# Beam, Fulcrum, Torque, Law of the Lever and Mechanical Advantage

Posted by PITHOCRATES - April 30th, 2014

# Technology 101

(Originally published May 1st, 2013)

## A Lever is a Rigid Beam on a Fulcrum

Archimedes said, “Give me a place to stand, and I shall move the Earth with it.”  At least we think he did.  Archimedes of Syracuse was a Greek genius.  Mathematician.  Physicist.  Engineer.  Inventor.  And astronomer.  One of many of the ancient Greeks who advanced modern civilization.  By using math and science.  He did a lot.  And explained why things worked the way they did using math.  Like the Law of the Lever.

In the days before the twist-off bottle cap we used bottle openers.  Because try as we might we could not pry a bottle cap off with our hands.  Most grown men just didn’t have the strength to do that.  But a child could open a bottle if that child used a bottle opener.  For that bottle opener is a lever.  Giving the child leverage.  The ability to use a little bit of force to do a lot of work.

A lever is a rigid beam on a fulcrum.  Like a seesaw.  A common playground fixture.  If two kids of equal weight are on either end of the seesaw and the fulcrum is in the center these kids can effortless push up and down.  But if a grown adult sits on one end and a child is on the other the weight of the adult will drop his side of the seesaw down.  Leaving the child up in the air on the other side.

## As the Lever increases in Length the more it will Amplify the Input Force we Apply

Now that’s no fun.  Having the seesaw permanently tipped in one direction.  However, even two people of different weights can enjoy playing on the seesaw.  All they have to do is move the fulcrum towards the heavier person until the seesaw balances.  So that there is a short length of seesaw between the fulcrum and the heavy person.  And longer length of seesaw between the fulcrum and the lighter person.  This creates the same amount of torque on both side of the fulcrum.

Torque is the turning force created by a force acting about a fulcrum.  The force in this case is the weight of the people on the seesaw.  Which we calculate by multiplying their mass by the force of gravity.  With the force of gravity being constant the greater the mass the greater the weight.  This weight pressing down on the beam creates torque.   And the further away from the fulcrum the greater the turning force.  Such that a lighter weight at a greater distance from the fulcrum can balance a greater weight at a shorter distance from the fulcrum.  Allowing a child to play on a seesaw with someone of far greater mass.  Because the lever amplified the smaller force of the child.  Allowing the child to move a heavier weight.  To illustrate this consider the following table.

This is just a visual aid.  The numbers don’t represent anything.  It just shows a relationship between force and the length of the lever.  In this example we need 1000 units of force to move something.  If we use a lever that is 10 units from the fulcrum we need to apply 100 units of force.  If we have a lever that is 40 units from the fulcrum we only need to apply 25 units of force.  If we have a lever that is 80 units from the fulcrum we only need to apply 12.5 units of force.  As the lever increases in length the more it will amplify the input force we apply.  Which is why a child can open a bottle with a bottle opener.

## A Wheelbarrel combines the Lever with the Wheel and Axle

A lever gives us mechanical advantage.  The amplification of a small input force into a larger output force.  Such as a hand-held bottle opener.  But what about the kind that used to be fastened to pop machines?  When you bought a glass bottle of pop out of a vending machine?  The fulcrum is the fixed bottle opener.  And the lever is the bottle.  A can opener was often on the other end of a bottle opener.  Instead of a grip to latch onto a bottle cap this end had a triangular knife.  When we lifted up on the lever it pressed down and pierced a hole in a can.

A wheelbarrel allows us to move heavy loads.  This device combines two simple machines.  A wheel and axle.  And a lever.  The wheel and axle is the fulcrum.  The lever runs from the fulcrum to the handles of the wheelbarrel.  We place the load on the lever just before the axle.  When we lift the far end of the lever we can tilt up the load and balance it over the axle.  The lever amplifies the force we apply.  And the wheel and axle reduce the friction between this load and the ground.  Allowing us to move a heavy load with little effort.

Today’s pop bottles have screw-top caps.  Some people still use a lever to help open them, though.  A pair of pliers.  We use the pliers because we don’t have the strength to grip the cap tight enough to twist it open.  The pliers are actually two levers connected together at the fulcrum.  The pliers amplify our hand strand-strength to get a very secure grip on the bottle cap.  While our hands compress the two levers together getting a firm grip on the cap we can then use our arm to apply a force on the handles of the pliers.  Providing a torque to turn the bottle cap.  Very simple machines that make everyday life easier.  Thanks to the knowledge Archimedes handed down to us.

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# Magnets, Magnetic Field, Electromagnet, Electromechanical Solenoid, Stator, Armature, DC Electric Motor and Automobile Starter Motor

Posted by PITHOCRATES - January 1st, 2014

# Technology 101

(Originally published April 18th, 2012)

## Electric Current flowing through a Wire can Induce Magnetic Fields Similar to those Magnets Create

We’ve all played with magnets as children.  And even as children we’ve observed things.  If you placed a bar magnet on a table and approached it with another one in your hand one of two things would happen.  As the magnets approached each other the one on the table would either move towards the other magnet.  Or away from the other magnet.  That’s because all magnets are dipoles.  That is, they have two poles.  A north pole.  And a south pole.

