My astronomy project:
I must also know the distance in the DEC worm gear chassis. This distance is 14 mm.
From this measurements I get the following:
In its closets position: 33 + 14 = 47 mm distance between the two shafts.
In its outward position: 37.5 + 14 mm = 51.5 mm distance.
I don't know if the distances are equal between the DEC and RA axis, I have to measure the RA shaft distance too.
The mounting block of the RA stepper motor is a little bit different.
The space where the RA stepper motor is installed.
Motor installed and adjusted to its closets position, you need small hands to work inside here or proper tools.
I get the distance 27.5 mm, to that I add the 2.5 mm from the stepper motor shaft and get 30 mm.
Move the stepper motor to its outward position.
I get the distance 33 mm and that gives together with the shaft 35.5 mm.
The RA axis is more complicated to find the distances to. The stepper motor shaft is not in center of the hole. The shaft center of stepper motor is not in line with the center of the worm gear. We need some Pythagoras calculation here.
It's side shifted by 11.5 mm. The distances in the chassis that hold the RA worm gear is the same 14 mm.
As you maybe remember from mathematics lesson in school you have A2 + B2 = C2
When motor is in closets distance we have A = 30 + 14 = 44 mm, B = 11.5 mm, from this we can calculate C, with the calculator we find it to be C = 45.5 mm.
When motor is in outward position we have A = 35.5 + 14 = 49.5 mm, B = 11.5 mm, from this we can calculate C, with the calculator we find it to be C = 50.8 mm.
It's not the same as for the DEC axis, then we had the distances from 47 to 51.5 mm, it differs about 1 mm, close enough to have the same length of the timing belts. Note this was not a precision measure, I will check it once more later and maybe do it a different way.
Interesting result from this calculation was, when fewer than 16 teeth I get a warning that it's to few teeth, less then 6 teeth in mesh. After this I redesigned to have 60 teeth and 16 teeth. It gives a ration of 3.75:1, close to the spur gear box (3.9:1). Another alternative is to have an idler pulley that wrap the timing belt around the small pulley.
Timing belt length:
Timing belt calculator:
I have not decided yet which timing pulleys to use, maybe GT2 60 teeth and 12 teeth that gives a 5:1 ratio. An alternative are 60 teeth and 15 teeth that gives a 4:1 ratio. Very small gears with few teeth give less smooth precision so maybe it's better to use a 15 teeth timing pulley. If it will fit I use a 6 mm wide timing belt. When I know what setup to use I can setup my values in a timing belt length calculator and have the correct timing belt length.
Timing belt quality:
I found this about timing belt quality, it's from the 3D printer world. They also have problem with backlash, Wikipedia:
What can be important, they say that small teeth number give more backlash and breake the belts.