CENTER OF GRAVITY

OUTLINES - Definition - Location Of COG- Factors Affecting Location Of COG in the body- Determination Of Total body COG

- Mathematical method

- Laboratory method- Determination Of Segmental Body COG- Value Of Determination of COG

INTRODUCTION

2 Types of Forces affecting HB

↓Internal Force & External Force

↓ GRF , GF , Resistance , Friction ,Pressure

DEFINITION OF CENTRE OF GRAVITY

- Gravitational Force (GF) : Force that pull The Body Downward.

- Centre of gravity (COG) :• is the balancing Point • Where the body is concentrated & equally distributed

• It is the point of exact center where the body rotates in

all directions • called center of mass• Sum of all forces = 0 & sum of moments =0

LOCATION OF COG- It Depends on The Body’s Shape & position- If Distribution of mass is symmetrical :• Square block or cylinder At the center of object

- If distribution of mass is asymmetrical :• Limbs of Hb Nearer to the larger & heavier end

- In a normal Person Standing position anterior 2nd sacral vertebra

N . b : The exact location is not the same between individuals since there are factors affecting it

FACTORS AFFECTING LOCATION OF COG IN THE BODY

1. Age

2.Sex

3.Movements of segments ( upward / downward / bending ..)

4.Addition and subtraction of weight

AGEThe ratio of body’s mass changes while growing up

leading to a change in COG location

COG drops down as age is increasing

COG in newborns is higher than in adults

why ??

There is no balance in body’s mass in newborn . You’ll find upper body part heavier than lower one High COG

While development , redistribution of body mass occurs lowering COG reaching ant of 2nd vertebra

Newborn

• Above umbilicus

2 years

• At Level of umbilicus

5 years

• Below umbilicus

Adults

• Anterior to second sacral vertebra

SEXHigher in males than females

COG is affected by muscular distribution

In males : oThe muscles of upper division weights more than lower division oBody build

=> COG higher o57 % of standing height

In females oThe pelvis is wider & lower than male’s pelviso55% of standing height

MOVEMENT OF SEGMENTSCOG moves toward the heavy mass

flexion of right arm COG moves :Upward Forward To the right

While running , COG will move outside of the body so the person will run forward

to return it to it’s normal place or else he will fall

ADDITION WEIGHT

This weight can be :

In front or Behind the trunk

If the weight was behind the trunk

=> COG moves backward

=> person will make a forward trunk movement or else the backward weight will pull him back

If the weight was in front the trunk

=> COG will move forward

=> person will make a backward trunk movement

=> leads to increase lumbar lordosis and back pain later on .

SUBTRACTION OF WEIGHTIn case of amputationoCOG moves away from amputated limb toward the healthy side

oTo have a normal gait and distributed body segment , the artificial limb’s weight & the normal limb’s weight should be identical

This identical limb will balance in body’s weight thus returning COG to normal

DETERMINATION OF THE LOCATION OF COG

First , locate the first action line of COG after you hang or balance the object (Ex. Book( regular body)).

Second , turn around the object 90 degree and locate the 2nd action line .

Third ,the meeting of the 2 action lines is the position of the COG.

DETERMINATION OF THE LOCATION OF COG IN IRREGULAR SHAPES

DETERMINATION OF TOTAL BODY COG:It can be determined using mathematical or laboratory method.

Mathematical Method :

1. With regarding to sex:”Croskey formula” .

2. Without regarding to sex:”Palmar formula”.

Regarding to sex:

A. In female the height of COG measured from heel =Total body height x 55.44 /100

B. In male the height of COG measured from heel =Total body height x 56.18/100

The percentage location of COG in female is 55.44 and in male is 56.18.

Regardless to sex:

Height of female and male COG measured from heel=total body height x55.7/100 +1.4

EXAMPLE ON CHANGE OF THE LOCATION OF THE TOTAL BODY COG BY 2 FORMULAS

A female of 150 cm height .

A. “Palmar formula” =150x55.7/100 +1.4= 84.95cm

B. “Croskey formula” =150x 55.44/100 =83.16 cm.

BONY LAND MARKS• Spine of the scapula.• Iliac crest.• Xiphoid process.• Anterior superior iliac spine .• Greater trochanter.

