This instructable will guide you through the construction and relationship between nautilus gears.

I have been fascinated by these items ever since I first saw them in an online video, I am also challenged by the opinion that they have no practical use.

Please note, I am an Engineer but I am by no means an expert on gears, I have found calculations online and made some assumptions and conclusions of my own, if I am incorrect anywhere please feel free to correct me, just please be nice about it :-).

## Step 1: What Is a Nautilus Gear?

A nautilus itself is a shellfish, shown in the picture.

A nautilus gear is an odd shaped gear that follows a Fibonacci spiral.

We are all familiar with the Fibonacci sequence 1,1,2,3,5,8,13,21...

You find the next number in the sequence by adding the last two together, so for example the next number from the sequence above would be 13 + 21 = 34.

Nautilus gears only work in pairs where both gears are the same size, this results in a 1:1 gear ratio but the delivery of this ratio is quite unusual. If you rotate the driver gear at a constant speed, the driven gear will rotate at a constantly varying speed.

## Step 2: Speed Theory

In the table below I am attempting to show how the speed of a driven nautilus gear varies over a single rotation.

I am using the formula: number of teeth (driver) x speed (driver) = speed (driven) x number of teeth (driven)

To simplify the equation, I am assuming the input speed to be 1rpm.

*the radii used are based on the gears I will make in later steps, there is some rounding so don't take these numbers as absolute.

## Step 3: Creating a Nautilus Gear

The 3D model for the gears was created using Fusion 360.

I started out by creating the structure, this went as follows:

Square 10x10

Square 10x10

Square 20x20

Square 30x30

Square 50x50

Square 80x80

I then used the centre arc tool to create an arc from the corner of each square to create a quarter circle.

I removed the construction outlines and added a spline to reclose the shape.

The shape was extruded to 4mm.

I then drew a simple gear tooth using a triangle 7mm across the base and 7mm tall, I used the filet tool to round all the edges. Please note that this is only rough and not sound gear design, there are complex mathematics involved in gear tooth design.

I laid the tooth onto the start of the curve and used the pattern following path tool to duplicate the tooth around the gear.

I then drew a central hub and added an unnecessary fancy design to cut down on the required print material.

The stl file is included if you want to skip this step

## Step 4: Printing

I printed the gears using a UP2! 3D printer.

I set the printer to medium infill and .4mm layer thickness to get a quick print.

This consumed 38g of ABS and took 48mins.

In retrospect I should have used a finer layer thickness as the hub fell out of my final print.

## Step 5: Set Up and Testing

Once produced, I needed to make a decision about mounting the gears, I could print a mount but the printer I used had been loaned to me and i had now returned it.

I decided to use some Mechano, unfortunately the centers on the gears did not match up with the Mechano so I had to make the adjustable support you see in the pictures. This part was all don on the fly and I don't have any real design for this but you are all clever people and I'm sure you can make up a better mount!

I attached some red plastic to make the motion of the gear speed clearer to see, the gears are a little hypnotic to follow themselves.

As I tried to run the gears, my lack of gear design knowledge became apparent. I needed to remove the curved bumper between the large and small end of the curve but keep the teeth. The first and last teeth needed to be shaped with a file in order to run semi smoothly.

I left a long drive shaft off one gear in order to attach my drill as a motor but got a bit carried away and damaged the hub on the first one.

I redesigned for 2 gears which you can see in the video. The system does run though it is a little jittery at the change over with the flats.

You can clearly see the output gear varying in speed.

## Step 6: Idea for a Use...

I do a little work with control of pumps and I may be wrong here but let throw it out.

The stoke of pump requires more force at the end of the stroke than the start, torque is inversely proportional to speed so as the gear is in the fast portion of the cycle its torque is low, as is slows, the torque increases. This may make pumps run a little more efficiently... opinions.....

**If you liked this ible, please vote for me in the 3D design contest.**