100 
  
  
  
  
  
  
   
y 
Trunk 
Thigh 
Leg 
Foot 
Fig. 5 Center of Body Segment Gravity Flg. 6 Cardinal Planes of the Body in a 3-D Space 
2.3.2 Center of Body Gravity (COG) 
The biomechanical modeling of human body consists linked rigid body segments by joints. The equation of center of 
body gravity (COG) is written as: 
n n 
N mx, 2 my, n 
BBM ny 7 8 
Ym, im, (is xm = 
n=l n=l os 
M = Y m, AG, =m, IM, 
n 
dy mz, n 
— nzl 
N mz, (5) 
11 
X 
G 
y 
G 
n=l 
X, = YAGx,Y, = S AGy,,Z, = 5 AGz, (6) 
n=1 n=l n=l 
(X,. Y,, Z, ) is COG of segment X. YZ. ) is COG of total segment 
2.3.3 Moment of inertia, Angular Acceleration, Kinetic Energy 
In rotary movement, the moment of inertia, angular velocity and kinetic energy are important and are related to each 
other. The moment of inertia is used to describe not only the weight of a body also how far from the axis of rotation the 
center of gravity of the body lies. The equation for of moment of inertia I is 
Izmr 7) 
where M is body mass weight and 7 is the rotational radius from the COG. The relationship among kinetic energy E. 
2 cns TF. 
angular acceleration (0 ^ and moment of inertia Iis 
1 
E--—Io' i 
2 
The sum of kinetic energy Et during sit-to-standing sequence is given by the equation: 
Et «| EG) (9) 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences’, Zurich, March 22-24 1995