One of the most difficult and yet common mechanical systems is a gear train. A great way to transmit mechanical power from one place to another or to increase or decrease power (torque) or increase or decrease the speed of something.

The problems are always that to make efficient gears needs quite a lot of drawing and mathematical skill as well as the ability to machine complex shapes.

For a lot of amateur work it isn't necessary to have maximum efficiency and therefore we can get away with a much easier to make, even with hand tools, system.

A gear is basically a series of teeth on a wheel.

http://automata.co.uk/gears.htm

provides a very good explanation of how gears work and how to work out gear ratios.

(Note in the diagram above they have labeled an incorrect number of teeth on the gears - sorry)

## Step 1: Formula and Maths (the Bad News)

Formula for drawing and making gear teeth are all over the web BUT they seem, to the beginner, very complicated.

from http://www.engineersedge.com/gear_formula.htm

So I decided to simplify the issue and it works very well at both large scale and small scale. At small scale it works best with machine cutting with laser cutters for example when very small gears can successfully be made this way.

## Step 2:

## Step 3: The Easy Way

So how.

1. the shape of the teeth is simplified to be half a circle

## Step 4: Working Out the Size of Everything

2.We can now easily sort out some simple maths to make our gear

- a. How big/small do we need the gear teeth to be, (diameter) - The smaller the gear the smaller the teeth need to be.
- b. All the teeth that are going to mesh, (connect), together must be the same size so calculate your smallest gear first.

3. Lets start with a gear tooth size of 10 mm

I want a gear with 5 teeth on it so the circle will be 10 x 10mm round (circumference)= 100 mm

To draw that circle I need to find the diameter so I use a bit of maths and a calculator a divide the circumference (100 mm) by Pi = 3.142

This gives me a diameter of 31.8mm I can draw this with a compass and then fit exactly 10 circles 10mm diameter round it with my compass.

If your able this is easier to do with even the most basic drawing software. If your using software you should be able to rotate the tooth circle round the main circle and will need to know how far to rotate each tooth - This is easily calculated by 360 deg / the number of circles so for our 10 circles 360/10=36 deg rotation for each tooth.

## Step 5: Making the Tooth Shape.

delete the top of one circle and the bottom of the next circle. To make this work out there must be an EVEN number of teeth

4. We have our first gear. This can be cut in wood or metal with basic hand tools, saws and files.

5. It is easy to repeat this process for any number of gears as we need them. Keep the circle size the same and they will fit together.

## Step 6: You Have Your Gear

6 Because this semi-circle shaped gear tooth is easy to cut you can do it with hand tools, a sabre (jig) saw or even a coping saw.

In the past I have made a template of 9 or 10 teeth from plywood and use it as a guide for my hand router and cut the gear teeth with little trouble.

If you have access to a laser cutter these can be cut from 3 or 5 mm acrylic and work well down to very tiny sizes.

## Step 7: UPDATE

Just to add this to these ideas. Some time ago i tried making simple plywood circles and gluing on the outside a cut down timing belt from a car. This worked as well and is a LOT quicker to do.

You need to select a diameter that will suite the teeth spacing on the belt. I elected to cut between 2 teeth and make my join there.

## 44 Discussions

10 days ago

Thank you, that is really helpful to me.

Question 1 year ago on Step 3

Rick,

I have tried to make several gears with the circle unit, but my compass and triangles are not up to the job. Do you know of a web drawing tool I could use?

Answer 1 year ago

There are a number of FREE CAD tools that will help you. A google search should find some.

Sketchup is perhaps the best known although has a steep learning curve.

A 2D CAD tool is perhaps best for drawing these gears.

1 year ago

great! that's really useful with new lasercut tecnology which is becoming more and more accessible!

2 years ago

very good instructions, but it's you're not your

Reply 2 years ago

As far S I know this is my original idea, unless you can show otherwise?

Reply 2 years ago

what

Reply 2 years ago

your comment "a very good instruct able but it isn't your..."

I assume this continues you're idea???

2 years ago

Guys,

anyone can easily design gear by using this gear calculator

http://www.mechanicalengineercalculator.com/helica...

http://www.mechanicalengineercalculator.com/gear-calculation/

3 years ago

I don´t know how did you learn to count in school, but it seem to be that the small gear has got only 5 teeth (a 5 5 cavities, wich do not count as teeth). The same happens with the drawing of your explanations

Reply 3 years ago

I learned to count very well thanks.