These poles produce a magnetic field.  Outside of the magnet this field ‘flows’ from north to south.  Inside the magnet it ‘flows’ from south to north.  So imagine this magnetic force traveling through the magnet from south to north and right out of the north pole of the magnet.  Where it then bends around and heads back to the south pole.  Something most of us saw as children.  When we placed a piece of paper with iron filings over a bar magnet.  As we placed the paper over the magnet the iron filings moved.  They formed in lines.  That followed the magnetic field created by the magnetic dipole.  You can’t see the direction of the field but it only ‘flows’ in one direction.  As noted above.  If the north pole of one magnet is placed near the south pole of another the magnetic field ‘flows’ from the north pole of one magnet to the south pole of the other magnet.  Pulling them together.  If both north poles or both south poles are placed near each other they will repulse each other.  Because the magnetic field is ‘flowing’ out from each north pole.  Or into each south pole.  The magnets repulse each other because the magnetic field is trying to flow from north to south.  If one magnet was able to rotate this repulsion would rotate the magnet about 90 degrees.  To try and align one north pole with one south pole.  As the momentum pushed the magnet past the 90 degree point the force would reverse to attraction.  Rotating the magnet about another 90 degrees.  Where it will then stop.  Having aligned a north and a south pole.

It turns out this ability to move things with magnetic fields is very useful.  Both in linear motion.  And rotational motion.  Especially after we observed we could create magnetic fields by passing an electric current through a wire.  When you do a magnetic field circles the wire.  To determine which direction you simply use the right-hand rule.  Point your thumb in the direction of the current flow and wrap your fingers around the wire.  Your fingers point in the direction of the magnetic field.  Fascinating, yes?  Well, okay, maybe not.  But this is.  You can wrap that wire around a metal rod.  Creating a solenoid.  And all those induced magnetic fields add up.  The more coils the greater the magnetic field.  That ‘flows’ in the same direction in that metal rod.  Creating an electromagnet out of that metal rod.  If you ever saw a crane in a junk yard picking up scrap metal with a magnet this is what’s happening.  The crane operator turns on an electromagnet to attract and hold that scrap metal.  And turns off the electromagnet to release that scrap metal.

## A DC Electric Motor is Basically a Fixed Magnet Interacting with a Rotating Magnet

If that metal rod was free to move you get something completely different.  For when you pass a current through that coiled wire the magnetic force it creates will move that metal rod.  If it’s not restrained it will fly right out of the coil.  Which is interesting to see but not very useful.  But the ability to move a restrained metal rod at the flick of a switch can be very useful.  For we can use a solenoid to convert electrical energy into linear mechanical movement.  As in a transducer.  An electromechanical solenoid.  That takes an electrical input to generate a mechanical output.  Which we use in many things.  Like in a high-speed conveyor system that sorts things.  Like a baggage handling system at an airport.  Or in an order fulfillment center.  Where things fly down a conveyor belt while diverter gates move to route things to their ultimate destination.  If the gate is not activated the product stays on the main belt.  When a gate is activated a gate moves across the path of the main conveyor belt and diverts the product to a new conveyor line or a drop off.  And the things that operate those gates are electromechanical solenoids.  Or transducers.  Things that convert an electrical input to a mechanical output.  To produce a linear mechanical motion.  To move that gate.

Solenoids are useful.  A lot of things work because of them.  But there is only so much this linear motion can do.  Basically alternating between two states.  Open and closed.   In or out.
On or off.  Again, useful.  But of limited use.  However, we can use these same principles and create rotational motion.  Which is far more useful.  Because we can make electric motors with the rotational motion created by magnetic fields.  The first electric motors were direct current (DC).  And included two basic parts.  The stator.  And the rotor (or armature).  The stator creates a fixed magnetic field.  With permanent magnates.  Or one created with current passing through coiled wiring.  The armature is made up of multiple coils.  Each coil insulated and separate from the next one.  When an electric current goes through one of these rotor coils it creates an electromagnet.

So a DC electric motor is basically a fixed magnet interacting with a rotating magnet.  Current passes to the rotor winding through brushes in contact with the armature.  Like closing a switch.  Current flows in through one brush.  And out through another.  When current goes through one of these rotor coils it creates an electromagnet.  With a north and south pole.  As this magnetic field interacts with the fixed magnetic field produced by the stator there are forces of attraction and repulsion.  As the ‘like’ poles repel each other.  And the ‘unlike’ poles attract each other.  Causing the armature to turn.  After it turns the brushes ‘disconnect’ from that rotor wiring and ‘connect’ to the next rotor winding in the armature.  Creating a new electromagnet.  And new forces of repulsion and attraction.  Causing the armature to continue to turn.  And so on to produce useful rotational mechanical motion.

## An Automobile Starter Motor combines an Electromechanical Solenoid and a DC Electric Motor

Everyone who has ever driven a car is thoroughly familiar with electromechanical solenoids and DC electric motors.  Because unlike our forefathers who had to use hand-cranks to start their cars we don’t.  All we have to do is turn a key.  Or press a button.  And that internal combustion engine starts turning.  Fuel begins to flow to the cylinders.  And electricity flows to the spark plugs.  Igniting that compressed fuel-air mixture in the cylinder.  Bringing that engine to life.

So what starts this process?  An electromechanical solenoid.  And a DC motor.  Packaged together in an automobile starter motor.  The other components that make this work are the starter ring gear on the flywheel (mounted to the engine to smooth out the rotation created by the reciprocating pistons) and the car battery.  When you turn the ignition key current flows from the battery to the electromechanical solenoid.  This linear motion operates a lever that moves a drive pinion out of the starter (while compressing a spring inside the starter), engaging it with the starter ring gear.  Current also flows into a DC motor inside the starter.  As this motor spins it rotates the starter ring gear on the flywheel.  As combustion takes place in the cylinders the pistons start reciprocating, turning the crankshaft.  At which time you let go of the ignition key.  Stopping the current flow through both the solenoid and the DC motor.  The starter stops spinning.  And that compressed spring retracts the drive pinion from the starter ring gear.  All happening in a matter of seconds.  So quick and convenient you don’t give it a second thought.  You just put the car in gear and head out on the highway.  And enjoy the open road.  Wherever it may take you.  For getting there is half the fun.  Or more.

