ENGR 107 - Introduction to Engineering 1

ENGR 107 – Introduction to Engineering

Simple Machinesand

Mechanical Advantage

(Lecture #4)

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Simple Machines

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A mechanical device that changes the magnitude or direction of a force.

Simple Machines

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Simple Machines The six classical simple machines are:

Lever

Wheel and axis

Pulley

Inclined plane

Wedge

Screw

All complex machines are constructed from one or more of these simple machines.

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Simple Machines

Simple machines can be classified as follows: Those dependent on the vector resolution of forces

Inclined plane Wedge Screw

Those in which there is an equilibrium of torques Lever Pulley Wheel

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Lever

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Wheel and Axle

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Pulley

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Inclined Plane

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Wedge

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Screw

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Simple Machines A simple machine uses an applied force to do work

against a load. Work done on the load is equal to the work done by

the applied force. Can be used to increase the force acting on the load, at

the expense of a proportional decrease in the distance that the load is moved.

The ratio of the force acting on the load to the force applied to the simple machine is known as the mechanical advantage.

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Mechanical Advantage

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The factor by which a simple machine multiplies the force or torque applied to it.

Mechanical Advantage

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Mechanical Advantage

MA = output force / input force

applied forceforce acting on load

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Mechanical Advantage

MA = distanceapplied force

/ distanceload moved

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Mechanical Advantage

WorkIN

= WorkOUT

Force applied x distanceapplied force

= Force acting on load x distance

load moved

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Lever

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Pulley

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Pulley

r1

r2

input output

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Torque (Moment)

The tendency of a force to rotate an object about an axis, fulcrum or pivot.

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Torque (Moment)

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Torque

= F x d

d = Distance measured from the point of rotation to the applied force

F = applied force perpendicular to the measured distance

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Mechanical Advantage

MA = 2 /

1 = r

2 / r

1

output input

output input

= torquer = radius

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Mechanical Advantage

2 = MA x

1

F2 x d

2 = MA x (F

1 x d

1)

F2 = MA x F

1 x (d

1 / d

2)

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Gears

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Gears

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Gears

Gears may be considered a simple machine. Two or more gears working in tandem can

produce a mechanical advantage. Gear ratio Unequal number of teeth

Gears in a transmission are analogous to wheels in a pulley.

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Mechanical Advantage

MA = 2 /

1 = #Teeth

2 / #Teeth

1

output input

output input

= torque#Teeth = # of teeth on gear

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Velocity Reduction

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VR = 1 / MA

Velocity Reduction

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Velocity Reduction

VR = 1 /

2 = r

1 / r

2

outputinput

= torquer = radius

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Pulley

r1

r2

input output

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Gears

input output

r1

r2

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Angular Speed

A measure of the speed of rotation about an axis.

Often specified in revolutions per minute (rpm).

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Angular Speed

2 = VR x

1

1 = angular speed of input wheel or gear

2 = angular speed of output wheel or gear

output input