Download After completing this topic, the students will be able to

國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
After completing this topic, the students will be able to
1. define the quantities related to or derived from forces
2. describe the instruments that are commonly used to measure the force or strength
3. explain the factors that influence the change of force or strength
4. distinguish the difference between force and strength
Readings:
1. Chaffin’s book, pp.101-124, 146-158, 167-170
2. Frankel and Nordin
Relationship of Force and Body
A. Force
1. an action that changes the state of rest or motion of a body to which it is applied
2. external force vs. internal force
3. strength: maximum force that a body can be loaded
-- muscle strength: the maximum force that a muscle can develop under prescribed condition
4. stress: load per unit
B. Body
1. indicates 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
2. rigid body vs. deformed body
C. Effects of forces on a body
1. motion of that body in dynamic sense
2. deformation of that body in static sense
3. biological changes
a. growth
b. injury
c. degeneration
External Forces Acting on Human Body
A. Classification
1. force of gravity (g)
a. the force resulting from the action of the earth to draw all objects towards the earth’s
center
b. depending on the mass of the body being acting on
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國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
2. ground reaction force
a. the force acting on a body when the body is in contact with the ground
b. depending on the mass of the body and the contraction force of the related muscles
3. friction force
a. the resistance to motion of two moving objects or surfaces that touch
b. depends on the kind of materials in contact with each other and the normal force of one
object acting on the other
4. air or water resistance
a. the resistance met by a body moving through air or water
b. depending on the surface area directed forward and the velocity of the body
5. Note: moment of force (M) = force  perpendicular distance from axis to point of application
B. Force transducers
1. capacitive sensors
a. consisting of electrically conducting plates that lie parallel to each other, separated by a
distance that is small compared to the linear dimensions of the plates
b. the space between the plates is filled with non-conducting electrical material
c. A change in force produces a change in the thickness of the non-conducting material that is
inversely proportional to a current which can be measured
F  1/Q
where F= force, Q= total charge of on each plate
2. conductor sensors
a. consisting of 2 layers of conductive material and a conductive material in between
b. An increase in force produces a decrease in electric resistance between 2 plates
3. piezoelectric sensors
a. non-conducting crystal that exhibits the property of generating an electrical charge when
subjected to mechanical strain, e.g. quartz
b. compressive forces produce a change in the electric charges on the surfaces where the
force has been applied.
c. shear forces produce a change in the electric charges on the surfaces perpendicular to the
applied forces
d. advantage: wide range in measurement of force
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國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
F
Si
O
O
Si
Si
Q
O
F
4. strain gauze
a. strain: normalized change in its dimension under a stress
b. made in electric types
-- electrical resistant transducer: wire
-- piezoresistive transducer: silicon
+
force
v
1
2
electric voltage
-
5. selection of force transducers
a. purposes of use
-- measuring forces on rigid surface: piezoeletric or strain gauge sensors
-- measuring forces on soft or uneven surface: capacitor or conductive sensors
-- measuring pressure distribution: capacitor or conductive sensors
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國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
b. accurancy
-- piezoeletric or strain gauge sensors: 5% errors
-- capacitor or conductive sensors: 20% errors
c. cost
-- piezoeletric or capacitor sensors:high
-- conductive or stain gauge sensors: low
C. Force Platform System
1. four corner type force plate
a. for measurement of ground reaction forces
b. 1895 Marey built the first force plate
c. a rectangular plate with force transducers mounted at each corner
Fy1
Fy4
Fy3
Fz4
Fx4
Fy
Fx
Fx3
Fx1
Fy2
Fz1
Fx2
Fz
Fz2
Fz3
d. center of pressure: the point where the total ground reaction forces act
COPx 
x  ( Fxo  Fxy )  ( Foo  Foy ) 
1 