The most useful bony landmarks for measuring the height of total body COG are: Anterior superior iliac spine .Greater trochanter.

MEASUREMENT OF TOTAL BODY HEIGHT1. Initially , place an object over the top of the head.

2. Second, calculate the body height from the heel to the tragus from lateral side.

3. Third , use Palmar or Croskey formula.

4.Forth , find the relation of the total body center of gravity height to either bony or soft tissue land mark .

THE LABORATORY METHOD

“BOARD and Scale Method” or “Balance Board Method”

TRANSVERSE PLANE

TRANSVERSE PLANE

TRANSVERSE PLANES1=150 N first reading

S2=500Nsecond reading

Weight’s man =700N

S2= Wb + Wm provided by scale

Wm provided bye scale=S2-Wb=500-150=350N

*Wm provided bye scale=Upward force=R

TRANSVERSE PLANETo find X:

At equilibrium: summation T=0

TN + Tm + TR=0

Projection along positive direction

-Wm.X + R.L=0

X=-RL/-Wm

=350.100/700=50cm

The C.O.G in transverse plane of the subject’s body is 50 cm above the ground when he is standing measured from the foot.

T:Tork: rotator effect created by applied force also known as moment of force

FRONTAL PLANEWe apply the same procedure as transverse plane but the person is standing facing straight ahead

SAGITTAL PLANEWe apply the same procedure as transverse plane but the person is standing facing to one side

DETERMINATION OF SEGMENTAL BODY COG

Body Segments:The body is made up of eight segments, these segments are:1-Head and Neck 5-Hand 2-Trunk 6-Thigh3-Arm 7-Leg4-Forearm 8-Foot

The location of COG of each body segment is toward the heavier end, which is approximately 4/7 of segment length measured from distal end.

How to determine COG of any segment?

-First, the location of proximal and distal end of each segment should be in appendicular and axial skeleton, then measure the segmental length of this segment.

-Second, Mathematically multiply the segmental length by 4/7 in order to find the location of segmental COG,

Then measure the final result from the distal end.

Segments: Proximal end Distal end

Appendicular skeleton

1.Arm Acromion process Axis of elbow joint

2.Forearm Axis of elbow joint Axis of wrist joint

3.Hand Axis of wrist joint Middle finger tip

4.Thigh Greater trochanter Axis of knee joint

5.Leg Axis of knee joint Lateral malleolus

6.Foot Heel Tip of toes

Axial skeleton 7.Head and Neck Sternal notch Tragus (midpoint between (top of head) 2 shoulders)

8.Trunk Crotch Sternal notch

(midpoint between

2 hip joints )

If the body segments move in flexion as in the upper or lower limb , the COG of the entire part can be computed from the center of gravity of each segments.The single segment may be found outside the limb if it is flexed.

VALUE OF DETERMINATION OF COG

• Total Body COG• Segmental COG

TOTAL BODY COGDuring gait training of any patient the key of sucessful handling to control and support patients at the pelvis which is the COG .

The therapist may assist by grasping the patients belt or steadying the pelvis .

Total COG help to enhance the performance of athletes .

SEGMENTAL COG

In amputee patient it help to design the weight of artifical limb that will be equal to the amputated limb .

If the artifical limb increase the segmental COG will change so the total COG will change as a result they may place overload on a diseased part which cause pain .

SEGMENTAL COG

It help to determine the leverage effect of gravity .

In segment is more difficult to lift in extended position than in flexed .

Change of body segment position

away from the joint cause

an increased need for muscle

activity .

REFERENCES• Hand out• www.slide.share (Lecture to dr. shimaa Essa)• Basic Biomechanics Book-chapter13,Equilibrium and human

movement

• Handout

• http://thumb1.shutterstock.com/display_pic_with_logo/374293/374293,1271146890,4/stock-vector-full-length-profile-front-back-view-of-a-standing-naked-man-50821411.jpg

• faculty.mu.edu.sa ( Majmaah University)

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