Download Introduction to Biomechanics

Introduction to Biomechanics
柴惠敏
台灣大學 物理治療學系
Content of Physical Therapy
CLINICAL
aspect
TEACHING
aspect
RESEARCH
aspect
Introduction to Biomechanics
 About Biomechanics
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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
Applications of Biomechanics
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physical therapy and rehabilitation
ergonomics or industrial medicine
sports medicine
movement science or kinesiology
performance arts
bioengineering
forensic medicine
entertainment arts
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
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%
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
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
Development of Biomechanics
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Galioleo Galilei
William Harvey
Stephen Hales
YC Fung
WT Dempster
DB Chaffin
D Winter
Frankel and Nordin
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
Types of Injury Mechanism
Factor
Trauma Type
Outcomes
sudden
force
impact
trauma
contusions, fractures,
ligament sprain,
dislocations, death, etc.
repetitive
activity
overuse
injuries
tendinitis, osteoarthritis,
myofascial pain, nerve
entrapment, etc.
Knowledge Needed in
Biomechanical Studies
• Mathematics
• Physics
• Mechanics: statics, dynamics,
fluid mechanics
• Biology and Medicine
• Neurophysiology
• Behavior science
Subjects of Study for
Human Biomechanics
• disable vs. able
• athletes vs. non-athletes
• workers vs. non-workers
• kids vs. adults
• elderly vs. young
Biomechanics--Methodology
• anthropometric methods
• kinesiological methods
– kinematic method: focus on movement
– kinetic method: focus on forces
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biomechanical modeling methods
mechanical work capacity methods
bioinstrumentation methods
classification & time prediction methods
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
Fundamental Physical Quantities
Physical Quantity
Length (L)
Mass (M)
Time (T)
Electric Current
Temperature
Luminous Intensity
Amount of Substance
SI Unit
metre (m)
kilogramme (kg)
second (s)
ampere (A)
degree Kelvin (K)
candela (cd)
mole (mol)
Derived Quantities: Example 1
• Displacement:
d = x 2 – x1
• Velocity:
v = dx/dt = x.
• Acceleration:
a = dv/dt = ..
x
time
Derived Quantities: Example 2
• angle:
 = 2 - 1
• Velocity:
.
 = d  /dt = 
• Acceleration:
 = d  /dt = ..
time
Derived Quantities: Example II
• Force derived from
– mass
– time
– distance
acceleration=
force=1 N
• F=ma
• Newton (N) = kg·m/s2
m=
1 kg
1 m/s2
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
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
Unit Conversion
• Metric System
– CGS system
– MKS system
– SI system (Systeme International d'Unites;
the International System of Units)
• for details:
http://physics.nist.gov/cuu/Units/index.html
• English System
Unit of Mass
• In MKS system: 1 kilogram (kg)
• In CGS system:
– 1 g = 10-3 kg
• In English system:
– 1 foot (lb) = 0.454 kg
– 1 kg = 2.205 lb
– 1 ounce = 28.350 g = 1/16 lb
Unit of Length
• In MKS system: 1 meter (m)
• In CGS system:
– 1 cm = 10-2 m
• In English system:
– 1 foot (ft) = 0.305 m
– 1 m = 3.281 ft
– 1 inch = 25.4 mm = 1/12 ft
Standard Prefix
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Giga (G) =109
mega (M) = 106
kilo (k) = 103
centi (c) = 10-2
milli (m) = 10-3
micro () = 10-6
naro (n) = 10-9
Introduction to Biomechanics
• About Biomechnics
• Physical Quantities
 Review of Basic Mathematics
– Plane Geometry
– Trigonometry
– Vector
• Review of Basic Statics
• Review of Basic Dynamics
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
Triangle
h
a
Area = a·h
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

