# Belt length

• Looking to make a belt driven coupling to my Z axis and wondered if someone could give my belt calc a lookover?

GT2 40 toot GT2 16 tooth
Center/center distance = 26.679
Belt length = 110mm

I've sketched up the belt drive with the formulas from http://www.roymech.co.uk/Useful_Tables/Drive/Timing_belts.html This is based on a few assumptions I'm not entierly sure about

Pulley diameter from the Parametric Pulley Library

`````` GT2_2mm_pulley_dia = tooth_spacing (2,0.254);

tooth_spacing(tooth_pitch,pitch_line_offset)
= (2*((teeth*tooth_pitch)/(3.14159265*2)-pitch_line_offset)) ;
``````

That works out to the diameters on the sketch for 40T and 16T - do I need to account for belt thickness here?

• Assuming you are trying to find the correct center/center distance for a given belt length? If so, you should NOT subtract the pitch line offset in the calculator.

Your calculator is giving you the physical pulley OD, not the pitch diameter the belt will travel.

For GT2 belts a 16t pulley should be 10.19mm PD and the 40t should be 25.46mm PD

• Found a table with some examples off a chinese vendor on ali, seems the numbers aligned pretty well. Wait and see when the GT2-110mm belts arrive i guess

If anyone wanna copy the pulley parametric fusion sketch it should be shared publicly to use for whatever (Wanted to solve the formulas for center center distance given total length and teeth; but that was a bit too much maths to suffle around) Alternatively get lucky with google and find calculator to look at the math: https://www.pic-design.com/calculators/belts-and-pulleys/calculator.htm

• @nhof said in Belt length:

Assuming you are trying to find the correct center/center distance for a given belt length? If so, you should NOT subtract the pitch line offset in the calculator.

Your calculator is giving you the physical pulley OD, not the pitch diameter the belt will travel.

For GT2 belts a 16t pulley should be 10.19mm PD and the 40t should be 25.46mm PD

indeed, that contradics the chinese, but I never put too much trust in their data:P

thanks for the input, will adjust the model and have the parts printed for when the belts arrive:)

• Look closely at the sketch, the pitch offset is only 0.254mm so it might actually be right depending on how the sketch is made up. I can't really see whether the belt length is being measured from the calculated pulley diameters (which would be incorrect) or from the pitch diameter (which would be correct). If the line it's measuring is slightly outside the pulley circles it should be correct.

• @nhof said in Belt length:

Look closely at the sketch, the pitch offset is only 0.254mm so it might actually be right depending on how the sketch is made up. I can't really see whether the belt length is being measured from the calculated pulley diameters (which would be incorrect) or from the pitch diameter (which would be correct). If the line it's measuring is slightly outside the pulley circles it should be correct.

It was the incorrect OD, set the offset to 0 and it matched your numbers for the PD, adjust the center/center distance to give an even 110mm belt length again. About 1mm difference in the distance.

• Cool, the numbers for the pulleys are pretty easy to check manually as well.

It's just tooth count * belt pitch which will give you pitch circumference, for 16t it's 32mm pitch circumference. Circumference is 2pi*r so just divide by pi to get the pitch diameter. You can also use pitch circumference to easily calculate steps/mm for your system

32mm/pi = 10.186mm P.D. To get the actual pulley OD you then subtract 2x pitch line offset, 10.186mm - 2*0.254mm = 9.678mm pulley OD. This matches the numbers you have.

You really only need to worry about the pitch line offset if you're making your own pulleys or bending the belt backwards around an idler (corexy setup or similar)

• Thank you for the input!

This will in turn drive a screw, so as far as the belt drive go I should only need the 16:40 gear ratio. Into a 2mm pitch screw should give me 4000 steps/mm and optimal layer heights for any multiple of 0.025 which is seemed quite convenient as I'll likely use from 0.1mm and up in 0.05mm steps. (1.8deg steppers x16 microstepping) Well thats wrong, Prusa cal thingy ignores microstepping for optimal z height for screws?! Oh well, different gear ratio it is then..

Found a page with simpler math for working out the center distance from the two pitch diameters and belt length without having to resort to nasty trig functions so will incorporate that

``````K=4 * L - 6.28 * (D + d)
a=K^2
b=(D - d)^2
c=(a - 32 * b)^0.5
C=(K + c) / 16
`````` 