the center of gravity for each body segment on each line
5. Draw or overlay grid on transparency over markings
6. Choose an arbitrary reference point as origin of coordinate system
1. Lower left point = 0
2. X and Y (horizontal and vertical) axes
7. Measure the distances of each segmental Center of Gravity from X and Y axes
8. List each segment weight (as percentage)
9. Calculate center of gravity distances from X and Y axes separately (formula above)
10. Measure and plot each total distance from their respective axes
11. Draw two perpendicular lines parallel to their axes through their points
12. The intersection of the two lines represents the total body's Center of Gravity through those two dimensions

Kreighbaum, E., Barthels KM, (1996). Biomechanics; A Qualitative Approach for Studying Human Movement, Allyn & Bacon, 586-587.

### Two or More Segments

When determining torque on a joint due to the body parts weight (1 dimensions only):

1. Begin with traced or printed photo of the subject in the position of greatest effort.
1. Typically where the combined center of gravity of body segments are the furthest horizontal distance from the fulcrum joint
2. On body segments in motion, draw dots on joints representing proximal and distal points
3. Connect dots with straight lines
4. Distinctly mark the center of gravity for each body segment on each line
5. Draw or overlay vertical lines on transparency over markings
6. The first or last line (0 point) should be placed on joint fulcrum
7. Measure the perpendicular distance of each segmental Center of Gravity for joint fulcrum (0 point)
8. List each segments weight (as percentage)
9. Calculate combined center of gravity distance from fulcrum joint (formula above)
10. Measure and mark combined center of gravity