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7/29/2019 426-46 Lever Systems
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Lever Systems
Classified systems of torque
Relative positions of force, resistance, and
axis of rotation vary in the different types orclasses of levers
As with any torque calculations, operations
on levers determine the tendency for someforce to produce rotation around a fixedpoint.
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Components of a Lever System
Fulcrum The center or axis of rotation of thesystem.
Moment Arm
The distance from any force orweight that produces torque to the fulcrum.
Force Arm The distance from an applied force tothe fulcrum. (The moment arm of the force.)
Resistance Arm
The distance from the resistance
to the fulcrum. (The moment arm of theresistance.)
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Classes of Levers
1. First Class The applied force and the
resistance are on opposite sides of the
fulcrum.
2. Second Class The resistance is between
the applied force and the fulcrum.
3. Third Class The applied force isbetween the resistance and the fulcrum.
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First Class Lever
fulcrum
applied force
resistance
arm
resistanceforce
arm
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Second Class Lever
fulcrum
resistanceapplied
force
resistance
arm
force arm
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Third Class Lever
fulcrum
resistance
applied force
resistance arm
forcearm
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Torque Produced in Lever
Systems Two Torques
1. Torque produced by the applied force
2. Torque produced by the resistance
The direction in which a lever system
moves is dependent on the relative lengths
of the force and resistance arms as well asthe magnitudes of force and resistance.
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Mechanical Advantage
This is the effectiveness of a lever at moving a
resistance. It is a calculated value:
Mechanical
Advantage
Because of their different configurations, the mechanical
advantage of a first class lever can favor the force orresistance depending on the placement of the fulcrum. A
second class lever always favors the force arm. A third
class lever always favors the resistance arm.
ceArmtansisRe
ForceArm=
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fulcrum
applied force
resistance
arm
resistanceforce
arm
The fulcrum in a first class lever system can often vary in position
to favor the force arm or the resistance arm.
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fulcrum
resistanceapplied
force
resistance
arm
force arm
In a second class lever system, the mechanical advantage favors
the force arm. (The force arm will always be longer.)
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fulcrum
resistance
applied force
resistance arm
force
arm
The mechanical advantage of a third class lever system favors the
resistance arm. (The resistance arm is always longer.)
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Resistance and Force Arms
Resistance Arm: Abbreviated DRA
Force Arm: Abbreviated DFA
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Levers In The Musculo-Skeletal
System Most are third class levers
This system produces a disadvantage for
force but an advantage for speed of
movement
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DFA
DRA
FM
R
FRO
Levers In The Musculo-Skeletal
SystemMost of the musculo-skeletal system
consists of third class levers. That is,
the resistance arm is longer than the
force arm.
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Levers In The Musculo-Skeletal
System
A
B
The musculo-skeletal lever
systems generally favor
speed over strength.
Although the mechanicaladvantage favors the
resistance arm, in the time
that the muscle insertion
moves a given distance
(red arrow), the resistance
moves a much greater
distance (blue arrow).
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Levers In The Musculo-Skeletal
System
A
B
In other words, the end of a
limb is moving at a greater
velocity than the attachments
of the muscles that produce
that movement.
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Strength vs. Speed in Skeletal Muscle
mechanical advantage = (DFA)/(DRA)If DFA < DRA the mechanical advantage is < 1
Example:
A muscle inserts 3 cm from a joint axis (DFA = 3 cm)The distance to the weight that the muscle is resisting is
30 cm (DRA = 30 cm)
mechanical advantage = 3 cm / 30 cm = .1
This means that, when FM and R are both perpendicularto the limb, FM must be 10 times greater than R to
move the resistance.
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Strength vs. Speed in Skeletal
Muscle In a muscle
contraction on a limb
like the arm or leg,the resistance moves
through the same
angular displacement
as the muscleinsertion.
q
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Strength vs. Speed in Skeletal
Muscle In moving through a
given angulardisplacement (q), the
velocity of theresistance is equal tothe angular velocity inrad/sec times DRA
The velocity of the
muscle insertion isequal to the angularvelocity in rad/sectimes DFA
q
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Strength vs. Speed in Skeletal
Muscle
DFA
DRA
FM
R
FRO
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Strength vs. Speed in Skeletal
Muscle The velocity of the resistance:
vR= (w rad/sec)(DRA)
The velocity of the muscle insertion:
vM = (w rad/sec)(DFA)
The velocity of the resistance compared to the
muscle insertion = vR/vM
= (w rad/sec)(DRA)/ (w rad/sec)(DFA) = DRA/DFA
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Strength vs. Speed in Skeletal
Muscle If DFA = 3 cm and DRA = 30 cm,
The relative speed of the resistance to the muscle
insertion = DRA/DFA = (30 cm)/(3 cm) = 10
This means that the resistance is moving at 10
times the velocity of the muscle insertion.
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Levers in the Musculo-Skeletal
System Not all levers in the
musculo-skeletal
system are third class.When performing toe
rises the ankle
becomes a second
class lever system.
fulcrum
DRA
DFA
R
FM