## Gear Ratio

### Gear Ratio Definition

Contents

What is Gear Ratio

The gear ratio of a gear train is the ratio of the angular velocity of the input gear to the angular velocity of the output gear, also known as the speed ratio of the gear train. The gear ratio can be computed directly from the numbers of teeth of the various gears that engage to form the gear train.

In simple words, the gear ratio defines the relationship between multiple gears.

Gear Ratio = Output Gear Teeth / Input Gear Teeth

For example – If our motor is attached to gear with 60 teeth and this gear is then attached to a gear with 20 teeth that drives a wheel, then

the Gear Ratio is 60:20, or more accurately 3:1

• If you do not want to count gear’s teeth (or if they do not exist), the gear ratio can also be determined by measuring the distance between the center of each gear to the point of contact.

For example – if our motor is attached to a gear with a 1″ diameter and this gear is connected to a gear with a 2″ diameter attached to a wheel –

From the center to the edge of our input gear is 0.5″

From the center to edge of our output gear is 1″

the Gear Ratio is 1/0.5 or more accurately 2:1

• They prevent slippage between the gears – therefore axles connected by gears are always synchronized exactly with one another.
• They make it possible to determine exact gear ratios – you just count the number of teeth in the two gears and divide. So if one gear has 60 teeth and another has 20, the gear ratio when these two gears are connected together is 3:1.
• They make it so that slight imperfections in the actual diameter and circumference of two gears don’t matter. The gear ratio is controlled by the number of teeth even if the diameters are a bit off.

### What Gear Ratio tells us about Speed?

• The gear ratio tells us how fast one gear is rotating when compared to another.

If our input gear (10 teeth) is rotating at 5 rpm, and it is connected to our output gear (50 teeth), our output gear will rotate at 1 rpm.

How?

Our gear ratio is 50:10 = 5:1

If our small gear rotates 1x, our large gear only rotates 1/5. It takes 5 rotations of our small gear to take 1 rotation of our large gear. Thus our large gear is rotating at 1/5 the speed = 1 rpm.

What if our gear ratio where 1:3?

In this case, our input gear is 3x larger as large as our output gear.

If our input gear were rotating at 20 rpm. Each rotation would result in 3 rotations of our output gear. Our output would be 60 rpm.

### Use of Gears

• To reverse the direction of rotation
• To increase or decrease the speed of rotation
• To move the rotational motion to a different axis
• To keep the rotation of two-axis synchronized

### Torque

#### What is Torque and What Torques tell us?

• Torque is a twisting force
• It doesn’t do any ‘work’ itself- it is simply an application of energy.

Work happens, when torque is applied and movement occurs.

• “Torque is a force that tends to rotate or turn things.
• You generate a torque any time you apply a force using a wrench.
• Tightening the lug nuts on your wheels is a good example.
• When you use a wrench, you apply a force to the handle.
• This force creates a torque on the lug nut, which tends to turn the lug nut.

### Important Points

• English units of torque are pound-inches or pound-feet.
• The SI unit is the Newton-meter.
• Notice that the torque units contain a distance and a force. To calculate the torque, you just multiply the force by the distance from the center.
• In the case of lug nuts, if the wrench is a foot long, and you put 200 pounds of force on it, you are generating 200 pound-feet of torque.
• If you use a two-foot wrench, you only need to put 100 pounds of force on it to generate the same torque.