# Stepper - Gear/Circumference Ratios

#### PathogenIX

Joined Oct 14, 2020
21
Ok here goes,
I want to modify my printers Y axis

TLDR: How do i get the same distance travelled using belts/gears without altering the printers firmware.

Currently the stepper has a 20 teeth pulley wheel attached.

Pulley Wheel 20 Teeth
Circumference = 38.3903mm
38.3903mm / 200 Steps = 0.1919515mm PerStep1

I have a 2Phase Stepper Motor 42. 5mm shaft diameter.

I also have a Conveyor Roller 30mm Diameter.

Roller
Circumference = 94.2478mm
94.2478mm / 200 Steps = 0.471239mm PerStep2

If i connect the stepper shaft to the roller shaft with a coupling.
Then one rotation of the stepper will be one rotation of the roller. But how would I get PerStep2 to = PerStep1 using either gears or a belt system...

I can see its very close to a 2-1 ration but is being "close" enough for accuracy?
I have some spare GT2 timing belts and pulley heads to use.

I feel like i've got the right idea but need help.

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#### KeithWalker

Joined Jul 10, 2017
1,582
We don't know how your printer is made so it is difficult to understand exactly what you are trying to do. You state that you want to modify your printer's Y axis but you don't mention how you want to modify it. You ask how to get the same distance travelled using belts and gears but you don't say what it should be the same as.
If you are using a toothed belt and pulleys, forget about diameters and simply use the ratio between the numbers of teeth on the pulleys.
Regards,
Keith

#### PathogenIX

Joined Oct 14, 2020
21
We don't know how your printer is made so it is difficult to understand exactly what you are trying to do. You state that you want to modify your printer's Y axis but you don't mention how you want to modify it. You ask how to get the same distance travelled using belts and gears but you don't say what it should be the same as.
If you are using a toothed belt and pulleys, forget about diameters and simply use the ratio between the numbers of teeth on the pulleys.
Regards,
Keith
So i should be using this chart to find the correct pulley to match?
Can you link a good calculator/explaination for picking the correct pulley? (All my searches have brought up belt length calculations...)
Printers an Ender3 "Pro"

The roller should match the same rotation as the stepper motor which is 1.8 degrees.
The build plate is 24cm²
The belt should idealy be looped or be able to do 1 1/2 full rotations.
Image of Y axis
Belt drives a 20tooth pulley with GT2 belt that runs around a same size toothless idler to the Build plate.

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#### KeithWalker

Joined Jul 10, 2017
1,582
I would help but if I could but you have still not explained exactly what you are trying to do. Are you replacing the stepper motor with a different one?

#### shortbus

Joined Sep 30, 2009
8,429
So i should be using this chart to find the correct pulley to match?
Why? that is just a list of available pulleys, sprockets really. Forget diameters and think teeth. Those belts and sprockets are just a silent low power replacement for a roller chain and sprockets. The belt it's self can be any length needed to connect the two sprockets.

You need to give more information to what you want or are doing. If it is just to print on a longer paper you will probably also need to modify your firm ware as you call it, or the printout will be skewed by the different movement of the page.

#### bwilliams60

Joined Nov 18, 2012
1,386
I am not sure what younare trying to do but gear ratios are calculating by driven/drive. I am with the rest though on the fact that you really haen't explaineed what you are doing or why?

#### PathogenIX

Joined Oct 14, 2020
21
Ok so i want to convert the Yaxis (Build plate) on my ender3 to a conveyor belt for queued printing not infinite printing (Que = list of files to print with Ymove code placed 100% between each print) [Not an issue have software/codes setup already]
I do not plan on changing the Zaxis angle.

I have two rollers that are 30mm diameter.
I have a standard 1.8 degree stepper motor that i want to use to drive the belt (I can use two if needed for torque)

I need to work out how to translate the movement across to the roller and have it equal the same distance the yaxis travels on the original y axis. So 5mm Yaxis Bed = 5mm Yaxis Conveyor.

When you talk about using teeth to work out movement would it be like this? 20 Teeth Driver, 60 Teeth Roller = 1/3 Ratio?

#### MrChips

Joined Oct 2, 2009
23,069
If I understand this correctly, you want to modify your Creality Ender-3 3D printer so that you have a longer print bed.

This requires a longer belt and longer track. It also requires modifying the firmware.

It would be simpler to buy another printer.

#### PathogenIX

Joined Oct 14, 2020
21
If I understand this correctly, you want to modify your Creality Ender-3 3D printer so that you have a longer print bed.

This requires a longer belt and longer track. It also requires modifying the firmware.

It would be simpler to buy another printer.
Yes the bed will be "longer". But looped with a conveyor belt...
I have spare 2020 extrusion i plan to use for the frame of the conveyor
It doesnt need to register as an infinite length as i can send gcode between files to reset back to home position.
I'm originally planning on building this as a seperate machine but no point ordering controllers if i cant even get the formula i need to do the basics...

I don't mind small firmware changes to calibrate for the change but nobody seems to know what formula i need to work out the translation of movement... Its all good saying i should modify the firmware but it's no good without the correct number to replace in the code...

There are lots of videos of people having done this but nobody explains how they worked out the change of rotation...

Accurate 3D file attached incase people are still having hard time understanding what i'm aiming for...

#### Attachments

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#### MrChips

Joined Oct 2, 2009
23,069
Perhaps no firmware change is required.
Build a longer bed. Move the Y-home micro-switch and change Y=0 or Y offset setting.

Or have mutiple selectable optical Y-home sensors.

#### KeithWalker

Joined Jul 10, 2017
1,582
When you talk about using teeth to work out movement would it be like this? 20 Teeth Driver, 60 Teeth Roller = 1/3 Ratio?
No! 3:1 ratio.

