Foundations of Physical Science Workshop: Gears. Gears CPO Science.

Foundations of Physical Science

Workshop: Gears

GearsCPO Science

Key Questions

How do gears work?

What is the Law of Gearing?

How can Gear Ratios be used to design machines?

Overview Build gear machines

Deduce the rule for calculating the number of turns for each gear in a pair of gears

Apply ratios to design machines with gears

Design a gear machine to solve a specific problem

Simple Machines Include: rope and pulley

wheel and axle systems

gears

ramps

levers

screws

Gears as Simple Machines

Simple machines can change the direction and/or magnitude of an Input Force

What are the variables? Teeth – Each sized

gear has a particular # of teeth. How many does each size have?

Turns – Each gear turns an exact amount of times, which we can count. How many times does each one turn?

Gear Investigation #1 Build 3 Gear

machines Top Gear – Input

Gear

Bottom Gear – Output Gear

Looking at the Results Can you derive a mathematical

formula which relates the # of turns of the Input Gear to the # of Turns of the Output Gear?

What is the relationship?

Use the # of Turns

Use the # of Teeth

Mathematical Relationship (Input gear turns x Input gear teeth) = (Output

gear turns x Output gear teeth)

Make the equation easier to use by substituting 1.Let Ni = # of turns of the Input gear2.Let Ti = # of teeth of the Input gear3.Let No = # of turns of the Output gear4.Let To = # of turns of the Output gear

5.Ni x Ti = No x To

The Law of Gearing

Ni x Ti = No x To

Can we write it another way?

Complex Gear Machines Make a machine that

uses at least 2 pairs of gears- Not this one--- make your own

Record the position and # of teeth on each gear in the Data Table

Record and count how all the gears rotate

Use what you have learned and the table to work out the gear ratios

Gear Assembly for Complex Machine

Looking at the Pairs of Gears Use Table 2 to figure out how to

calculate the final gear ratio

Final Gear Ratio Each pair of

gears has a gear ratio

This ratio (fraction) can be reduced

There can be more than two pairs of interfacing gears in total

Find the Gear Ratios of all pairs

Final Gear Ratio Reduce each Gear Ratio fraction from Table 2

12:24 = 12/24 = 1/2

Multiply all Gear Ratio fractions

½ x ½ = ¼ = 1:4

This is the Final Gear Ratio

1:4 or 4:1? The gear ratio depends on what gear you use as

input and what gear you use as output.

If the final gear ratio fraction is less than 1, like 1:2 = ½, the output gear turns less than the input gear. This is used for power, like when using a low gear to go uphill on a bike.

If the final gear ratio fraction is more than one, like 4:1 = 4/1, the output gear will turn more than the input gear. This is used for speed, like using a high gear when going really fast downhill on a bike.

Designing Gear Machines What is the objective? Speed vs. Power

What is the desired Final Gear Ratio? – factor it to lowest possible values

Look at the gears you have to work with

Use the available ratios to get the final gear ratio you need

How about spin direction?

Factoring Gear Ratios Example

Gear Ratio Desired – 6:1

1.Factor 6/1 3 x 2 = 62.Check Available Ratios – 1:3, 1:2, 2:3,

3:1, 2:1, 3:23.Is it possible? Yes 3/1x 2/1= 6/1= 6:14.Attach Gear pairs that give desired

Final Ratio

5.It may require more than two pairs of gears

How Can You Make-9:1

4:1

18:1

The highest possible ratio with the gears provided

3/1 x 3/1 = 9/1

2/1 x 2/1 = 4/1

3/1 x 3/1 x 2/1 = 18/1