lecture in Biomechanics for Biomedical engineering students

1. ANGULAR KINEMATICS

2. ANGULAR KINEMATICS
 Same as linear kinematics, but…
 There is one vector
along the moment arm.
 There is one vector perpendicular
to the moment arm.
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3. ANGULAR KINEMATICS
 Translational vs Rotational
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4. ANGULAR KINEMATICS
Vectors
 Remember :
 Vectors are representative of the Magnitude of a resultant Force.
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5. ANGULAR KINEMATICS
Vectors
 A vector is an abstract mathematical object with two properties: or
magnitude (length), and direction
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6. ANGULAR KINEMATICS
Moment Arm
 The Moment Arm (M) is:
 the perpendicular distance from the line of
resultant force to the fulcrum (joint axis), A ,
.
or
 The distance from axis of rotation to the
point of muscle insertion, B.
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7. ANGULAR KINEMATICS
Moment Arm
 Torque, or rotational force, is:
 A product of the rotational
component( )× the moment arm.
or
 The resultant force of muscular
contraction ( ) × perpendicular distance
from to axis of rotation.
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8. ANGULAR KINEMATICS
Angular Kinematic Analysis
Angular Kinematics
 Description of the circular motion or rotation of a body
Motion described in terms of (variables):
 Angular position and displacement.
 Angular velocity.
 Angular acceleration
Rotation of body segments
 Flexion of forearm about transverse axis through elbow joint centre
Rotation of whole body
 Rotation of body around centre of mass (CM) during somersaulting.
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9. ANGULAR KINEMATICS
Absolute and Relative Angles
Absolute angles
 Angle of a single body segment, relative to
(normally) aright horizontal line (e.g. trunk,
head, thigh)
Relative Angles
 Angle of one segment relative to another (e.g.
knee, elbow, ankle)
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10. ANGULAR KINEMATICS
Units of Measurement
Angles are expressed in one of the following units:
 Revolutions (Rev)
 Normally used to quantify body rotations in diving, gymnastics
etc.
 1rev = 360 or 2 π radians
 Degrees )
°
(
 Normally used to quantify angular position,
distance and displacement.
 Radians (Rad)
 Normally used to quantify angular velocity and acceleration.
 Convert degrees to radians by dividing by 57.3
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11. ANGULAR KINEMATICS
Method of Problem Solution
 Problem Statement:
 Includes given data, specification of showing all quantities involved.
 Free-Body Diagrams:
 Create separate diagrams for each ofthe bodies involved with a
clear indication of all forces acting on each body.
 Fundamental Principles:
 The six fundamental principles are applied to express the conditions
of rest or motion of each body.
 The rules of algebra are applied to solve the equations
for the unknown quantities.
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12. ANGULAR KINEMATICS
Method of Problem Solution
Solution Check:
 Test for errors in reasoning by computed results are correct,
 Test for errors in computation by substituting given data and
computed results into previously unused equations based on the six
principles,
 Always apply experience and physical intuition to assess whether
results seem “reasonable”
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13. ANGULAR KINEMATICS
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Free Body Diagrams
Space diagram represents the sketch of the physical problem.
Thefree body diagram selects the significant particle
or points and draws the force system on that particle or point.
Steps:
1) Imagine the particle to be isolated or cut free
from its surroundings.
 Draw or sketch its outlined shape.

14. ANGULAR KINEMATICS
Free Body Diagrams
Steps:
2) Indicate on this sketch all the forces that act on the particle.
 These include:
i. Active forces
 Tend to set the particle in motion
e.g. from cables and weights.
ii. Reactive forces
 caused by constraints or supports that prevent motion.
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15. ANGULAR KINEMATICS
Free Body Diagrams
3)Label known forces with their magnitudes and directions.
4)Use letters to represent magnitudes and directions of unknown
forces.
5)Assume direction of force which may be corrected later.
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16. ANGULAR KINEMATICS
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Free Body Diagrams
 Free Body Diagram is the most important analysis tool
 It aids in identification of external forces.
 Procedure
Identify the object to be isolated.
Draw the object isolated (with relevant dimensions).
Draw vectors to represent all external forces.

17. ANGULAR KINEMATICS
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Free Body Diagrams
Internal / External Force
 Depends on choice of object

18. ANGULAR KINEMATICS
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Free Body Diagrams
 First step in the static equilibrium analysis of a
rigid body is identification of all forces acting
on the body with a free-body diagram.
 Select the extent of the free-body and detach it
from the ground and all other bodies.
 Indicate:
 Point of application
 magnitude, and direction of external forces.
 Rigid body weight.

19. ANGULAR KINEMATICS
Free Body Diagrams
Indicate point of application and assumed
direction of unknown applied forces.
These usually consist of reactions through
which the ground and other bodies oppose the
possible motion of the rigid body.
Include the dimensions necessary to compute
the moments of the forces.
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20. ANGULAR KINEMATICS
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Free Body Diagrams
Problem 1:
A fixed crane has a mass of 1000 kg and is used
to lift a 2400 kg crate. It is held in place by a pin
at A and a rocker at B. The center of gravity of
the crane is located at G.
Determine the components of the reactions at A
and B.

