1. Introduction to Biomechanics
柴惠敏
台灣大學 物理治療學系

2. Content of Physical Therapy
CLINICAL
aspect
TEACHING
aspect
RESEARCH
aspect

3. Introduction to Biomechanics
About Biomechanics
Applications of biomechanics
Definition of biomechanics
Development of biomechanics
Scopes of biomechnics
Physical Quantities
Review of Basic Mathematics
Review of Basic Statics
Review of Basic Dynamics

4. Applications of Biomechanics
physical therapy and rehabilitation
ergonomics or industrial medicine
sports medicine
movement science or kinesiology
performance arts
bioengineering
forensic medicine
entertainment arts

5. Who Should Take This Class?
industrial/ production/ manufacturing/ process engineer
orthopedic/ occupational medicine/ rehabilitation medicine physician or nurse
physical therapist/ occupational therapist
ergonomist/ biomechanist/ kinesiologist
coach/ athlete/ sports manager
industrial hygienist/ safety manager/ labor relations manager
forensic medicine physician, staff, spy.....
entertainment specialist/ actor or actress

6. Jobs in Ergonomic Students
400 attendees in occupational ergonomics summer class at UM
engineer 11%
occupational medicine physician or nurse 16%
orthopedic or rehabilitation medicine physician/ PT/ OT 45%
ergonomist/ biomechanist 4%
safety manager/ labor relations managers 8%
other 16%

7. Broad Definition of Biomechanics
the study of the physical science and mechanics of living systems
Physical properties of biological materials
Biological signals and their measurements
Biomechanical modeling and simulation
Applications of biomechanics
Biomechnics is a discipline of science, newly developed and in the process of becoming established.

8. Limited Definition of Biomechanics
the science that examines forces acting upon and within a biological structure and effects produced by such forces (Hay, 1973)
forces: external and internal forces
effects: movements of segments of interest
deformation of biological materials
biological changes in the tissues
Biomechnics is a discipline of science, newly developed and in the process of becoming established.

9. Development of Biomechanics
Galioleo Galilei
William Harvey
Stephen Hales
YC Fung
WT Dempster
DB Chaffin
D Winter
Frankel and Nordin

10. Scopes of Musculoskeletal Biomechanical Research
the functioning of muscles, tendons, ligaments, cartilage, and bone
the load and overload of specific structures of living systems
factors influencing performance

11. Types of Injury Mechanism
Outcomes
Trauma Type
Factor
sudden force
impact trauma
contusions, fractures, ligament sprain, dislocations, death, etc.
repetitive activity
overuse injuries
tendinitis, osteoarthritis, myofascial pain, nerve entrapment, etc.

12. Knowledge Needed in Biomechanical Studies
Mathematics
Physics
Mechanics: statics, dynamics, fluid mechanics
Biology and Medicine
Neurophysiology
Behavior science

13. Subjects of Study for Human Biomechanics
disable vs. able
athletes vs. non-athletes
workers vs. non-workers
kids vs. adults
elderly vs. young

14. Biomechanics--Methodology
anthropometric methods
kinesiological methods
kinematic method: focus on movement
kinetic method: focus on forces
biomechanical modeling methods
mechanical work capacity methods
bioinstrumentation methods
classification & time prediction methods

15. Introduction to Biomechanics
About Biomechanics
Physical Quantities
Dimension system
Unit conversion
Standard prefix
Review of Basic Mathematics
Review of Basic Statics
Review of Basic Dynamics

16. Fundamental Physical Quantities
Physical Quantity SI Unit
Length (L)
Mass (M)
Time (T)
Electric Current
Temperature
Luminous Intensity
Amount of Substance
metre (m)
kilogramme (kg)
second (s)
ampere (A)
degree Kelvin (K)
candela (cd)
mole (mol)
Length: the distance between two precise marks
Mass: the amount of material
Time: solar day/ 24/ 3600 = sec
electric current: the amount of electricity passed by 1 volt in 1 second against a resistance of 1 ohm.
Attractive force generated by magnetic fields between 2 parallel wires conducting electric current in opposite directions

17. Derived Quantities: Example 1
Displacement:
d = x2 – x1
Velocity:
v = dx/dt = x
Acceleration:
a = dv/dt = x
time . ..

