>>958460
Well if you think about gears you can work out the ratio from the number of teeth, this might seem intuitive but you need to know why.
If you think about toothless wheels it's the circumference that matters, twice the circumference means twice the distance and so half the number of turns.

A single start worm has one tooth, but the tooth is wound around the entire length. The tooth is then in a different configuration because the angle of the tooth means you have to angle the gear which is why a worm has to be perpendicular to the gear.
So the number of starts is just the number of teeth.

If you consider one turn of a one tooth worm gear advances the driven gear by one tooth you will see where the ratio comes from.

A two start worm has two teeth that are wound around the shaft.
If you look at the end of the shaft you see they start at opposite sides of the cylinder.
One turn of the worm will advance two teeth of the driven gear because the first start or tooth of the worm advanced one tooth of the driven gear while the second start advances the second tooth.
This is because the pitch is increased to accommodate the second start, the distance between the turns of the first start is double and so it skips a tooth of the driven gear which the second start takes up

Tldr: Starts is number of teeth

Your ratio is the number of teeth in the worm wheel divided by the number of starts on the worm.

The ration you use will depend a bit on how fine of an adjustment you want to achieve, how much space you have for the parts, and how much load will be on them. If you have room for a 50mm diameter worm wheel and a 50kg load you probably want to steer toward a coarser ratio- the teeth in a 60:1 worm set will effectively be twice as thick/strong as a 120:1 set.

A smaller ration isn't automatically more precise than a higher one. But a higher ration will be more forgiving. In a 360:1 set one turn of the worm will move the worm wheel 1 degree. In a 60:1 it will move it 6 degrees. If your method of input to the worm is precise enough (servo with encoder for example) then you might be fine with a 60:1 or maybe even lower. What angular resolution are you shooting for on the worm wheel?

>>958467
Ultimately the antenna mounted on the pan-tilt head will have to track very tiny RF chips over a fairly large distance.
The angular accuracy of the antenna (not up to me) could get as close as 0.1 degrees in theory, only if some advanced design technique actually works, else it's going to be around 2 degrees.
My aim for the resolution of the moving head is therefore around 0.1 degrees and I'm currently thinking of using a stepper motor, since servos have a limited travel, steppers can be geared down as much as I want becaue of their infinite degrees of travel,
At least, that's where I'm currently at with my research.

>>958464
Thanks, especially the part about the starts at the end of the shaft made me able to visualise it and I have a good idea about it now.

Still, would there be any advantage over for example a 60 tooth wormwheel and 1 starts of the worm vs 120 tooth wormwheel and 2 starts of the worm?
The ratio would be the same, but do more starts have some advantage?

>>958477
Not a servo like for RC, a real servo motor like is used in countless applications like CNC etc. I would take a servo with encoder for positioning over a stepper any day: steppers get hot when holding position, really hot, servos stay cool as hell. Encoders are cheap and can easily do 1000 steps for example; the drive modules are just as cheap as the commonly found stepper drivers and can work with the same step/dir software.

With 1000 steps on the worm and a 60:1 ratio you are way finer than your needed 0.1 degrees. That's with direct drive.

>>958481
Aren't servos just a heck of a lot more expensive than steppers?
And I thought it's the rotary encoder that limits the servo's move range since after one rotation it will measure the same position again, removing the benefit of an encoder in this case?

I can't seem to find any well suited servos, since they have to be mounted on the pan-tilt head they have to be small and the driver will have to be included in the same head as well.
Any servo I can find is very big and very expensive.

>>958477
There may be some advantage in extra driving force available, I'm not sure.
Usually multi start is used for things like lead screws on a cnc where it allows things to move faster because its driving a nut instead of turning a gear you can fiddle with.
Worm gear drives are usually single start because the whole point in the first place was to get the best ratio. A 120 tooth gear will be twice the size or require much finer teeth.

A stepper is usually driven constantly to hold its position, that's why they get hot and use electricity. But they are quiet.
A servo has a gear train internally and is noisy but is reactive to changes in the load. Which might not be what you want however if its too slow to react it can be useless for certain things.
The less gearing between the output and the encoder the better but you could gear down the encoder from the output to increase the travel at the cost of resolution.
Alternative is incremental encoder like how a computer mouse used to work, or like how the scroll wheel on a computer mouse still does work, typically it's quadrature encoding to give the direction and rate.
You can build yourself a servo just by connecting a motor to a sensor and making a simple controller.
When I was at school it was part of the electronics course to make one from two potentiometers and an operational amplifier that fed an h bridge and a dc motor.
Saying that you do get multi turn pots so that's an option I guess.
Other than that you could use the old grey code wheels(important to use grey code and not binary!) or a punched disc for optical. I think the new trend is magnetism, you can buy an 8 pin dip ic that will tell you the angle of a magnet held above it. Attach the magnet to your shaft and away you go!

Anything above hobby servos will probably be prohibitively expensive but don't underestimate the torque they can put out. If you can balance your system properly with a counterweight for example it reduces torque requirements

>>958477
>The angular accuracy of the antenna (not up to me) could get as close as 0.1 degrees in theory, only if some advanced design technique actually works, else it's going to be around 2 degrees.
That's pretty impressive. I assume this works by lobe switching/monopulse/conical scan?
My aim for the resolution of the moving head is therefore around 0.1 degrees and I'm currently thinking of using a stepper motor, since servos have a limited travel, steppers can be geared down as much as I want becaue of their infinite degrees of travel,
One thing you should be wary of when using mechanical reduction to improve precision is that most mechanical reduction methods will introduce their own element of hysteresis to the system (i.e. gear slop in a servo). If you can use a single jackscrew or single worm driving a large rack/gear, that would be better than multi-stage gear reduction, but it's still something to keep in mind - especially if it has to be built to 3D printer tolerances.