Electric motors have come a long way since our first DC motors.  Thanks to the advent of AC power distribution and polyphase motors.  Brought to us by the great Nikola Tesla.  While working for the great George Westinghouse.  Pretty much any electric motor today is based on a Tesla design.  But little has changed on the automotive starter motor.  Because batteries are still DC.  And before a car starts that’s all there is.  Once it’s running, though, a polyphase AC generator produces all the electricity used after that.  A bridge rectifier converts the three phase AC current into DC.  Providing all the electric power the car needs.  Even charging the battery.  So it’s ready to spin that starter motor the next time you get into your car.

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# FT200: “Only force can make people live in a world without choice.” —Old Pithy

Posted by PITHOCRATES - December 13th, 2013

# Fundamental Truth

## College Students and Hippies of Yesteryear have a Soft Spot for their Communist Heroes

The hippies in the Sixties saw a brotherhood of man.  They wanted to link arms and sing Kumbaya.  Live in their communes.  Get high.  Have unprotected sex with multiple partners who bathed infrequently.  While being one with nature.  And poop and pee in the great outdoors.  Like the animals.  Only with less grooming.  For they hated the Man.  And didn’t want anything to do with their parent’s generation.  They protested any figure of authority.  Protested the Vietnam War.  And protested against their government.  Speaking truth to power.  And yearned to bring the Marxist-Leninist revolution to America.

The hippies were rabid anti-capitalists.  Which is why they loved communism.  Where there were no possessions.  No religion.  Or greed or hunger.  Just imagine all the people sharing all the world.  Words from John Lennon’s song Imagine).  Former Beatle.  And one of the leaders of the counterrevolution.  Not to be confused with the other Lenin.  Vladimir Ilich Lenin.  Of Soviet Marxism-Leninism fame.  Or, rather, infamy.  One of many icons of the counterrevolution.  Along with Mao Zedong.  Ho Chi Minh.  Fidel Castro.  And, of course, Che Guevara.  Whose bearded and beret-wearing image adorns many a university dorm room wall and student t-shirt to this day.

College students today, just as the hippies of yesteryear, still have a soft spot for their communist heroes.  Thanks to many of these hippies of yesteryear having joined the establishment.  And are now teaching our kids in college the evils of capitalism and the goodness of government.  Despite their one-time fierce opposition to the Man.  Guess things change once you get money.  Like someone in the rock band The Who said when asked if he still hopes to die before he gets old (a line from My Generation-a song about youthful angry rebellion against their parent’s generation).  The reply was that being old wasn’t all that bad when you were rich.  Something the old hippies of the Sixties no doubt discovered.  And best of all they got rich by taking money from the capitalist pigs.  Their students’ rich parents.  Or the taxpayers who worked in that detested capitalist system.

## Nations with the Marxist Brotherhood of Man with No Possessions have been the Worst Places to Live

It is ironic that without capitalism these communist-loving parasites could not be parasites.  For if no one was creating economic activity there would be no income to tax.  Or to pay for the one thing growing more expensive than health care.  College tuition.  Interestingly, there is no ‘Obamacare’ for our colleges and universities.  No.  They never label them greedy despite their being the greediest of them all.  But you know who they do label as greedy?  The taxpayers who oppose higher taxes to pay for the ever higher cost of higher education.  They’re the greedy ones.  Not the old hippies of the Sixties.  And their fellow anti-capitalists.

Another interesting thing about these anti-capitalists?  They yearn for one-party rule.  Which is why public education teaches our kids to distrust capitalism and to trust government.  And our colleges and universities teach our kids to be ashamed of their nation’s past.  And the importance of diversity.  Which is code for anything that isn’t American.  For America was founded by rich white slave-owners who stole the land from the Native Americans.  And America’s imperialist aggression is the only source of strife in the world today.  While ignoring the expanding communist revolution that was spreading out from the Soviet Union into the Eastern Europe, Asia, the Middle East, Africa and the Americas.  The one ideology that has killed more people than any other.  Through state oppression, wars and famine.

Yes, this brotherhood of man where there are no possessions have been in fact the worst places to live.  The Soviet Union, Eastern Europe, Mao’s Peoples Republic of China, North Korea, Vietnam, Cambodia, Cuba, etc.  These are all nations that had gulags or reeducation camps for political prisoners.  Those people who spoke—or thought—truth to power.  They all had police states where the people lived in fear of their government.  They suffered for the want of the most basic items (soap, toilet paper, etc.).  There was state censorship.  They persecuted anyone practicing any religion.  The people suffered from constant hunger.  And the occasional famine.  They killed anyone trying to escape their communist utopia.  Or sent them off to hard labor and torture.  If they escaped successfully then the state punished any family remaining behind.  To warn others what would happen if they escaped their communist utopia.

