426-46 lever systems

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


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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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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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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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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Muscle

DFA

DRA

FM

R

FRO


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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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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

426-46 lever systems

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