18. Derived Quantities: Example 2
angle:
 = 2 - 1
Velocity:
 = d  /dt = 
Acceleration:
 = d  /dt = 
time . ..

19. Derived Quantities: Example II
Force derived from
mass
time
distance
F = m a
Newton (N) = kg·m/s2
acceleration=
1 m/s2 m=
1 kg
force=1 N

20. Scalar vs. Vector Quantities
Scalar quantities
quantities with magnitude only
e.g. speed of 5 m/s
Vector quantities
quantities with magnitude and direction
e.g. velocity of 5 m/s to right

21. Dimensionless Quantities
percentage
percentile
the fifth percentile
the 25th percentile = 1st quartetile
the 50th percentile = 2nd quartertile median
the 75th percentile = 3rd quartetile
the 95th percentile
the 99th percentile
the 100th percentile = 4th quartetile

22. Unit Conversion Metric System English System CGS system MKS system
SI system (Systeme International d'Unites; the International System of Units)
for details:
English System

23. Unit of Mass In MKS system: 1 kilogram (kg) In CGS system:
1 g = 10-3 kg
In English system:
1 foot (lb) = kg
1 kg = lb
1 ounce = g = 1/16 lb

24. Unit of Length In MKS system: 1 meter (m) In CGS system:
1 cm = 10-2 m
In English system:
1 foot (ft) = m
1 m = ft
1 inch = 25.4 mm = 1/12 ft

25. Standard Prefix Giga (G) =109 mega (M) = 106 kilo (k) = 103
centi (c) = 10-2
milli (m) = 10-3
micro () = 10-6
naro (n) = 10-9

26. Introduction to Biomechanics
About Biomechnics
Physical Quantities
Review of Basic Mathematics
Plane Geometry
Trigonometry
Vector
Review of Basic Statics
Review of Basic Dynamics

27. Plane Geometry angles, sides, and area of a triangle
angles, sides, and area of a polygon
radius, diameter, circumference, and area of a circle
arc length and area of a sector of a circle

28. Triangle
Area = a·h h a

29. Angle define an angle between 2 lines units used to measure angles
degree (deg)
radians (rad) = 57.9 degrees
orthogonal projections of a line segment onto two perpendicular axes 

30. Trigonometric Relationship
Sine (sin): sin  = a / c
Cosine (cos): cos  = b / c
Tangent (tan): tan  = a / b
Arc Sine:  = sin-1 (a / c)
Arc Cosine:  = cos-1 (b / c)
Arc Tangent:  = tan-1 (a / b) a b c 

31. Trigometric CalculationB C b a c
Law of sine
Law of Cosine

32. Solutions of An Arbitrary Triangle
knowing 3 sides to determine the angles
knowing 2 sides and 1 angle to find the rest of the angles and sides
knowing 2 angles and 1 side to find the rest of the angles and sides
determine of area of a triangle

33. Area of Triangle
given 2 sides and 1 angle
given 3 sides
where

34. Characteristics of Vector
magnitude
point of
application
sense
line of action

35. Vector Calculation vector addition or subtraction vector decompostion
parallelogram law
triangle construction
vector decompostion
expressed by unit vectors:  
for 2D system: FR = SFx + SFy  
for 3D system: FR = SFx + SFy + SFz 

36. Unit Vector x z y
Vector FR
= Fx + Fy + Fz Fx Fz Fy

37. Composition of Vectors
Graphic method
Algebraic method: (xi yi zi)

38. Introduction to Biomechanics
About Biomechnics
Physical Quantities
Review of Basic Mathematics
Review of Basic Statics
Force
Mechanical advantage
Centroid
Equilibrium
Free body diagram
Force couple
Review of Basic Dynamics

39. Mechanical Forces An entity that changes the state of motion of a body
not necessary to be in contact
e.g. gravity on an airplane
unit: Newton (N) = kg·m/s2
a force that causes linear acceleration of a free mass of 1 kg at 1 m/s2

40. Unit of Force In MKS system: 1 Newton (N) In CGS system:
the force that tends to cause a body with a mass of 1 kg to undertake a linear acceleration of 1 m/s2
In CGS system:
1 dyne = 1 g·cm/s2 = N
In English system:
1 lb·ft/s2 = kg·0.305 m/s2
= kg·m/s2 = N

41. Weight A specific type of force that is the result of gravity
earth’s gravity
for a mass of 1 kg = 9.81 N
for a mass of 1 lb = 4.45 N
Gravity varies from 9.78 to 9.83 at sea level, depending on latitude.
Standard gravity = N

42. Forces External forces (Loads) Internal forces force of gravity
ground reaction force
friction force
air or water resistance
Internal forces
muscle forces
forces from tendon, ligament, or other connective tissues

43. Force of Gravity
gravitational force: an acceleration resulting from the earth
g = 1 m2/s
W = mg
1 kg weight = 9.81 N