## The Great Flaw of Socialism is being unable to Determine What is the Greater Good

Why did these communist states have police states and brutally oppress their people?  Because they had to.  When the communists built the Berlin Wall it wasn’t to keep people from West Berlin out of East Berlin.  It was to stop people escaping from East Berlin to West Berlin.  For the East Germans were suffering a terrific brain drain.  Capitalists believe in liberty.  The freedom to do what they want.  And to get paid for their services.  A highly skilled doctor expects a higher salary than a janitor.  And that just isn’t going to happen in a communist state.  You get what the state gives you.  No more.  Creating a heck of a free rider problem.  When your economic system works based on the Marxist premise from each according to ability to each according to need what you get is a lot of people showing little ability and a lot of need.  For the more ability you had the harder they forced you to work.  While the greater your need the more you got.  Such a system encourages people to do the minimum and not be extraordinary.  Which is why Sony, Samsung, Microsoft, Apple, The Beatles, etc., did not come from communist countries.

A communist state has a planned economy.  Instead of a free market economy.  Communist state planners manage the economy from top down.  Telling the raw material industry what materials to extract.  They tell what factories get these raw materials and what they are to build.  Etc.  Whereas in a free market economy the economy is driven bottom up by the consumers.  When consumers start buying a lot of one thing the price for that one thing rises.  Attracting other businesses into the market to meet that rising demand.  Who place orders with their wholesalers.  Who place orders with their manufacturers.  Who place orders with their industrial processors.  Who place orders with their raw material extractors.  Hundreds of thousands of decisions happen as this consumer demand travels up the stages of production in a free market economy.  Giving the people what they want.  And not what a state planner decides to give to the people.

This is why communist (and socialist) states are oppressive dictatorships.  Because state planners decide for the people.  Which must start with the supreme decision maker.  The Joseph Stalin, the Mao Zedong, the Ho Chi Minh, the Kim Jong Un, the Raul Castro, the Hugo Chávez, etc.  And these people don’t take polls or hold elections.  Well, at least elections that are legitimate.  Kim Jong Un continues the state policy of his predecessors.  No economic reform.  Money goes to the military first (especially for his nuclear toys) and whatever is left over may go to the people.  And anyone who disagrees with him or thinks wrong goes to the gulag.  Or is executed.  Like his uncle.  While the people suffer the want of the most basic things.  Like food.  North Korea to this day still suffers the occasional famine because of its economic policies.  But one problem the North Koreans don’t have?  Deciding where to go for lunch.

“Where do you want to eat?  I don’t know, where do you want to eat?”  This can go on until someone forceful makes the decision for the group.  Often making no one happy.  But it will end the endless “where do you want to eat?”  This is the great flaw of socialism.  Being unable to determine what is the greater good.  Because people rarely agree on what’s best for other people.  Just look at the recent budget agreement that made few people happy.  They were unhappy because they disagreed on what was the greater good.  People are different.  One size does not fit all.  You just can’t please all of the people all of the time.  So you have to force your will on the people.  The only mechanism that makes socialism work.  Force.  Because people can rarely agree on where to go to lunch let alone national policy.  And this is why all communist/socialist states end in brutal dictatorships.  Because only force can make people live in a world without choice.

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# Rotational Motion, Windmill, Waterwheel, Steam Engine, Compressed Air and Electric Power

Posted by PITHOCRATES - July 24th, 2013

# Technology 101

## The Combination of Force and Current of Moving Water on a Waterwheel produced Rotational Motion

Through most of history man has used animals for their source of power.  To do the heavy work in our advancing civilizations.  And they worked very well for linear work.  Going long distances in a straight line.  Such as pulling a carriage.  Or a plow.  Things done outdoors.  A long place typically from where people ate and slept.  So animal urine and feces wasn’t a great problem.  But the closer we brought them to our civilized parts of society it became a problem.  For it brought the smell, the flies and the disease closer to our civilized part of life.

Animals were good for linear work.  But as civilization advanced rotational work became more important.  For as machines advanced they needed to spin.  The more advanced machines needed to spin at a fairly high revolutions per minute (rpm).  We have used animals to produce rotational motion.  By having them walk in a small circle.  To slowly turn a mill stone.  Or some other rotational machine.  But it was inefficient.  As animals can’t work continuously.  Especially when walking in a circle.  They have to rest.  Eat.  And they have to urinate and defecate.  Making it unclean.  And unhealthy.

The first great industrial advance was water power.  Using a waterwheel.  Spun by a current of water.  Either a large force of water moving slow and steady.  Like in a river.  Or a small force of water moving fast and furiously.  Like in a small waterfall.  This combination of force and current produced rotational movement.  And useable power.  The waterwheel produced a rotational motion.  This rotational motion drove a main drive shaft through a factory.  Gear trains could speed up the rpm produced by a slow river current.  Or reduce the rpm produced by a fast waterfall current.  To produce a constant rotational speed.  That was strong enough to drive numerous loads attached to the main drive shaft via belts and pulleys.

## Compressed Air Systems allowed us to produce Rotational Motion at our Workstations

Water power was a great advancement over animal power.  But it had one major drawback.  You needed a moving current of water.  Which meant we had to build our factories on the banks of rivers.  Or under a waterfall.  One of the reasons why our first industrial cities were on rivers.  The steam engine changed that.  With a steam engine providing our rotational motion we could put a factory pretty much anywhere.  And the power of steam could do a lot more work than a moving current of water.  So factories grew larger.  But they still relied on a rotating main drive shaft.  Then we started doing something else with our steam engines.  We began compressing air with them.

