DemosDemos

Nails and two pipesNails and two pipes 8:40 ratio winch using Legos, string, 8:40 ratio winch using Legos, string,

and weightsand weights Lego gear boxLego gear box Pulley seatPulley seat

Six fundamental devices used Six fundamental devices used over and over in machines:over and over in machines:

1.1. WheelWheel

2.2. The Inclined Plane (wedge)The Inclined Plane (wedge)

3.3. ScrewScrew

4.4. LeverLever

5.5. PulleysPulleys

6.6. Gears (toothed wheels)Gears (toothed wheels)

The Wheel – found around 4000 The Wheel – found around 4000 B.C.B.C.

The first wheels were The first wheels were used as potters’ used as potters’ wheels. These wheels wheels. These wheels were found in were found in archeological sites in archeological sites in and around and around Mesopotamia (modern Mesopotamia (modern Iraq).Iraq).

http://www.nationalarchives.gov.uk

Wikipedia

FlywheelFlywheel a heavy wheel for opposing and a heavy wheel for opposing and

moderating (by its inertia) any moderating (by its inertia) any fluctuation of speed in the machinery fluctuation of speed in the machinery with which it revolves with which it revolves

a similar wheel used for storing kinetic a similar wheel used for storing kinetic energy (as for motive power) energy (as for motive power) Merriam-Webster Online

Inertia is the resistance to changes in motion. Inertia is proportional to mass. Heavy objects have inertia.

3500 B.C. the rolling wheel 3500 B.C. the rolling wheel appears in Mesopotamiaappears in Mesopotamia

Wheels greatly reduced the effort Wheels greatly reduced the effort from having to slide heavy loads.from having to slide heavy loads.

The wheel idea probably came from The wheel idea probably came from the use of rolling logs to carry loads.the use of rolling logs to carry loads.

Wheel and Axle appear in Wheel and Axle appear in 2000 B.C. in Egypt2000 B.C. in Egypt

This early wheel is a solid, wooden This early wheel is a solid, wooden disc that spins around a pole called disc that spins around a pole called the the axleaxle..

http://www.ohtm.org/wheel.html

Homo Sapiens have been around for 200,000 years. So humanssurvived without the wheel for many thousands of years.

Domestication of large animalsDomestication of large animalsexploits the usefulness of wheelsexploits the usefulness of wheels

leading to the beginning of agrarian leading to the beginning of agrarian societiessocieties

Jared Diamond identifies only 14 Jared Diamond identifies only 14 domesticated large mammal species domesticated large mammal species worldwide. The five most useful worldwide. The five most useful (cow, horse, sheep, goat, and pig) (cow, horse, sheep, goat, and pig) are all descendants of species from are all descendants of species from Eurasia. Of the remaining nine, only Eurasia. Of the remaining nine, only two (the llama and alpaca both of two (the llama and alpaca both of South America) are indigenous to a South America) are indigenous to a land outside the temperate region of land outside the temperate region of Eurasia. Eurasia.

What does this mean for Native What does this mean for Native Americans, Africans, Australians, Americans, Africans, Australians, and most South Americans?and most South Americans?

Culture and technological progress Culture and technological progress depends on an advantageous depends on an advantageous geography.geography.

UC Berkeley

EurasiaEurasia

Wikipedia

Shown in pink arethe Temperate Zoneshaving Four Seasons and Grasslands.

Large continuous Temperate zone in which domesticated animals could evolve and spread out.

Machines with rotary motion Machines with rotary motion have wheels. Wheels transmit have wheels. Wheels transmit

forces.forces. Your car’s Your car’s

crankshaftcrankshaft Water TurbineWater Turbine Steering WheelSteering Wheel Water MeterWater Meter Can OpenerCan Opener A WinchA Winch A Clock’s HandsA Clock’s Hands Car WheelsCar Wheels Sewing MachineSewing Machine Flywheel in Flywheel in

lawnmower enginelawnmower engineGrist Mill in Napa Valley

Palm Springs

Hand Winch

The WheelThe Wheel

The axle rotates with more turning The axle rotates with more turning force (torque) than the wheel, but force (torque) than the wheel, but the wheel travels a larger distance the wheel travels a larger distance than the axle.than the axle.More on this after we get to LeversMore on this after we get to Levers

The Winchwww.m-w.com/mw/art/winch.gif

Axle – where rope is taken up

Wheel, where gear teeth are.