44. Ground Reaction Force
A reaction force from the ground as the weight is in contact with the ground
6 degree of freedom
Fx − Mx
Fy − My
Fz − Mz

45. Degree of Freedom (DOF)
A minimal number of variables required to solve an equation
A minimal number of kinematic variables (coordinates) required to specify all positions and orientations of the body segments in the system
A minimal number of kinetic variables required to describe the force

46. Moment Moment (M) = Torque (T) rotational effect of a force
tending to cause angular acceleration and displacement
Any non-axial force has this effect.
M = F·d
unit: Nm F d M

47. Holding A Ball D3 =? What if the attachment
of the biceps is more distal?
Wball d2 d1 d3
Wforearm

48. Friction Force resistance between 2 objects static friction Fs = s N
where N = normal force
s = coefficient of static friction
dynamic friction
Fk = k N
k = coefficient of dynamic friction

49. Skiing on the Snow 600 N 30 N if  = 0.05 fixed if  = 1
No friction if = 0

50. Air or Water Resistance
the resistance encountered by a body moving through air or water
Fa = Av2c
where A = surface area of the body
directed forward
v = velocity of the body
c = constant

51. Water Resistance – Same Surface Area
view from the front view from the side

52. Water Resistance – Different Surface Area
view from the front view from the side A A

53. Internal Force Muscle force Tension from connective tissue
Joint reaction force

54. Joint Reaction Force W 
FJR = W
MJR = W·dcos
MJR
FJR d

55. Mechanical Advantage
ratio between the length of the force arm and the length of weight arm

56. Types of Lever first-class lever second-class lever third-class lever
Fx = Wx’ x x’
Wforearm

57. Centroid The point that defines the geometric center of an object
If the material composing a body is homogeneous, the weight can be neglected

58. COM of One Body Segment X= [ L (S-S’) / W ] +X’ W X WX = SL S X’ W

59. Newton’s First Law law of inertia If F = 0 then v = constant
A particle remains at rest or in a uniform state of motion if it is not acted upon by any net external force
If F = 0 then v = constant
By Isaac Newton, 1686

60. Newton’s Second Law law of acceleration F = ma
Acceleration of a particle is proportional to the unbalanced force acting on it and inversely proportional to the mass of the particle
F = ma
By Isaac Newton, 1686
1 kg
1 N
1 m/s
acceleration

61. Newton’s Third Law law of action and reaction Faction = F reaction
For every action, there is an equal and opposite reaction
Faction = F reaction
action
reaction
By Isaac Newton, 1686

62. Equilibrium
a condition in which an object is at rest if originally at rest, or has a constant velocity if originally in motion
 F = F resultant = 0 AND
 M = M resultant = 0

63. Free Body Diagram (FBD)W
GRF d
COP
COM
Ankle

64. Composition of Force Vectors
Graphic method
Algebraic method: (xi yi zi)

65. Force Couple
two parallel forces that have the same magnitude, opposite directions, and are separated by a perpendicular distance
F1 = - F2  F = 0
M = (r1 – r2 )F
= 2 r1 F  0 r1 r2 F1 F2

66. Introduction to Biomechanics
About Biomechnics
Physical Quantities
Review of Basic Mathematics
Review of Statics
Review of Dynamics

67. Dynamics
the study of the motion of bodies and the unbalanced forces that produce motion

68. Equation of Motion Newton’s 2nd Law: (Law of Acceleration) F = ma
A particle acting upon by an unbalanced force experiences an acceleration that has the same direction as the force and a magnitude that is directly proportional to the force
F = ma

69. Analysis Methods in Dynamics
Direct dynamics
F known  acceleration  displacement
e.g. using force plate
Inverse dynamics
displacement known  acceleration  F
e.g. using video-based motion analysis

71. Measurement Lord Kelvin
When you can measure what you are speaking about and express it in numbers, you know something about it.

72. Basic Concepts in Physics
Matter
Inertia
body

73. Matter basic substance of the universe composed of atoms and molecules
occupy only one place at one time

74. Inertia
physical property of matter, which resists any change in the state of motion
inertia  mass

75. Body
Indicate an object that may be real or imaginary but represents a definite quantity of matter (mass), with certain dimensions, occupying a definite position in space

76. Particle
Imaginary entity similar to body, but it implies an infinitely small quantity of matter (with zero dimensions) that occupies a definite position in space , or on or within a body
These variation are not postural defects. They are part of child’s method of response to the demands of gravity.

77. Point
Refers to a specific, infinitely small, location in space or on or in a body
no any quantity of matter
no inertia