BIOMECHANICS APPLICATION NO .1Human body center of mass and static stabilityDr mahmud R Ismail ,2016

Analyzing the motion of an object Kinematic analysis ; Position, velocity

& acceleration of an object Projectile motion Weight of an object Stability of the object

Some Applications of CG

Stability Definition

Segments method for calculating center of mass

The X and Y coordinates of the whole body CG can be found from the following equations ;

Find the center of mass for the female player and check its static stability , at the instant shown

Application on Human Body EXAMPLE

To be able to calculate the CG of the body shown in the picture , it is important to draw the picture in a proper scale .This can be done either manually by drawing the picture on scale paper or simply by using the computer .

Label the center of all joints of the body(wrest ,Knee, Hip ,….)

Get the coordinates (x,y) for all joints as shown in figure 2

Solution

Joints coordinates

Collect all joint and the extreme points as in the following table

Point x yR Finger 156 243R Wrist 131 224R Elbow 102 198R Shoulder 60 155L Finger 88 12L Wrist 97 40L Elbow 87 101L Shoulder 72 149R Toe 67 467R Heel 102 449R Ankle 88 441R Knee 76 354R Hip 58 267L Toe 178 288L Heel 158 277L Ankle 167 286L Knee 131 335L Hip 87 257Vertex 44 89Neck 66 152Trunk Mid ShoulderTrunk Mid Hip

66 15272.5 262

The mass ratio of any segment can be found from tables such as ,the following table

The length ratio for any segment can be found from tables such as the following

-------------(1)

1- The coordinates of segments can be found from the following equations

Sample of calculation ;CG of Right Hand ;Xcm= 131+(74.74/100)(156-131) =149.69 pixYcm= 224+(74.74/100) (243-224)= 238.2 pix

1. Construct the final table to calculate the X and Y coordinates of the center of gravity of the whole body

Segment Distal to Proximal CG Mi x y Mi . xi  Mi .yi

    (%) (%) (pix) (pix)

R Hand R Finger to R Wrist74.74% 0.56% 149.69 238.20 0.84 1.33

R Forearm R Wrist to R Elbow45.59% 1.38% 115.22 209.85 1.59 2.90

R Upper arm

R Elbow to R Shoulder

57.54% 2.55% 84.17 179.74 2.15 4.58

L Hand L Finger to L Wrist74.74% 0.56% 90.27 19.07 0.51 0.11

L Forearm L Wrist to L Elbow45.59% 1.38% 91.56 73.19 1.26 1.01

L Upper arm L Elbow to L Shoulder

57.54% 2.55% 80.63 121.38 2.06 3.10

R Foot R Toe to R Heel40.14% 1.29% 87.95 456.23 1.13 5.89

R Shank R Ankle to R Knee43.52% 4.81% 81.22 391.86 3.91 18.85

R Thigh R Knee to R Hip36.12%

14.78% 64.50 298.42 9.53 44.11

L Foot L Toe to L Heel40.14% 1.29% 166.03 281.42 2.14 3.63

L Shank L Ankle to L Knee43.52% 4.81% 146.67 313.68 7.05 15.09

L Thigh L Knee to L Hip36.12%

14.78% 102.89 285.17 15.21 42.15

TrunkMid-Shoulder to Mid-hip

37.82%

42.58% 68.46 193.60 29.15 82.44

Head-NeckVertex to Base of Neck

48.41% 6.68% 55.35 121.50 3.70 8.12

1- Finally the X and Y coordinates of the whole body can be found from the equations 2 ;

---------------(2) 2- From these equations we find ;

X=80.23 pixel and Y= 233.29 pixel Hence CG point = ( 80.23 , 233.29 )

Checking for stability ,Draw downward vertical line from CG to the base

Open picture by using Paint program

Application with Computer

From view activate , ruler, grid and status bar

Resize picture to 500 X 500 pixels

1- Locate points of all joint and line between them 2- for any joint the X,Y coordinates can easily found just by locating mouse curser on them and read from the left bottom corner

Finally make the tables and follow the procedures of the example

The End