Making a T2.5 pulley

I've no idea how I didn't see it until it came off the laser cutter. But that first pulley (see previous post) was never going to be suitable to drive a T2.5 belt! The teeth are both enormous and really widely spaced.

So I tried the gear extension in Inkscape (menu - Extensions - Render - Gears - Gear ) to see if my laser cutter was up to the job of creating a pulley (cog) with enough definition to work with a T2.5 timing belt (the pitch between the teeth is just 2.5mm)

I found that 36 teeth with a pitch of 2.5mm created a cog without about the same outer diameter as the previous one, that I based the rest of my designs around. And while it was much better than the original (laser-cut) pulley, it wasn't quite right....

On a straight, linear section, the teeth appear to line up and mesh correctly. But as soon as there's any kind of bend in the belt....

While everything appears to line up at the 12, three, six and nine o'clock positions, it's clear that the tooth pitch doesn't quite match the pitch of the belt. Now, I'm pretty sure that the belt has a pitch of 2.5mm. It's labelled T2.5. It matches exactly the belts on my Tronxy 3d printer, which has a 2.5mm pitch (and has been correctly set up with this as the belt pitch and prints with an accuracy of +/- 0.1mm

So I tried a few different laser-cut pulleys - one with 38 teeth, with a pitch of 2.4mm, one with 40 teeth and a pitch of 2.3mm and one with 42 teeth and a pitch of 2.2mm.
The first pulley was a better fit, but still not quite right....

With an increased number of teeth, with a smaller pitch (distance between them) the different pulleys all had roughly the same outer diameter. Next up, 40 teeth with a pitch of 2.3mm

The teeth and belt lined up pretty much perfectly! Just to be sure that this is the one we wanted to go with, I thought I'd at least try the next pulley down, with 42 teeth and a 2.2mm pitch:

It's pretty close. But not a better fit that the previous one. So it looks like the best fit is a pulley with 40 teeth and a 2.3mm pitch for our T2.5 timing belt. Seems a bit weird. Either the laser cutter is over/under shooting (tbh, it's been a while since it was last calibrated, so it might actually be cutting slightly too large/small) or the larger diameter means we need a tighter tooth pitch (usually the pulleys on a stepper motor have just 10-16 teeth in a much smaller radius). 

But, for whatever reason, through trial and error we've managed to create a laser-cut pulley that matches our timing belt. That's good enough for now!

Right! Let's put the rest of it together.....