A current of air can fill masts of sails and push ships across oceans.  Air has mass.  So moving air has energy.  We’ve used windmills to turn millstones to crush our wheat.  Where a large force of a slow moving wind current filled a sail.  And pushed.  But these small currents of air required large sails.  If we compressed that volume of air down and pushed it through a very small air hose we could get a force at the end of that hose similar to what we got with a sail catching a large volume of air.  This allowed us to create rotational motion at a workstation.  Without the need of a rotating main drive shaft.  We could connect an air hose to a handheld drill.  And the compressed air in the air hose could direct a jet of high pressure air onto an ‘air-wheel’ inside the handheld drill.  Which spun the ‘air-wheel’ at a very high rpm.  Spinning the drill bit at a very high rpm.

Compressed air was a great advancement over a rotating main drive shaft.  Instead of belts and pulleys connecting to the main shaft you just had to plug in your pneumatic tool to an air line.  The steam engine’s rotational motion would drive an air compressor.  Typically turning a crankshaft with two pistons attached to it.  When a piston moves down the cylinder it draws air into the cylinder.  When the piston moves up it compresses the air in the cylinder.  The compressed air exits the cylinder and enters a large air tank.  From this air tank they run a network of pipes throughout the factory.  From these pipes hang air hoses with fittings that prevent the air from leaking out.  Keeping the whole system charged under pressure.  Then a worker takes his pneumatic tool.  Plugs it into the fitting on a hanging air hose.  As they snapped together you’ll hear a rush of air blow out.  But once they snap together the joined fittings became airtight.  When the worker presses the trigger on the pneumatic tool the compressed air blows out at a very high current.  Spinning an ‘air-wheel’ that provides useful rotational
motion.

## Electric Power generated Rotational Motion eliminated the need of Steam Engines and Compressed Air Systems

As good as this was there were some drawbacks.  It takes time to produce steam when you first start up a steam engine.  Once you have built up steam pressure then you can start producing rotational motion so the air compressor can start compressing air.  This takes time, too.  Then you need a lot of piping to push that air through.  A piping system than can leak.  It was a great system.  But there was room for improvement.  And this last improvement we made was so good that we haven’t made another in over 100 years.  A new way to provide rotational motion at a workstation.  Without requiring a steam boiler.  And air compressor.  Or a vast piping system charged with air pressure.  Something that allows us to plug in and go right to work.  Without waiting for steam or air pressure to build.  And that last advancement was, of course, electric power.

When voltage (force) pushes an electrical current through a wire we get useable power.  Generators at a distant power plant produce voltages that push current through wires.  And these wires can run anywhere.  In the air.  Or underground.  They can travel great distances at dangerous high voltages and low currents.  And we can use transformers to change them to a safer low voltage and a higher current in our factories.  And our homes.  Where we can use that force and current to produce useful rotational motion.  Using electric and magnetic fields inside an electrical motor.

Animals were a poor source of rotational power.  The windmill and the waterwheel were better.  The windmill could go anywhere but the rotational motion was only available when the wind blew.  Waterwheels provided continuous rotational motion but they only worked where there was moving water.  Keeping our early factories on the rivers.  The steam engine let us build factories where there was no moving water.  While an air compressor driven by a steam engine made it much easier to transfer power form the power source to the workstation.  While electric power made that transfer easier still.  It also eliminated the need of the steam engine and the pneumatic piping system.  Allowing us to create rotational motion right at the point of work.  With the ease of plugging in.  And pressing a trigger.  Allowing machines to enter our homes to make our lives easier.  Like the vacuum cleaner.  The clothes washer.  And the air conditioner.  None of which your average homeowner could operate if we depended on a main drive shaft in our house.  Or a steam engine driving a pneumatic system.

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# Wheel and Axle

Posted by PITHOCRATES - May 8th, 2013

# Technology 101

## The Key to the Wheel and Axle is the different Angular Velocities of the Outer Surfaces of the Axle and Wheel

Have you ever tried to turn a screw using only your fingers?  You might be able to get it started and spin it a few rotations.  But eventually you’ll be unable to turn the screw any further.  If you use a screw driver, though, you’ll be able to turn the screw all the way in.  Why?  For the same reason you can turn the handle on the spigot when you want to water the grass.  And why you can open the door when you enter your home.  Because of a wheel and axle.

The wheel and axle is one of six simple machines.  The others being the lever, the inclined plane, the pulley, the wedge and the screw.  The wheel and axle are two circular parts whose outer surfaces rotate at different speeds.  Think of a large wagon wheel.  Wooden spokes connect the outer rim of the wheel (the felloes) to the hub.  Imagine the wheel turning one quarter turn.  The end of the spoke at the felloes has to cover more distance than the end of the spoke at the hub.  Therefore the spoke end at the felloes travels faster than the spoke end at the hub.

In the ideal machine power in equals power out.  And power equals the torque (twisting force) multiplied by the angular velocity (how fast something spins around).  The key to the wheel and axle is the different angular velocities of the outer surfaces of the axle and wheel.  If power remains the same while the angular velocity changes then the torque must change.  Let’s use some meaningless numbers to illustrate this point.  The angular velocity is 4 and the torque is 2 on a wheel’s surface and the angular velocity is 2 and the torque is 4 on an axle.  Power in equals 8 while power out also equals 8.  But the torque increases.  So using the wheel and axle gives us mechanical advantage.  The ability to amplify force to do useful work for us.

## Mechanical Advantage amplifies our Input Force to do Useful Work for Us

What makes a screwdriver work is the handle on it that we grip.  Which represents the outer surface of the wheel.  While the metal shaft the handle fastens to is the axle.  The handle provides a larger surface for our hand to grip.  Allowing us to apply a greater turning force (torque) to the handle than we could to the metal shaft.  The angular velocity of the surface of the handle is greater than the metal shaft.  So the torque of the metal shaft is greater than the torque we apply to the handle of the screwdriver.

