COG and EQUILIBRIUM

Center Of Gravity(COG)Definition:(center of mass)

COG is an imaginary point that the body weight can be assumed to be concentrated and equally distributed, around which body can rotate freely in all direction.At which summation of all moments equal zero

Location of COGDepends on the body’s shape and position.

In objects possess a symmetrical shape and it’s mass are equally distributed it is located exactly in the center.For asymmetrical irregular bodies the COG will be nearer the larger and heavier end.In normal standing adult person its located anterior to the second sacral vertebra .

The position of COG in symmetrical and asymmetrical mass.

Factors affect the location of COG in the human body

1. Age• In newborn: above the umbilicus.• At two years: at level of umbilicus.• At five years: below the level of the umbilicus.• In adults: anterior to the 2nd sacral vertebra.

Age Affecting Location of COG in the Body:

The line represents the height of COG and the point represents the umbilicus.

2-SexThe COG in males is higher than in females

Because of The different mass distribution

2-SexThe COG in males is higher than in females

Because of The different mass distribution

in males the upper portion is heavier than the lower portion and then COG is higher. On the other hand the female pelvis is wider and lower than the male pelvis

3 -Position of Any Segment in Relation to Total Body Segments:COG shifts towards the heavy mass

For example:flexion of right arm leads to movement of

COG upward, forward and to the right.COG during running moves outside the body

4 - Addition and Subtraction of Weight:

a- Addition of weight:Carrying a weight behind the trunk

(backpack)Carrying a weight in front of his trunkin pregnant women and person who has belly

abdomen.

b- Subtraction of weight:amputation alters the whole body weight and

the location of the COG.So during making an artificial limb the

weight of the artificial limb should be equal to the weight of the healthy limb.

Determination of COG Locationbalancing :an object in one position locates

the action line of the COG.

The intersection of these two action lines gives the location of the COG.

1) Determination of Total Body COG

1-MathematicaI Method:With regarding to sex:

"Croskey formula".

Croskey formulaHeight of male COG measured from heel =

Height of female COG measured from heel =

2-Laboratory MethodBoard and Scale Method

In Frontal plane

Clockwise Torque (1) = Counterclockwise Torque (2)

Force 1 x Distance 1 = Force 2 x Distance 2 

W x X = R x L

Where S1= weight before adding person

S2=weight after adding person

In Frontal and Sagittal plane

2 )Determination of Segmental Body COGapproximately 4/7 of the segment length

measured from distal end.

Then find mathematically the location of the segmental COG by multiplying the segmental length by 4/7. The final product is then measured from the distal end.

During Motion Via this method the COG of the entire part

can be computed from the COG of each segment

Value of Determination of COG1-Gait training2-to improve the players' performance

3- Segmental COG must be known especially in amputation.

4-controlling the lever arm during different techniques

Gait training

The action line of gravity.Weight "W" does not change its direction as

the arm is elevated or lowered.a = lever arm: a1, a2, a3 = changes in lever

arm

INTERNAL FORCEMuscle Force

The size and structure of the muscle affect the magnitude of the force exerted by this muscle.

physiological cross section (PCS): The PCS is a perpendicular section,

which cuts all muscle fibers at its thickest part while the muscle is in the midway between complete, contraction and complete stretch.

PSC changes according to muscle shape

1- If the muscle fibers are oriented in a parallel or fusiform shape in which the muscle fibers run parallel to the muscle tendon, the PCS is a single section which cuts all muscle fibers.

2- If the muscle fibers are oriented in a pennate shape in which the fibers pass obliquely at an angle with a central tendon, the PCS is achieved by multiplying the muscle width by the sum of perpendicular lines that cut all muscle fibers. All muscle fibers must be included and each muscle fiber must not cut twice.

Force exerted by multipennate |muscle is more than fusiform because it has

greater PCS

factors that affect the magnitude of the muscular forcea- Arrangement of musclefibers; fusiform or

penriate.b- Width of the muscle; circumference.c- Sex; PCS and muscle force is bigger in

male than female.d- Age; PCS and muscle force decreases by

aging.

Muscle strength: Is the maximum ability of the muscle to

lift weight for one time. It is the maximum force (tension) which the muscle can produce per unit cm2 (PCS).

It was found that each cm2 of the muscle could produce muscular tension of 3-4 kg and up to 9 kg. If a muscle has PCS of 10 cm2, its muscle strength reaches 90 kg.cm2.