However I perhaps did not express the idea quite as succinctly or precisely as I should have.

Text corrected.

(i will restrain myself from commenting on your spelling.)

Reply 2 years ago

touché

Reply 2 years ago

:-)

2 years ago

Very nice, and I really can use that wood link to gears below. I am using a couple of gears for an exhibit panel..you turn the gears and see the text exposed in the 'window' in the gear! Will be fun for the kids to turn it and find out the message:)

Cheers !

2 years ago

Might check out: http://joostn.github.com/OpenJsCad/

Found that and haven't had to worry about gears since.

3 years ago

I have a 53mm diameter robot arm. The shaft of the servo that rotates it is off-center, obviously inside the arm. The distance from the shaft center to the arm is about 17mm. Therefore the diameter of the pinion gear will be around 34mm. In order for the arm to rotate centered (without blocking the interior wire passages with an attached artificial shaft) is to create inward facing teeth - an internal spur gear with an outer diameter of 53mm. So in the real world, these are the parameters we begin with:

Maximum diameter of confinement: 53mm

Pinion gear diameter: 34mm

So now the question is how many teeth each of the gears should have. I have not found the maths for this anywhere on the internet. This is a real world example, and I claim that all the lessons on how to build gears ignore the most crucial factor when determining the number of teeth for each gear: The confinement area.

Can anyone please help who actually has real world experience (so you can relate to building gears other than classroom theory)? Thanks.

Reply 3 years ago

1. This idea works well for simple low tec and low force gears. You have to select the tooth circle size to suite the diameter you require. It may not be possible to get all sizes to fit as the gear teeth must be the same size on each gear which now defines the diameters of other gears.

2. I am a honors degree qualified engineer I somehow resent the suggestion I don't have real world experience. I worked in various high tec Industries for 28 years before becoming a teacher. I could do your calculations for you if I have all the relevant information but I won't you should be able to take the information given and turn it into what you want - That's called understanding,.

3. IF you want to manufacture "real" gears then you need to follow some of the links I supplied particularly the

http://woodgears.ca/gear_cutting/template.html

link which is a gear calculator package. You will find many on line that should you be able to input the correct parameters will generate gear tooth patterns for you.

IF your unable to cut the gears that any competent engineering shop should be able to cut them to your specification.

3 years ago

This doesn't make any sense. I have two specific diameters. I need to calculate the number of teeth to make the teeth mate. One diameter is 34mm and the other is 53mm. These are not negotiable for my project. The 34mm gear is an external toothed spur gear and the 54mm gear is an internal toothed spur gear. So the question everyone must be asking is, what is the maths required to calculate the two integers? If you don't care what size each gear is, then you are not needing actual gears for a real world application. Please explain the calculation of how many teeth are required for any two gear sizes in a way that results in the teeth mating accurately. Like I said, my ratio is 34:53, external spur pinion and internal driven spur wheel.

Reply 3 years ago

You know what, I think you are entirely obfuscating what you think you want. Upon rereading your comment you just need a gearing RATIO of 34:54, and you think that what this means is the diameters are 34mm to 54mm, they would be if two circles could spin (they wouldn't, you'd be off by a factor, besides the point).

You want 34 TEETH to 54 TEETH which is a different diameter. Odds are you'll need to have multiple stages, but otherwise you want a .6296 ratio. So if you had a 8.18t pinion gear you'd want a 13t pinion gear. Play with the numbers and you realize you can go with a 10t pinion and a 17t spur gear, that comes pretty close to what you want, that being said you need to come up with your own solution, or provide more details on your needs. That is after all why people pay engineers.

Reply 3 years ago

That's unfortunately not how the real world works. A "real world application" would involve the engineer planning a little ahead of time ;)

Two gears meshing has a lot of very specific requirements. Not only is that not how a 34:53 gear made, the exterior gear would have to be non-circular in order to spin around (or the middle gear is not circular).

If you are looking for two gears like that I would suggest a custom gear solution, it'll cost $1,000 to a few thousand each pair.

Otherwise, work your system around. There are plenty of compact gear ratios like planetary sun and moon gears that might only set you back a few hundred if you don't want to just use metal spur gears over multiple stages.

http://www.rushgears.com/ has a great collection of all the possibilities while using spur gears.