The mechanical advantage amplifies our input force to do useful work for us.  To turn a screw that our fingers aren’t strong enough to turn.  Just as the handle on the water spigot allows us to twist it open.  And the door knob allows us to twist open the latching mechanism to open a door.  Things we couldn’t do without a large handle to grasp and twist.  To amplify our limited force.  To do useful work.

The old-fashioned water well is another example.  Across the top of the well is an axle.  A length of rope long enough to reach the water below is attached to a bucket.  The other end is attached to the axle.  Also attached to the axle is a wheel that we can turn by hand.  Or a hand crank.  As we turn the wheel or crank the rope wraps around the axle.  Pulling up the bucket full of water.  The speed of our hand spinning the wheel or the crank is greater than the speed of the spinning axle.  That is, our input angular velocity is reduced.  Which increases the torque on the axle.  Allowing it to pull up a heavy bucket of water that we couldn’t do as easily without the wheel and axle.

## Using more Gears in a Gear Train can greatly Reduce the Angular Velocity which Greatly Increases the Output Force

We can amplify our input force more by adding some additional wheels.  And some gears.  For example, when we started harvesting sugarcane we used a mechanical press to squeeze the juice out of the cane.  And we did this by running the sugarcane through a couple of rollers with a narrow gap between them.  Crushing and pulling this cane through these rollers, though, required a lot of force.  Which we produced with a couple of wheels and axles.  One axle was the roller.  Attached to this axle was a large wheel.  Only we didn’t turn this wheel.  This wheel was a large gear.  Its teeth meshed with the teeth of a smaller gear on another axle.  Attached to this second axle was another wheel.  With a hand crank attached to it.

When we turned this wheel we rotated the small gear on the hand-crank axle.  This gear turned the larger gear attached to the roller axle.   Which pulled and crushed the cane through the press.  This reduced the angular velocity twice.  Thus increasing the torque twice.  Which twice amplified our input force.  Using more gears in a gear train can greatly reduce the angular velocity from the input axle to the output axle.  Greatly increasing the output force.  Like in a motor vehicle.  The engine spins at a high angular velocity.  The power output of the engine spins a gear train inside a transmission.  Greatly reducing the output angular velocity.  While greatly increasing the turning force sent to the drive wheels.

High-spinning electric motors have replaced the hand-crank on modern sugarcane presses.  These use a gear train or a belt and pulley system (or both) to reduce the spinning speed of the electric motor.  So when the force turns the rollers it doesn’t pull the cane through dangerously fast.  It pulls it through slow but with great force.  Which will flatten the cane and squeeze every last drop of fluid from it.  Or someone’s hand if it gets caught in the rollers.  Which usually have hand-guards around them to prevent that from happening.  But some people still operate machines that have no such guards as they hand-feed the cane into the press.  This is a disadvantage of using mechanical advantage.  For it can cause great harm just as easily as it can do useful work for us.

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# Beam, Fulcrum, Torque, Law of the Lever and Mechanical Advantage

Posted by PITHOCRATES - May 1st, 2013

# Technology 101

## A Lever is a Rigid Beam on a Fulcrum

Archimedes said, “Give me a place to stand, and I shall move the Earth with it.”  At least we think he did.  Archimedes of Syracuse was a Greek genius.  Mathematician.  Physicist.  Engineer.  Inventor.  And astronomer.  One of many of the ancient Greeks who advanced modern civilization.  By using math and science.  He did a lot.  And explained why things worked the way they did using math.  Like the Law of the Lever.

In the days before the twist-off bottle cap we used bottle openers.  Because try as we might we could not pry a bottle cap off with our hands.  Most grown men just didn’t have the strength to do that.  But a child could open a bottle if that child used a bottle opener.  For that bottle opener is a lever.  Giving the child leverage.  The ability to use a little bit of force to do a lot of work.

A lever is a rigid beam on a fulcrum.  Like a seesaw.  A common playground fixture.  If two kids of equal weight are on either end of the seesaw and the fulcrum is in the center these kids can effortless push up and down.  But if a grown adult sits on one end and a child is on the other the weight of the adult will drop his side of the seesaw down.  Leaving the child up in the air on the other side.

## As the Lever increases in Length the more it will Amplify the Input Force we Apply

Now that’s no fun.  Having the seesaw permanently tipped in one direction.  However, even two people of different weights can enjoy playing on the seesaw.  All they have to do is move the fulcrum towards the heavier person until the seesaw balances.  So that there is a short length of seesaw between the fulcrum and the heavy person.  And longer length of seesaw between the fulcrum and the lighter person.  This creates the same amount of torque on both side of the fulcrum.

Torque is the turning force created by a force acting about a fulcrum.  The force in this case is the weight of the people on the seesaw.  Which we calculate by multiplying their mass by the force of gravity.  With the force of gravity being constant the greater the mass the greater the weight.  This weight pressing down on the beam creates torque.   And the further away from the fulcrum the greater the turning force.  Such that a lighter weight at a greater distance from the fulcrum can balance a greater weight at a shorter distance from the fulcrum.  Allowing a child to play on a seesaw with someone of far greater mass.  Because the lever amplified the smaller force of the child.  Allowing the child to move a heavier weight.  To illustrate this consider the following table.