21. ANGULAR KINEMATICS
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Free Body Diagrams
Homework Problem(Solution)
Create a free-body diagram for the crane.
Determine B by solving the equation for the sum of the moments of all
forces about A. Note there will be no contribution from the unknown
reactions at A.
Determine the reactions at A by solving the equations for the sum of
all horizontal force components and all vertical force components.
Check the values obtained for the reactions by verifying that the sum
of the moments about B of all forces is zero.

22. ANGULAR KINEMATICS
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Free Body Diagrams
 Problem 2
 A man raises a 10 kg joist, of length 4 m, by pulling on a
rope.
 Find:
 The tension in the rope.
 The reaction at A.

23. ANGULAR KINEMATICS
The three forces must be concurrent for
static equilibrium.
Therefore, the reaction R must pass
through the intersection of the lines of
action of the weight and rope forces.
Utilize a force triangle to determine the
magnitude of the reaction force R.
Utilize a force triangle to determine the
magnitude of the reaction force R.
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Free Body Diagrams
Problem 2(Solution)
Create a free-body diagram of the joist. Note that the joist is a 3
force body acted upon by the rope, its weight, and the reaction at A.

24. ANGULAR KINEMATICS
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Lever Systems
A lever is a rigid bar (bone( that turns about an axis of rotation or
fulcrum (joint).
Most motion at the major joints results from the body's structures
acting as a system of levers.
Many of the muscles and bone systems of the body act as levers.
Lever arm: Is the perpendicular distance from theaxis of rotationto
the line along which the force acts.

25. ANGULAR KINEMATICS
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Lever Systems
 Levers are classified into three classes, first, second and third class
according to the position of three point which are:
1. F (or A): Fulcrum point (point at the joint).
2. W (or R): the Resistance force (weight or load)
3. M (or F): the applied force(muscle force or active force).

26. ANGULAR KINEMATICS
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Lever Systems
1.In the first class lever, the fulcrum is
placed between the load and the active
force as in the head.
1.In the second class lever, the load is
placed between the fulcrum and the active
force as in the foot.
1.In the third class lever, the muscle force is
placed between the fulcrum and the load
as in the arm.

27. ANGULAR KINEMATICS
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Lever Systems: First Class
Designed for speed and range of motion when the axis is closer to
the force
Designed for strength when the axis is closer to the resistance

28. Neck extension Erector spinae and Splenius
ANGULAR KINEMATICS
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Lever Systems: First Class
FAR

29. ANGULAR KINEMATICS
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Lever Systems: Second Class
 Designed more for force.
ARF

30. Plantar flexion Gastrocnemius and Soleus
ANGULAR KINEMATICS
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Lever Systems: Second Class
 Designed more for force.

31. ANGULAR KINEMATICS
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Lever Systems: Third Class
 Designed more for speed and range of motion.
A FR

32. Elbow flexion Biceps Brachii and Brachialis
ANGULAR KINEMATICS
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Lever Systems: Third Class
 Designed more for speed and range of motion.

33. ANGULAR KINEMATICS
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Lever Systems
 The third class levers are the most common one in the body, the second
class levers are next in number and the first class levers are the least
common one.
 The functions of the levers are:
 Increase the effect of an applied force (Increasing the moment arms).
 Increase the effective velocity of movement
 Alter the resulting direction of the applied force.
 The muscle force acts against aresistance (weight, gravity, opponent,
etc.).

34. ANGULAR KINEMATICS
Lever Systems: Levers Comparison
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35. ANGULAR KINEMATICS
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36. ANGULAR KINEMATICS
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Lever Systems: Factors In Use of Anatomical Levers
A lever system can be balanced if the F and FA equal the R and
RA.

37. Balance with less
ANGULAR KINEMATICS
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Balance with more
Lever Systems: Factors In Use of Anatomical Levers

38. ANGULAR KINEMATICS
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Lever Systems: Factors In Use of Anatomical Levers
A lever system can become unbalance when enough torque is
produced.
Torque is the turning effect of a force; inside the body it caused
rotation around a joint.
Torque = Force (from the muscle) x Force Arm
(distance from muscle insertion from the joint).

39. Force is produced by the muscle.
FA the distance from joint (i.e .axis or
fulcrum) to insertion of the force
Resistance could be a weight, gravity, etc.
RA the distance from joint to the center of the
resistance.
ANGULAR KINEMATICS
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Lever Systems: Practical Application

40. ANGULAR KINEMATICS
Lever Systems: Summary
 The actual torque needed to move a given resistance depends on the
length of the FA and RA.
 As the FA increases or RA decreases, the required torque decreases.
 As the FA decreases or RA increases, the required torque increases.
 Inside the body, several joints can be "added“ togetherto increase
leverage (e.g. shoulder, elbow, and wrist.
 An increase in leverage can increase velocity.
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