Brake Pads apply a force at the perimeter of the wheel.

Why are ship wheels so large?

http://www.answers.com/topic/steering-wheel-ship

The Inclined Plane (Wedge)The Inclined Plane (Wedge)

The Inclined Plane is a ramp.The Inclined Plane is a ramp. Builders may have used earthen ramps Builders may have used earthen ramps

to place lintels when constructing to place lintels when constructing Stonehenge around 2800 B.C.Stonehenge around 2800 B.C.

Stonehenge

Egyptians used ramps to Egyptians used ramps to construct the Pyramids circa construct the Pyramids circa

2000 B.C.2000 B.C.

Lehner, Mark. The Complete Pyramids

How does the Inclined Plane How does the Inclined Plane Work?Work?

It takes a fixed amount of work to It takes a fixed amount of work to move something from one point to move something from one point to another.another.

Work = Force x DistanceWork = Force x Distance

By increasing the distance, the same By increasing the distance, the same amount of work can be done with less amount of work can be done with less force (less effort).force (less effort).

Twice the Distance, half the Effort (force).

Full Effort (full force) and shortest path for raising the object.

The mechanical advantage of a ramp is The mechanical advantage of a ramp is given by the ratio of its length to its width given by the ratio of its length to its width

In physics and engineering, mechanical advantage (MA) is the factor by which a machine multiplies the force put into it. education.jlab.org

The Arrowhead is a sharp The Arrowhead is a sharp wedgewedge

Broken arrowhead found summer of 2007 along a lake beach at 7500 feet in the Sierras.

This technology is prehistoric, developed maybe 30,000-50,000 B.C.

How does a Wedge Work?How does a Wedge Work?

A wedge or arrowhead is a A wedge or arrowhead is a moving moving inclined planeinclined plane..

The wedge separates whatever it is The wedge separates whatever it is pushed or shot into.pushed or shot into.

Examples are knives and axes.Examples are knives and axes. Wedges can also hold things, like Wedges can also hold things, like

door-stopsdoor-stops

Smaller force, larger Distance

Big Force,

Small Separation

The classroom doorstop works the same way. As the doorstopis pushed under the door, the wedge pushes the door up. The door pushes back on the wedge. This large forcecauses the wedge to grip the floor.

The Plow is a metal wedge that The Plow is a metal wedge that cuts furrows into the soilcuts furrows into the soil

The Sumerians used handheld The Sumerians used handheld wooden plows, but this technique wooden plows, but this technique failed in heavy, wetter, harder soils, failed in heavy, wetter, harder soils, such as those in Europe.such as those in Europe.

Wisconsinhistory.org

Sumerians lived in Mesopotamia

(Modern day Iraq)

Romans developed a metal Romans developed a metal blade and added a wheel (100 blade and added a wheel (100

A.D.)A.D.)

The plow’s blades cut and then turned The plow’s blades cut and then turned over the topsoil, creating a furrow for over the topsoil, creating a furrow for planting.planting.

Using oxen to pull the plow Using oxen to pull the plow the Romans were able to the Romans were able to cultivate much more landcultivate much more land

Romans exported agricultural products using wagons and weather-proof roads.

The ScrewThe ScrewA spiraling inclined planeA spiraling inclined plane

Any material Any material traveling in a screw traveling in a screw (sawdust, water) (sawdust, water) has to turn multiple has to turn multiple times to move times to move forward a short forward a short distance.distance.

Since the distance is Since the distance is increased, the effort increased, the effort needed to move the needed to move the material is reduced.material is reduced.

Screw ConveyorContinentalScrew.com

MA of an screws can be estimated by dividing the number of turns per inch.

education.jlab.org

Recall the “Apple Lathe”Recall the “Apple Lathe”

An apple spiraling through the coring blade takes less force (but many rotations) than pushing the apple straight through a blade.