This is just a visual aid.  The numbers don’t represent anything.  It just shows a relationship between force and the length of the lever.  In this example we need 1000 units of force to move something.  If we use a lever that is 10 units from the fulcrum we need to apply 100 units of force.  If we have a lever that is 40 units from the fulcrum we only need to apply 25 units of force.  If we have a lever that is 80 units from the fulcrum we only need to apply 12.5 units of force.  As the lever increases in length the more it will amplify the input force we apply.  Which is why a child can open a bottle with a bottle opener.

## A Wheelbarrel combines the Lever with the Wheel and Axle

A lever gives us mechanical advantage.  The amplification of a small input force into a larger output force.  Such as a hand-held bottle opener.  But what about the kind that used to be fastened to pop machines?  When you bought a glass bottle of pop out of a vending machine?  The fulcrum is the fixed bottle opener.  And the lever is the bottle.  A can opener was often on the other end of a bottle opener.  Instead of a grip to latch onto a bottle cap this end had a triangular knife.  When we lifted up on the lever it pressed down and pierced a hole in a can.

A wheelbarrel allows us to move heavy loads.  This device combines two simple machines.  A wheel and axle.  And a lever.  The wheel and axle is the fulcrum.  The lever runs from the fulcrum to the handles of the wheelbarrel.  We place the load on the lever just before the axle.  When we lift the far end of the lever we can tilt up the load and balance it over the axle.  The lever amplifies the force we apply.  And the wheel and axle reduce the friction between this load and the ground.  Allowing us to move a heavy load with little effort.

Today’s pop bottles have screw-top caps.  Some people still use a lever to help open them, though.  A pair of pliers.  We use the pliers because we don’t have the strength to grip the cap tight enough to twist it open.  The pliers are actually two levers connected together at the fulcrum.  The pliers amplify our hand strand-strength to get a very secure grip on the bottle cap.  While our hands compress the two levers together getting a firm grip on the cap we can then use our arm to apply a force on the handles of the pliers.  Providing a torque to turn the bottle cap.  Very simple machines that make everyday life easier.  Thanks to the knowledge Archimedes handed down to us.

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# Magnets, Magnetic Field, Electromagnet, Electromechanical Solenoid, Stator, Armature, DC Electric Motor and Automobile Starter Motor

Posted by PITHOCRATES - April 18th, 2012

# Technology 101

## Electric Current flowing through a Wire can Induce Magnetic Fields Similar to those Magnets Create

We’ve all played with magnets as children.  And even as children we’ve observed things.  If you placed a bar magnet on a table and approached it with another one in your hand one of two things would happen.  As the magnets approached each other the one on the table would either move towards the other magnet.  Or away from the other magnet.  That’s because all magnets are dipoles.  That is, they have two poles.  A north pole.  And a south pole.

These poles produce a magnetic field.  Outside of the magnet this field ‘flows’ from north to south.  Inside the magnet it ‘flows’ from south to north.  So imagine this magnetic force traveling through the magnet from south to north and right out of the north pole of the magnet.  Where it then bends around and heads back to the south pole.  Something most of us saw as children.  When we placed a piece of paper with iron filings over a bar magnet.  As we placed the paper over the magnet the iron filings moved.  They formed in lines.  That followed the magnetic field created by the magnetic dipole.  You can’t see the direction of the field but it only ‘flows’ in one direction.  As noted above.  If the north pole of one magnet is placed near the south pole of another the magnetic field ‘flows’ from the north pole of one magnet to the south pole of the other magnet.  Pulling them together.  If both north poles or both south poles are placed near each other they will repulse each other.  Because the magnetic field is ‘flowing’ out from each north pole.  Or into each south pole.  The magnets repulse each other because the magnetic field is trying to flow from north to south.  If one magnet was able to rotate this repulsion would rotate the magnet about 90 degrees.  To try and align one north pole with one south pole.  As the momentum pushed the magnet past the 90 degree point the force would reverse to attraction.  Rotating the magnet about another 90 degrees.  Where it will then stop.  Having aligned a north and a south pole.

It turns out this ability to move things with magnetic fields is very useful.  Both in linear motion.  And rotational motion.  Especially after we observed we could create magnetic fields by passing an electric current through a wire.  When you do a magnetic field circles the wire.  To determine which direction you simply use the right-hand rule.  Point your thumb in the direction of the current flow and wrap your fingers around the wire.  Your fingers point in the direction of the magnetic field.  Fascinating, yes?  Well, okay, maybe not.  But this is.  You can wrap that wire around a metal rod.  Creating a solenoid.  And all those induced magnetic fields add up.  The more coils the greater the magnetic field.  That ‘flows’ in the same direction in that metal rod.  Creating an electromagnet out of that metal rod.  If you ever saw a crane in a junk yard picking up scrap metal with a magnet this is what’s happening.  The crane operator turns on an electromagnet to attract and hold that scrap metal.  And turns off the electromagnet to release that scrap metal.

## A DC Electric Motor is Basically a Fixed Magnet Interacting with a Rotating Magnet

If that metal rod was free to move you get something completely different.  For when you pass a current through that coiled wire the magnetic force it creates will move that metal rod.  If it’s not restrained it will fly right out of the coil.  Which is interesting to see but not very useful.  But the ability to move a restrained metal rod at the flick of a switch can be very useful.  For we can use a solenoid to convert electrical energy into linear mechanical movement.  As in a transducer.  An electromechanical solenoid.  That takes an electrical input to generate a mechanical output.  Which we use in many things.  Like in a high-speed conveyor system that sorts things.  Like a baggage handling system at an airport.  Or in an order fulfillment center.  Where things fly down a conveyor belt while diverter gates move to route things to their ultimate destination.  If the gate is not activated the product stays on the main belt.  When a gate is activated a gate moves across the path of the main conveyor belt and diverts the product to a new conveyor line or a drop off.  And the things that operate those gates are electromechanical solenoids.  Or transducers.  Things that convert an electrical input to a mechanical output.  To produce a linear mechanical motion.  To move that gate.

