04/19/23Dr. Sasho MacKenzie - HK

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LEVERS

Some “rigid” structure that is hinged at one point and has two forces

applied at other points.

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Lever Terms• The hinge or pivot point is known as the

fulcrum ( ).

• One of the forces is the resistance force (FR) and opposes the intended movement.

• The other force is the applied force (FA) and that causes or tends to cause the lever to move.

04/19/23Dr. Sasho MacKenzie - HK

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Lever Arms (Moment Arms)• There are two lever arms for every lever. One

associated with each force.• The resistance lever arm (dR) is the perpendicular

distance from the line of action of the resistance force to the fulcrum.

• The applied lever arm (dA) is the perpendicular distance from the line of action of the applied force to the fulcrum.

FAdRdA

FR

04/19/23Dr. Sasho MacKenzie - HK

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Levers: What are they for?

• Oars, vaulting poles, golf clubs, and wheels are all levers, but the most important levers in kinesiology are bones and the muscles that move them.

Levers can do two things

1. Increase Force

2. Increase Speed

04/19/23Dr. Sasho MacKenzie - HK

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Levers can Increase ForceA lever can increase the effect produced by a muscular force. In other words, a smaller muscular force may balance out a greater resistance force.

FA

FR

dR

dA

Weight of head 50 N

Trapezius

dA = 5 cmdR = 2 cm

The force of the trapezius to hold the skull in equilibrium is given by:

FA x 5 cm = 50 N x 2 cmFA = 20 N

04/19/23Dr. Sasho MacKenzie - HK

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Levers can Increase SpeedA lever can increase the speed of an object. A relatively slow hand speed can result in a very high clubhead speed

In this golf example, the right hand is the applied force and moves 10 cm in the last phase of the swing, while the clubhead travels 100 cm. The left wrist is the fulcrum.

Both of these distances are covered in the same period of time. Hence the clubhead speed is 10 times that of the right hand.

100 cm

10 cm

FR

FA

04/19/23Dr. Sasho MacKenzie - HK

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Mechanical Advantage

Mechanical advantage or leverage is the ratio of how much force you get out relative to how much you put in.

The ratio of the applied force lever arm (dA) to the resistance force lever arm (dR).

M.A. = dA

dR

FRFA dR = 1dA = 2

M.A. = dA = 2 = 2 dR 1

04/19/23Dr. Sasho MacKenzie - HK

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First Class Levers

The fulcrum lies between the points of applied force and resistance force.

Examples: See-Saw, scissors, pliers

FRFA dRdA

First class levers can be used to gain a mechanical advantage by increasing the length of the applied lever arm (dA).

First class levers can also be used to increase the speed of movement by decreasing the length of the applied lever arm (dA).

04/19/23Dr. Sasho MacKenzie - HK

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Second Class Levers

The fulcrum lies at one end, and the applied lever arm is greater than the resistance lever arm.

Examples: Bottle opener, wheel barrow, nut cracker

FRFA

dR

dA

Second class levers can only be used to increase the effect of an applied force.

04/19/23Dr. Sasho MacKenzie - HK

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Third Class Levers

The fulcrum lies at one end, and the resistance lever is greater than the applied lever arm .

Examples: Tweezers and Tongs

FR FA

dR

dA

Third class levers can only be used to increase the speed of movement of the load.

04/19/23Dr. Sasho MacKenzie - HK

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Lever Arm is Moment Arm

A AFR = mg

FA

AFR = mg

FAdA

dR

The brachioradialis is a 3rd class lever because the resistance lever arm is greater than the applied lever arm.

04/19/23Dr. Sasho MacKenzie - HK

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Calf Raise Example

1000 N

0.15 m

0.05 m

Vertical Component of Achilles Tendon Force?

Vertical JointReaction Force ?

BB

1. Determine unknown forces.2. What class of lever?3. Does it increase speed or force?4. What is the M.A.?

A

C

*Assume Static Equilibrium

04/19/23Dr. Sasho MacKenzie - HK

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twoseg.for

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Levers can Increase SpeedA lever can increase the effective speed of a muscular contraction. A muscle contracting at 1m/s may displace the distal end of a bone at a rate of 10 m/s.

In this kicking example, the quadriceps shorten by 10 cm, while the point of the foot in contact with the ball travels 100 cm.

Both of these distances are covered in the same period of time. Hence the foot speed is 10 times that of the muscle contraction.

L = 100 cm L = 10 cm

FR

FA