What prompted the need What prompted the need for the screw?for the screw?

Once water was channeled into Once water was channeled into irrigation ditches, how could the irrigation ditches, how could the water be brought up to the fields?water be brought up to the fields?

Before the screw, laborers used Before the screw, laborers used Shadufs. Shadufs. (shadoo)(shadoo)

Shaduf

Archimedes, a prolific Greek Archimedes, a prolific Greek inventor is credited with coming inventor is credited with coming up with the screw as a means of up with the screw as a means of moving water uphill in 235 B. C.moving water uphill in 235 B. C.

Wikipedia

How did Archimedes figure this How did Archimedes figure this out?out?

Lifting along an inclined plane is easier Lifting along an inclined plane is easier than lifting something straight up.than lifting something straight up.

The spiral is a type of incline wrapped The spiral is a type of incline wrapped around a cylinder.around a cylinder.

By placing a screw at a low angle, By placing a screw at a low angle, water can be made to flow up – at water can be made to flow up – at some point along the screw’s cylinder some point along the screw’s cylinder water is flowing downstream. water is flowing downstream.

Screws and Augers TodayScrews and Augers TodayAugers are devices designed for moving material.

Modern Augers used to drain the Polders in HollandWikipedia

The LeverThe Lever The Lever is a rigid bar that rotates around The Lever is a rigid bar that rotates around

a fixed point (a fixed point (fulcrumfulcrum).). People figured out that it was easier to lift People figured out that it was easier to lift

a heavy object by wedging a board under a heavy object by wedging a board under the object and then pushing down on the the object and then pushing down on the other end of the board.other end of the board.

First class lever with fulcrum in the center.US Dept of Transportation

First Class Levers – First Class Levers – fulcrum in middlefulcrum in middle

SeeSawsSeeSaws ScalesScales DollieDollie CrowbarsCrowbars ScissorsScissors PliersPliers All these levers have their

Fulcrum between the loadand effort.

Archimedes explained the Archimedes explained the math behind the Levermath behind the Lever

Effort x Distance Effort x Distance of the effort from the Fulcrumof the effort from the Fulcrum = = Load X Distance Load X Distance of the load from the Fulcrumof the load from the Fulcrum

LoadEffort

FulcrumThis equation assumes the lever is not moving.

Torque: a twisting or spinning Torque: a twisting or spinning forceforce

Torque = Lever Arm X ForceTorque = Lever Arm X Force(Lever Arm is measured as the distance from the load/effort to the (Lever Arm is measured as the distance from the load/effort to the Fulcrum)Fulcrum)

When two torques are equal and opposite When two torques are equal and opposite the lever arm does not move.the lever arm does not move.

LoadEffort

Fulcrum

Torque due to EffortTorque due to Load

““If you give me a lever and a place to If you give me a lever and a place to

stand, I can move the worldstand, I can move the world ” ” ArchimedesArchimedes

StonehengeStonehenge Easter Island StatuesEaster Island Statues PyramidsPyramids

Statues around Easter Island,Chile. The theory is the statueswere moved by being rocked back and forth 400-1000 years ago. Wikipedia

Second Class LeversSecond Class LeversLoad is between the Load is between the Fulcrum and EffortFulcrum and Effort

WheelbarrowWheelbarrow Bottle OpenerBottle Opener Nut CrackerNut Cracker Tortilla PressTortilla Press

Royal Prestige Tortilla Press

What is the MA of the potato What is the MA of the potato ricer?ricer?

Find distance from Find distance from fulcrum to potato.fulcrum to potato.

Find distance from Find distance from fulcrum to your hand.fulcrum to your hand.

The ratio is the MA, or The ratio is the MA, or about 4.about 4.

Force on the potato is Force on the potato is 4X the force you apply 4X the force you apply with your hand.with your hand.

Third Class LeversThird Class LeversThe Effort is between the The Effort is between the

Fulcrum and the LoadFulcrum and the Load

TweezersTweezers Hammer (here the objective Hammer (here the objective

is to get the massive end of is to get the massive end of the hammer to move faster the hammer to move faster than your hand)than your hand)

Fishing Pole (here the Fishing Pole (here the objective is to quickly pull objective is to quickly pull the fish out with only small the fish out with only small movements of your hands)movements of your hands)

Clockmaker’s Tweezers

A Winch is a rotating lever?A Winch is a rotating lever?