2
Fz

COPy 
y  ( Foy  Fxy )  ( Foo  Fxo ) 
1 

2
Fz

NOTE: COP does not indicate COM or COG (vertical projection of COM on the ground)
2. central support type force plate: one centrally-instrumented pillar which supports an upper
flat plate
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國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
z
Fz
Fx
x
zo
xo
My
My - Fz·xo + Fxzo = 0
 xo 
Fx zo  M y
Fz
Internal Force Generated by Human Body
A. Classification
a. muscle force
-- the active force generated by muscle contraction in response to resist the external forces or
other internal forces
b. connective tissue tension
-- the passive forces generated from the tension of the connective tissues, such as tendons,
ligaments, fasciae, capsule, or skin
B. EMG Recording
1. Muscle activities and EMG signals
a. EMG signal: changes in electrical potential across the muscle finer membrane
b. resting potential of a muscle fiber = -90mV
c. action potential of a muscle fiber = 30-40 mV
d. motor unit action potential (MUAP): EMG signal from the depolarization of a motor unit
C. Relationship between force and EMG
1. not a linear relationship
2. EMG records the recruitment of motor unit
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國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
EMG
amplitude
(mv)
external load
D. Muscle strength measurement systems
1. localized static strength measurement systems
a. hand-held dynamometer
b. seated strength tester
2. localized dynamic strength measurement systems
a. Cybex isokinetic system
b. Kin-Com isokinetic system
3. whole body static strength measurement system
a. position of load cell can be adjusted to different heights
b. position of load cell can be adjusted to different directions
c. load cell can be attached with different handles
4. whole body dynamic strength measurement system
a. Isokinetic lift strength tester
-- Using simple electromechanical measuring system for performing a lifting task
-- components of the system
i. electronic load cell and velocity transducer connected to a readout device
ii. constant-velocity motor with adjustable speed control
b. Isoinertial strength test (Liftest test)
-- lifting loads with different weights until one’s psychophysiological limit is reached
-- used for personnel selection in US military department
Stress
A. Stress-Strain curve
1. stress: the load per unit area
2. strain: the deformation that occurs at a point in a structure under loading
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國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
3. stress-strain curve of visicoelastic material: elastic region and plastic region
4. yield point
5. failure point
ultimate
stress
stress
yield
point
plastic region
elastic region
ultimate
failure point
energy stored
strain
ultimate
strain
C. Stiffness
1. the slope of the stress-strain curve in the elastic region
2. metal >> glass > bone
D. External loads
1. tensile load: loads with opposite direction distract the surface of the structure, resulting in
tensile stresses and strains inside the structure
=
2. Compressive loads: loads with opposite direction compress the surface of the structure,
resulting in compressive stresses and strains inside the structure
=
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國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
3. Shear loads: loads parallel to the surface of the structure but opposite in direction, resulting in
shear stresses and strains and angular deformity inside the structure
=
4. bending loads: loads parallel to the surface of the structure and in the same direction,
resulting in the tensile stresses and strains at one side and compressive stresses and strains at
the other side of the structure; there are no stresses and strains along the neutral axis
=
5. torsion loads: loads parallel to the surface of the structure with twisting the structure,
resulting in the shear stresses and strains inside the structure; there are no stresses and strains
along the neutral axis
=
6. Combined loading
Quantities Derived From Force
A. Work (W)
1. product of the force along the direction of displacement and the displacement of a rigid body
in motion
2. W = Fd
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國立台灣大學九十學年度生物力學
Biomechanical Methodology – Force and Strength
B Power (P)
1. the work done per unit of time
2. P = W / t = Fd / t
C Momentum (L)
1. product of the mass and its velocity of a rigid body in motion
2. L = mv
D impulsive force and impulse
1. impulsive force: a large force applied to a rigid body through a small period of time (impact)
2. impulse: the product of impulse force and the time period
3. impulse = Ft
E. Potential energy (P.E.)
1. the potential of doing work due to the position or configuration of a rigid body
2. P.E. = mgh for a rigid body which is elevated to a height of h
P.E. = ½kx2 for a spring which is stretched x length beyond its neutral position
F. Kinetic energy (K.E.)
1. the work required to stop a moving body at velocity v or to move a body from rest to the
velocity v
2. K.E. = ½mv2-- product of the force along the direction of displacement and the displacement
of a rigid body in motion
3. law of conservation of energy: the total energy of a body at position 1 is equal to that of
position 2
G. Mass moment of inertia (I)
1. an inertial resistance to rotation or translation
2. depends on magnitude of the mass and its geometrical distribution
3. I = M / 
4. I = I0 + mr2
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