Solenoids are useful.  A lot of things work because of them.  But there is only so much this linear motion can do.  Basically alternating between two states.  Open and closed.   In or out.  On or off.  Again, useful.  But of limited use.  However, we can use these same principles and create rotational motion.  Which is far more useful.  Because we can make electric motors with the rotational motion created by magnetic fields.  The first electric motors were direct current (DC).  And included two basic parts.  The stator.  And the rotor (or armature).  The stator creates a fixed magnetic field.  With permanent magnates.  Or one created with current passing through coiled wiring.  The armature is made up of multiple coils.  Each coil insulated and separate from the next one.  When an electric current goes through one of these rotor coils it creates an electromagnet.

So a DC electric motor is basically a fixed magnet interacting with a rotating magnet.  Current passes to the rotor winding through brushes in contact with the armature.  Like closing a switch.  Current flows in through one brush.  And out through another.  When current goes through one of these rotor coils it creates an electromagnet.  With a north and south pole.  As this magnetic field interacts with the fixed magnetic field produced by the stator there are forces of attraction and repulsion.  As the ‘like’ poles repel each other.  And the ‘unlike’ poles attract each other.  Causing the armature to turn.  After it turns the brushes ‘disconnect’ from that rotor wiring and ‘connect’ to the next rotor winding in the armature.  Creating a new electromagnet.  And new forces of repulsion and attraction.  Causing the armature to continue to turn.  And so on to produce useful rotational mechanical motion.

## An Automobile Starter Motor combines an Electromechanical Solenoid and a DC Electric Motor

Everyone who has ever driven a car is thoroughly familiar with electromechanical solenoids and DC electric motors.  Because unlike our forefathers who had to use hand-cranks to start their cars we don’t.  All we have to do is turn a key.  Or press a button.  And that internal combustion engine starts turning.  Fuel begins to flow to the cylinders.  And electricity flows to the spark plugs.  Igniting that compressed fuel-air mixture in the cylinder.  Bringing that engine to life.

So what starts this process?  An electromechanical solenoid.  And a DC motor.  Packaged together in an automobile starter motor.  The other components that make this work are the starter ring gear on the flywheel (mounted to the engine to smooth out the rotation created by the reciprocating pistons) and the car battery.  When you turn the ignition key current flows from the battery to the electromechanical solenoid.  This linear motion operates a lever that moves a drive pinion out of the starter (while compressing a spring inside the starter), engaging it with the starter ring gear.  Current also flows into a DC motor inside the starter.  As this motor spins it rotates the starter ring gear on the flywheel.  As combustion takes place in the cylinders the pistons start reciprocating, turning the crankshaft.  At which time you let go of the ignition key.  Stopping the current flow through both the solenoid and the DC motor.  The starter stops spinning.  And that compressed spring retracts the drive pinion from the starter ring gear.  All happening in a matter of seconds.  So quick and convenient you don’t give it a second thought.  You just put the car in gear and head out on the highway.  And enjoy the open road.  Wherever it may take you.  For getting there is half the fun.  Or more.

Electric motors have come a long way since our first DC motors.  Thanks to the advent of AC power distribution and polyphase motors.  Brought to us by the great Nikola Tesla.  While working for the great George Westinghouse.  Pretty much any electric motor today is based on a Tesla design.  But little has changed on the automotive starter motor.  Because batteries are still DC.  And before a car starts that’s all there is.  Once it’s running, though, a polyphase AC generator produces all the electricity used after that.  A bridge rectifier converts the three phase AC current into DC.  Providing all the electric power the car needs.  Even charging the battery.  So it’s ready to spin that starter motor the next time you get into your car.

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# In the Face of Force and the Willingness to use that Force the Iranians back off the Hostile Rhetoric

Posted by PITHOCRATES - January 22nd, 2012

# Week in Review

The Iranians love diplomacy.  Because they see it as a sign of weakness and don’t respect it.  They respect only one thing.  Force.  And the willingness to use it.  Which they’ve seen of late.  And have backed off of their shutting down the world’s oil supply rhetoric (see After threats, Iran plays down U.S. naval moves by Robin Pomeroy and Hashem Kalantari, Reuters, posted 1/21/2012 on Yahoo! News).

Iran’s Revolutionary Guard Corps said on Saturday it considered the likely return of U.S. warships to the Gulf part of routine activity, backing away from previous warnings to Washington not to re-enter the area.

The statement may be seen as an effort to reduce tensions after Washington said it would respond if Iran made good on a threat to block the Strait of Hormuz – the vital shipping lane for oil exports from the Gulf.

The US said say all you want but that carrier will be there.  And it will respond to any hostile acts such as blockading the Strait of Hormuz.  As will their steadfast ally the Brits.  Who sent a serious naval asset to the region.  A Type 45 destroyer.  A single ship that can shoot down anything the Iranians can throw into the air long before hitting any US, UK or other friendly target.  And, of course, with that US carrier and its task force on station as well the response to that failed Iranian attack would have been devastating.  The Iranians would have had their asses handed to them.

They’ll talk until everyone is blue in the face.  To them diplomacy is unmanly and a sign of weakness.  They simply don’t respect it.  But project force and be willing to use that force and they will respect that.  Which is the only thing they will respect.

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