The hub (center) of the winch The hub (center) of the winch is the Fulcrum.is the Fulcrum.

The handle moves a greater The handle moves a greater distance than the spool where distance than the spool where rope is taken in.rope is taken in.

The spool turns with more The spool turns with more force (torque) but moves a force (torque) but moves a smaller distance than the smaller distance than the handle.handle.

The WinchThe Winch

A small force applied over a large distance A small force applied over a large distance causes the center of the winch to turn causes the center of the winch to turn with greater force, but more slowly.with greater force, but more slowly.

http://www.cvfsupplycompany.com

A Wheel is a rotating lever?A Wheel is a rotating lever?

The hub (center) of the wheel is The hub (center) of the wheel is the Fulcrum.the Fulcrum.

The outside of the wheel moves The outside of the wheel moves a greater distance than the a greater distance than the axle.axle.

Larger wheels cover a greater Larger wheels cover a greater distance than smaller wheels at distance than smaller wheels at the same rpm the same rpm (revolutions/minute)(revolutions/minute)

Road bicycles have larger Road bicycles have larger wheels than mountain bikes wheels than mountain bikes because road bikes are because road bikes are designed for speed and comfort.designed for speed and comfort.

Mechanical AdvantageMechanical Advantagethe factor by which a mechanism the factor by which a mechanism multiplies the force put into it multiplies the force put into it

PulleysPulleys

PulleysPulleys A pulley is a grooved wheel that a cable runs through.A pulley is a grooved wheel that a cable runs through.

The Pulley on the left is a first class pulley. The force The Pulley on the left is a first class pulley. The force needed to move the load is equal to the weight of the load. needed to move the load is equal to the weight of the load. This has a mechanical advantage of 1. Force=LoadThis has a mechanical advantage of 1. Force=Load

The Pulley on the right is a second class pulley. The force The Pulley on the right is a second class pulley. The force needed to raise the load is half but the load moves at half needed to raise the load is half but the load moves at half the speed of the rope. This pulley has a mechanical the speed of the rope. This pulley has a mechanical advantage of 2. The force is doubled.advantage of 2. The force is doubled.

Tension in the ropeis uniform.

Second pulleyused to directForce downward.This combines a first-class anda second-class pulley

Wikipedia

Mechanical AdvantageOf 3.

Mechanical AdvantageOf 4.

Wikipedia

GearsGears

http://www.geocities.com

Gears are good for:Gears are good for:

Increasing Torque & Decreasing Rotational Increasing Torque & Decreasing Rotational Speed Speed (known as gear or speed reduction)(known as gear or speed reduction)

Decreasing Torque & Increasing Rotation Decreasing Torque & Increasing Rotation SpeedSpeed (known as torque reduction)(known as torque reduction)

Changing the direction of the motion.Changing the direction of the motion.http://science.howstuffworks.com/gear.htmRefer to this url for useful info on gears.

Example of Torque reduction:Gear B turns twice as fast as Gear A, but Gear B turnswith ½ the torque compared to Gear A.

Torque is the turning force.Torque = F X (distance from teeth to axle)

Force is the same where teeth touch.

Example of Speed Reduction:Gear B turns with three times the torque as Gear A, but at 1/3 the speed.

This is speed reduction. The driver A turns 4 times faster than gear B, but the load gear turns with 4 times the torque.

The force at the teeth is the same for both wheels.

Since the load gear has a radius 4 times bigger than the driver, the torque is 4 times bigger for the big gear.

MA = 4

If you put a handle on Gear A, could this be a winch?

ResourcesResources

http://brunelleschi.imss.fi.it/genindice.asp?http://brunelleschi.imss.fi.it/genindice.asp?appl=LIR&indice=63&xsl=listagenerale&lingua=ENG&chiave=100appl=LIR&indice=63&xsl=listagenerale&lingua=ENG&chiave=100799799

http://science.howstuffworks.com/