Gears, Gears and More Gears

©2006 4H-CCS

Basic Physics Terms

In this lesson, we will review some basic physics terms anddemonstrate them using our LEGO® gearbox.

• Force and Torque• Mechanical Advantage• Newton’s Laws• Work and Power• Friction

©2006 4H-CCS

Gear Box

Please make the following modifications to the gear box from the Gear Box building Instructions.

Remove the motor and double beam.

Place bushingshere and here.

Remove the rotational sensor.

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Gear Box

Please make the following modifications to the gear box from the Gear Box Building Instructions.

Add pulley wheels and gray pegs (for handles).

Add another1x16 beamhere.

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Basic Terms - Force

What is a “force?”

A force causes something with mass to move (accelerate).

This can be summed up with Newton’s 2nd Law. F = m x a

Question: What force do we experience every single day?

(In fact, units of force are called “Newtons.”)

Answer: The force of gravity.

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Basic Terms - Torque

What is “torque?”

Torque can be thought of as rotational force.

Torque causes something with mass to rotate.

We are interested in “torque” because we deal withrotational motors and axles.

This motor produces a torque.

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Force and Torque

How are force and torque related?

A force here...

…produces atorque here.

moment armA force can create a torque by acting through a moment arm.

The relationship is = F x r. r is the length of the moment arm (in this case, the length of the wrench).

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Gears and Torque

Up to now, we have been talking about how gears changespeed. But they can also change torque.

Question: What is the gear ratio of this gear box?

That means the last axle rotates 75 times slower than the first axle. It also means the last axle has 75 times the torque as the first axle.

Answer: 75 to 1

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Gears and Torque

Try this experiment.

Have one person turnthis wheel.

And have another persontry to hold on to this wheel.

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Gears and Torque

Where does all this “torque” come from?

A torque on this axle...

…produces a force at the tooth.

F

The moment arm is the radius of the gear.Remember: = F x r

r

Consider a pair of gears that are meshed together.

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Gears and Torque

The force from the small gear’s tooth pushes againstthe large gear’s tooth. This creates an equal (and opposite)force in the large gear. This is Newton’s 3rd Law.

…and produces a larger torque on this axle.

F

The force acts through this larger moment arm...

r

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Gears and Torque

F1 = -F2

r2

r1

Analyzing the forces... 1 = F1 x r1 2 = F2 x r2

F1 = 1 / r1

F2 = 2 / r2

F1 = - F2

1 / r1 = -2 / r2

2 / 1 = r2 / r1The ratio of torques is the ratio of the gear radii.This is the gear ratio!

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Gears and Torque

Gears can increase the torque (and force) that they exerton something. This is known as mechanical advantage.

BUT, it comes at a price. Do you know what it is?

torque increases

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Basic Terms - Work

Work (in physics) is defined as a force acting over a distance.

W = F x d

Work in terms of rotation is a torque acting over an angle.

W = x

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Mechanical Advantage

Understanding the 2 components of work is the key to understanding mechanical advantage.

Question: Where would you hold the wrench for it to be most effective?

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Mechanical Advantage

If you hold the wrench here, you need a lot of force...

If you hold the wrench here, you don’t need as much force...

…but you don’t move very far.

…but your hand moves a long way.

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Mechanical Advantage

It takes the same amount of work to turn the bolt.You can opt for a lot of force and little distance.W = F x d

Or you can choose a little force but a lot of distance.W = f x DIn many of our machines, we want to increase our force, so we don’t mind going the extra distance.

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Mechanical Advantage

Question: Which ramp would you prefer to use to move a heavy weight to the top of the box?

Answer: This ramp requires less force, but you have to move the weight a longer distance.

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Mechanical Advantage

With our gear box, you were able to create a large torque here...

…but you had to turn this handle many times.Remember: W = x

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Power

Power is the rate at which work is done. It can be thought of as work per second.

Power = Work / sec.

Like work, power has 2 components, force and speed.

P = F x v (v stands for velocity).Question: Can you name 2 units for power?

Answer: Horsepower and watts.

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Power

Power has the same trade-offs as work. A motor produces the same amount of power.

So, you can make a robot that’s fast, but weak.

Or you can make a robot that’s slow, but strong.

The total power in must equal the total power out. (with an exception)...

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Friction = Bad

Friction is caused by two surfaces rubbing together.

Friction in our gear box causes a loss in the input power. It is lost in the form of heat and sound energy.

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Friction = Good

But friction is also what makes our robot move.

The turning wheel produces a frictional force against the ground, which causes the robot to move.

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Summary - Key Points

• A force causes something with mass to move.• Torque is rotational force.• Work has 2 components, force and distance.• Mechanical advantage lets you increase one

component of work at the expense of the other.• Gears are one way to get mechanical

advantage. They can increase the robot’s torque.

• Power is the product of force and speed.• A robot can either be slow and strong, or fast

and weak.• Friction causes both losses in power, but also

makes robots move on the ground.