#### PathogenIX

Joined Oct 14, 2020
21
Think i've got it down. So if i use 60 Teeth for the driver and 20 Teeth pulley for the Roller. Then increase the Rollers radius by 18.33mm I'd have accurate rotation translation?

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#### KeithWalker

Joined Jul 10, 2017
1,582
Ok so i want to convert the Yaxis (Build plate) on my ender3 to a conveyor belt for queued printing not infinite printing (Que = list of files to print with Ymove code placed 100% between each print) [Not an issue have software/codes setup already]
I do not plan on changing the Zaxis angle.

I have two rollers that are 30mm diameter.
I have a standard 1.8 degree stepper motor that i want to use to drive the belt (I can use two if needed for torque)

I need to work out how to translate the movement across to the roller and have it equal the same distance the yaxis travels on the original y axis. So 5mm Yaxis Bed = 5mm Yaxis Conveyor.
From your explanation it is difficult to visualize what you are trying to do.
I will take a guess that you want to move a conveyor belt a pre-determined distance for every step of a motor and you want to use toothed belt and pulleys to couple the motor to the conveyor belt.
First you need to know the distance the conveyor belt should travel for each step of the motor. From that you can calculate the angular motion of the conveyor belt drive roller per step.
Then you need to know how many steps per revolution for the motor. From that you can calculate the angular motion of the motor per step.
You can then use those two numbers to calculate the gear ratio.
You need two whole numbers for the gear ratio, so take the closest whole numbers to your answer and work back to find out how much to change the diameter of the drive roller to get the right distance for the conveyor per step.

#### shortbus

Joined Sep 30, 2009
8,429
Think i've got it down. So if i use 60 Teeth for the driver and 20 Teeth pulley for the Roller. Then increase the Rollers radius by 18.33mm I'd have accurate rotation translation?
Doesn't the original existing printer use sprockets and belts? It looks like it in the ad pictures.

If it does you just need to build a new *base* and have a longer 2020 extrusion for the guide to move on. I say new base because I'm assuming(don't have one of these and just going by what is shown on the website) the 2020 extrusion gets supported by the base. and the 2020 extrusion also supports the base/build plate.

You would then use the original belt sprockets, no need for any extra ones with new gear ratios at all. But since you now have a longer *bed* you will need a new belt to fit the extension.

You then need another new build/base plate too with all of the heating or what ever is used on the original bed. Since you will now have two beds.

Then you need to assign EACH base/build plate a position, like Mr.chips said earlier.

This type thing is done all the time in CNC machine work, two or more parts mounted to a machine table to be worked on one right after another. But there is no lessening of the actual working time of the operations, just like there won't be for this printer. Especially with a filament printer, since the heat from one pass is needed for the next pass to bond. The only reason they do it ine CNC machineing is the operator runs more than one machine at a time. While machine 1 is doing it's job, the operator is unloading and reloading machine 2.

So, I can't see how completely remaking this printer is going to do anything useful for you. But it's your project after all and I'm just giving you the facts as I know them. I've made things using 2020 extrusion before and know it's expensive to buy. And was a machinist/die maker so do know unless you have a machine shop for doing this to make it work as good as the original printer you would probably be better off and it will probably be less expensive to just buy another extra printer. Good luck with your project.

#### shortbus

Joined Sep 30, 2009
8,429
From your explanation it is difficult to visualize what you are trying to do.
Hi, you type faster than me. I think I've figured out what he is up to, check out post #14.

#### PathogenIX

Joined Oct 14, 2020
21
Thanks all the for info. KeithWalker gets what im trying to do @post #13.

My Yaxis is set at Ysteps/mm = 80
So 80 Steps = 1mm moved.

#### shortbus

Joined Sep 30, 2009
8,429
I think there is a nomenclature problem here. One with what each axis is called. The world I come from, they go as follows: "X" the longest axis of a table, usually moving left to right when the at the operator station or for this printer the movement in or out of the gantry. "Y" the in and out axis of the table, in a gantry machine like your printer the movement of the print head between the upright, on the gantry. "Z" the up and down axis away or toward the table.

Exactly where is the new conveyor belt going to go? How is it going to work in a 3D printer, that needs a build/base plate for the work(X axis), and a print head(Y axis)? Never saw one using a conveyor belt.

#### MrChips

Joined Oct 2, 2009
23,069
I too have a Creality Ender-3 printer.
X is left to right motion of extruder head while facing printer.
Y is the bed motion front to back.
Z is vertical axis driven by screw drive.

Both X and Y stepping motors use belt drives.

#### PathogenIX

Joined Oct 14, 2020
21
Crappy example here. The belt with be a lil longer in reality and endstops are going to be optional.
Conveyor Belt = Red
Drive Servo = Green
Roller bearing housing = Blue

Final goal will be relocating electronics out from underneath to the sides

#### mcardoso

Joined May 19, 2020
193
@PathogenIX,

I get what you are going for here. The best thing to do would be to modify the software to program a new mm/step value. Even then you'd want to get it close to the original mm/step travel value or you will lose print resolution and accuracy.

Stepper motors can be purchased with integral gearboxes from StepperOnline and other suppliers (no affiliation, just have bought from them before). I'd choose one of these over creating your own gear reduction or adding additional belts. The biggest enemy will be backlash (slop or lost movement in the motion system) which will make flat spots on the sides of a circle being printed. It is hard to design gearing without backlash. Belts can have low backlash but require careful thought into belt tension and applied loads.

I'll chime in and say that you need to think about how you are going to tension your conveyor belt. This will likely be super important to get good quality prints

TL/DR: Get the gear ratios close, buy a good premade gearbox. Do final adjustment in software, it needs to be perfect, not just close.