1. 2nd lecture
COG and EQUILIBRIUM

2. 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

3. Location of COG
Depends 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.

4. The position of COG in symmetrical and asymmetrical mass.

5. Factors affect the location of COG in the human body
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.

6. Age Affecting Location of COG in the Body:
The line represents the height of COG and the point represents the umbilicus.

7. 2-Sex
The COG in males is higher than in females Because of The different mass distribution

8. 2-Sex The 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

9. 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

10. 4 - Addition and Subtraction of Weight:
a- Addition of weight:
Carrying a weight behind the trunk (backpack)
Carrying a weight in front of his trunk
in pregnant women and person who has belly abdomen.

11. 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.

12. Determination of COG Location
balancing :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.

13. 1) Determination of Total Body COG
1-MathematicaI Method:
With regarding to sex:
"Croskey formula".

14. Croskey formula Height of male COG measured from heel =
Height of female COG measured from heel =

15. 2-Laboratory Method
Board and Scale Method
In Frontal plane

16. 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

17. In Frontal and Sagittal plane

18. 2) Determination of Segmental Body COG
approximately 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.

19. During Motion
Via this method the COG of the entire part can be computed from the COG of each segment

20. Value of Determination of COG
1-Gait training
2-to improve the players' performance
3- Segmental COG must be known especially in amputation.
4-controlling the lever arm during different techniques

21. Gait training

22. 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

23. INTERNAL FORCE Muscle 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.

24. PSC changes according to muscle shape

25. 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.

26. Force exerted by multipennate |muscle is more than fusiform because it has greater PCS

27. factors that affect the magnitude of the muscular force
a- 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.

28. 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.

29. Muscular contraction
Contraction refers to active shortening of a muscle with the distance between the two muscle attachments decreasing.

30. 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.

31. 2) Eccentric (lengthening) contraction:
the external forces are greater than the internal force.
The external load produces negative work on the muscle
the. highest magnitude of the muscular force (due to the length and the passive components sharing)
in the direction of the gravity

32. 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).

33. (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.

34. (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.

35. (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.

36. 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°.

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

38. 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.

39. 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)

40. A patient uses crutches to increase BOS
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.

41. 3- An increase in the BOS should be within limit
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

42. Graduation during gait training

43. 3- Relationship between Line of Gravity and BOS:
Line of Gravity a 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)

44. 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:

45. 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".

46. 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.

47. compensatory changing curvature of the spine lordosis,kyphosis-S soliosis

48. 6- Subject State Mass Vision-> feedback
Physical and Emotional State
Age
Speedbicycle

49. EQUILIBRIUM
Definition; 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.
Types of Equilibrium
Stable
Unstable
Neutral

50. 1-Stable Equilibrium
The lower the COG and the wider the base of support the more and more equilibrium will be established

51. 2- Unstable equilibrium
If the object is displaced slightly and it tends to increase its displacement
The COG drops to a lower point when compared to the original starting position e.g. a cone

52. 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

53. Conditions of Equilibrium
1- 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