Muscular contractionContraction refers to active

shortening of a muscle with the distance between the two muscle attachments decreasing.

1 )Concentric (shortenins) contraction:

the internal forces generated by the muscle are greater than the external forces applied

The muscle produces positive work on the external load (work = force x distance).

The movement occurs against gravity and the joint moves towards the inner range.

produces the lowest magnitude of the muscular force.

NB direct relationship between the muscle length and the tension produced by the muscle. As the muscle length decreases, the tension decreases.

2 )Eccentric (lengthening) contraction:the external forces are greater than the

internal force.The external load produces negative work on

the musclethe. highest magnitude of the muscular force

(due to the length and the passive components sharing)

in the direction of the gravity

overall muscle length does not change.The internal force generated by the muscle

equals the effects of the external forces.no mechanical work is done.produces intermediate magnitude of the

muscular force .(more than concentric and less than

eccentric).

(2) Direction of the muscle force:The direction of the muscle force

depends on the movement manner. When the distal part moves on the

proximal, the direction is upward. When, the proximal part moves on the distal, the direction is downward.

(3) Point of application of the muscle force:

The point of application is represented by the bony attachments at each end of the muscle i.e. the origin and the insertion. The most common point representing the muscular force is the insertion.

(4) Line of application of the muscle force:The line of application is represented by

the angle of pull or angle of insertion of the muscle, which is defined as the angle located between the action line of the muscle and its insertion at the bone. This angle of pull changes according to the range at which the muscle acts.

The effect of angle of pull of the muscle on the magnitude of the rotatory and nonrotatory component at three different angles of pull (a) at 30°, (b) at 90° and (c) at 120°.

STABILITYDefinition:Stability is the ability to maintain one's balance in both static and dynamic situations without use of mechanical devices.

Factors Affecting Stability:1-Center of gravity height.(standing and

kneeling_ high heel)2-Base of support (BOS). (supporting area

under the body)3-Relationship between line of gravity and

BOS.4-Characteristics of the supporting surface.5-Segmentation principle.6-Subject's state.

BOS:1 -An increase in the BOS will be associated

with an increase in the stability.2-The increase in the shape of the BOS occurs

in the direction of force being applied to the body.(wrestling)

A patient uses crutches to increase BOS. in A and B, the base increases in the anteroposterior direction, in C stability increases in the lateral direction.

3- An increase in the BOS should be within limit. During walking, the angle of the step determines the stability.

(angle between the line of force of the leg (F) and the vertical line. The force)

The same for the crutch

Graduation during gait training

3 -Relationship between Line of Gravity and BOS :

Line of Gravitya vertical line that passes through the GOG and falls within the BOS.

The nearer the line of gravity (LOG) to the center of BOS, the greater the stability.(stride standing and standing on toes)

Supporting Surface:a- Friction: up to certain limit or it will limit

motion -So basketball or football players wear rubber-

soled shoes-use crutches with rubber ends, blanket on the

bed b- Inclination of the supporting surface:

5- Segmentation Principle:"If there is deviation of a part of the body to

certain direction, there is another compensatory deviation of another part of the body to the opposite direction to maintain balance during this position".

A load carried as near as possible to the midline of the body will minimize the necessary movements of the body segments and also muscle and ligament strain.

compensatory changing curvature of the spinecompensatory changing curvature of the spinelordosis,kyphosis-S soliosislordosis,kyphosis-S soliosis

6 -Subject StateMassVision-> feedbackPhysical and Emotional StateAgeSpeedbicycle

EQUILIBRIUMDefinition;

Equilibrium is a state of balance in which all forces are equal. A body is said to be in equilibrium when the resultant of all forces acting upon it is zero.

1-Stable EquilibriumThe lower the COG and the wider the base of

support the more and more equilibrium will be established

2 -Unstable equilibriumIf the object is displaced slightly and it tends

to increase its displacementThe COG drops to a lower point when

compared to the original starting position e.g. a cone

3 -Neutral equilibrium;if it comes to rest in a new position without a

change in the level of the COG either upwards or downwards

E.g. A ball

Conditions of Equilibrium1- If the body is at rest, with the velocity

equaling zero, it is said to be in static equilibrium.∑F = 0, ∑M = 0

2- If the constant velocity is not zero, the equilibrium is called dynamic equilibrium