Trigonometric Relationship
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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)
c
a

b
Trigometric Calculation
• Law of sine
a
b
c


sin A sin B sin C
• Law of Cosine
a  b  c  2bc cos A
2
2
2
a
c
B
A
C
b
Solutions of An Arbitrary Triangle
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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
Area of Triangle
• given 2 sides and 1 angle
A  1 bc sin A  1 ab sin C  1 ca sin B
2
2
2
• given 3 sides
A  s(s  a)( s  b)( s  c)
where s  a  b  c
2
Characteristics of Vector
magnitude
point of
application
line of action
sense
Vector Calculation
• vector addition or subtraction
– parallelogram law
– triangle construction
• vector decompostion
• expressed by unit vectors:
– for 2D system: FR = SFx + SFy
– for 3D system: FR = SFx + SFy + SFz
Unit Vector
z
Fz
Vector FR
= Fx + Fy + Fz
x
Fy
y
Fx
Composition of Vectors
• Graphic method
• Algebraic method: (xi yi zi)
Introduction to Biomechanics
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About Biomechnics
Physical Quantities
Review of Basic Mathematics
Review of Basic Statics
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Force
Mechanical advantage
Centroid
Equilibrium
Free body diagram
Force couple
• Review of Basic Dynamics
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
Unit of Force
• In MKS system: 1 Newton (N)
– 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 = 10- 5 N
• In English system:
– 1 lb·ft/s2 = 0.454 kg·0.305 m/s2
= 0.138 kg·m/s2 = 0.138 N
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
Forces
• External forces (Loads)
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force of gravity
ground reaction force
friction force
air or water resistance
• Internal forces
– muscle forces
– forces from tendon, ligament, or other
connective tissues
Force of Gravity
• gravitational force: an acceleration
resulting from the earth
• g = 1 m2/s
• W = mg
– 1 kg weight = 9.81 N
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
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
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
F
d
• unit: Nm
M
Holding A Ball
D3 =?
What if the attachment
of the biceps is more distal?
d3
Wforearm
d2
d1
Wball
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
where N = normal force
k = coefficient of dynamic friction
Skiing on the Snow
600 N
30 N if  = 0.05
fixed if  = 1
No friction if = 0
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
Water Resistance –
Same Surface Area
view from the front
view from the side
Water Resistance –
Different Surface Area
view from the front
A
A
view from the side
Internal Force
• Muscle force
• Tension from connective tissue
• Joint reaction force
Joint Reaction Force
FJR = W
FJR
MJR = W·dcos
MJR

d
W
Mechanical Advantage
• ratio between the length of the force arm
and the length of weight arm
AL(force)
MA 
AL(weight)
Types of Lever
• first-class lever
• second-class lever
• third-class lever
Fx = Wx’
x’
x
Wforearm
Centroid
• The point that defines the geometric
center of an object
• If the material composing a body is
homogeneous, the weight can be
neglected
COM of One Body Segment
X= [ L (S-S’) / W ] +X’
W
X
WX = SL
S
X’
W
WX’ = S’L
L
S’
Newton’s First Law
• law of inertia
– 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
Newton’s Second Law
• law of acceleration
– Acceleration of a particle is proportional to
the unbalanced force acting on it and
inversely proportional to the mass of the
particle
• F = ma
1 kg
1N
1 m/s
acceleration
Newton’s Third Law
• law of action and reaction
– For every action, there is an equal and
opposite reaction
• Faction = F reaction
action
reaction
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
Free Body Diagram (FBD)
COM
W
d
Ankle
COP
GRF
Composition of Force Vectors
• Graphic method
• Algebraic method: (xi yi zi)
Force Couple
• two parallel forces that have the
same magnitude, opposite directions,
and are separated by a perpendicular
distance
• F1 = - F2  F = 0
F1
• M = (r1 – r2 )F
r1
= 2 r1 F  0
F2
r2
Introduction to Biomechanics
• About Biomechnics
• Physical Quantities
• Review of Basic Mathematics
• Review of Statics
 Review of Dynamics
Dynamics
• the study of the motion of bodies and the
unbalanced forces that produce motion
Equation of Motion
• Newton’s 2nd Law: (Law of Acceleration)
– 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
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
Measurement
• Lord Kelvin
When you can measure what you are
speaking about and express it in
numbers, you know something about it.
Basic Concepts in Physics
• Matter
• Inertia
• body
Matter
• basic substance of the universe
• composed of atoms and molecules
• occupy only one place at one time
Inertia
• physical property of matter, which resists
any change in the state of motion
• inertia  mass
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
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
Point
• Refers to a specific, infinitely small,
location in space or on or in a body
• no any quantity of matter
• no inertia