>>958495
yea exactly, it's still very theoretical in this project, and not up to me to design so can't really give much detail but lobe switching is indeed what we're planning to use in order to approach the 0.1 degree accuracy.
Though the 0.1 is like I said very theoretical and wasn't actually achieved yet (not by a long shot, still in early design stage)

>>958488
cncdrive.com

These guys have servos and they are not expensive, I have some of their drives and 45W motors on a small CNC and it's been great for 5 years. There are others.

But if you are more comfortable with steppers, whatever, they will work fine.

>>958495
If you have a large reduction put a position sensor on one of the last elements. If the gearing can't hold accuracy, don't depend on the motor spinning to determine accuracy then, use the sensor at the end of the line that actually drives the antenna.

Instead of spinning the motor X degrees, spin the motor until the sensor says you're Nth element has rotated Y times where you know what Y should be to get the mast where you want.

Have a provision in there as well if your sensor has stalled but the motor is spinning still to stop and throw an error-- something is binding or obstructing the antenna.

>>958495
Wouldn't it be possible to correct that by putting an encoder as close to the output as possible? in this casse, on the shaft the antenna is attached to?

What kind of gearing are you looking for?
Worm drive?
Spur drive?
Helicoidal drive?
Conical?

I can help you, just state what you need.

>>958547
I have little to no knowledge about different gearing, so I don't know exactly what to go for, but I was investigating worm gearing since it leads to a big reduction ratio, what I probably need in order to get the right resolution.
Now that I know what the difference is between different starts, I'd like to know what method I could use to model these gears for 3D printing.
Or perhaps you would recommend buying prefabricated gears which will have a higher accuracy (?)
I have different fabrication methods to my disposal, since it's a university project, but I would like to start fairly simple, preferably most parts 3D printed since the 3D printer is directly available to me at the moment.

I feel dumb looking at these replies.

>>958554
The problem with 3D printed gears is that they'll most definetly collide if the grain is coarse, or they'll eat themselves.

>>958567
Very true, but not necessarily a bad thing at the moment; it doesn't have to function perfectly in one try.
3D printing it as sort of a cheap/simple proof of concept would give me a lot of information already about how to proceed further. And if it is a direction worth proceeding, more money can be spent on perfecting the design for durability and accuracy.
Anyway, I think it's best to design everything myself including the gears, regardless of printing it in plastic or printing / machining metal, I will need models of the gears.
Any tips on how to proceed there?

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Why are you designing something that already exists?

Part of engineering is knowing when not to reinvent the wheel.

>>958591
Because it's a means to an end, it has been done before, yes. So I shouldn't stay on the one topic too long and finish this part using examples, advice and other projects as much as possible.
What is important however is using the project in combination with the antenna to track chips sizing less then a mm on a cm resolution. The moving head has to be designed as a proof of concept, that pointing a high precision antenna on a chip as small as a millimeter can be used to accurately track these chips.
Using an existing pan tilt head would just be boring, so the professor assigned me the taks of creating one myself, with an as high as possible accuracy. Hope to clear things up about the details now :)

>>958523
>>958525
Yes, but in that case the encoder itself needs to be as high resolution as your output needs to be (so, for instance, if the pan mechanism needs 360 degress of travel at 0.1 deg resolution then the encoder needs to have a resolution of at least 3600). If the encoder is somewhere else, then you can simply count multiple turns of a lower-resolution encoder.

>>958630
>If the encoder is somewhere else, then you can simply count multiple turns of a lower-resolution encoder

Yes, but then you have to consider the error of the drivetrain. There's going to be some lash and/or flex somewhere that you're not going to be able to all that reliably account for if the encoder isn't mounted directly to the shaft.

Of course, whether or not this is a problem is dependent on what OP means by "high resolution". I've got some 600PPR A/B encoders around that were dirt cheap (like $15) which give 2400 counts per revolution or 0.15° resolution in quadrature mode. I'd consider these "high resolution" simply because I haven't done anything (yet) that goes above that.

But these are among the lowest-count "high resolution" encoders you can get. You can easily source rotary encoders with an absurd 20,000PPR (80,000CPR in quadrature or 0.0045° resolution) for not necessarily excessive sums of money. That would track to the nearest centimeter at over 125m. If you need better than that, yes, you're going to need some kind of reduction, but, if not, a directly-coupled encoder is probably a better option.

Mileage may vary, depending on cost of gearbox/encoder and exactly what kind of use/environment you're talking about, of course.

OP here,
There are indeed a wide variety of rotary encoders with a very high resolution available.
Might indeed be best to put one of those directly on the shaft the antenna is attached to, like some of you already suggested, for the highest possible accuracy and dependent on which rotary encoder, highest resolution.
If this is the way to go, what motor would I best use?
A stepper sufficiently geared down, or would I go for a plain DC motor and make a PID controller / motor driver of my own to accurately move to a certain position?

On second thought such controller might not be necessary, the way this is going to work is that at a given moment the antenna will have found a chip it's 'looking towards'. Then it needs to return it's precise angle to calculate the position of the chip. For the rest, the motor just needs an algorithm to 'scan' the entire room until the antenna returns a 'true' that it's looking towards a responding chip, then calculate position.

I think first I'll select a motor, then model a pan-tilt head and make it work without a rotary encoder, research what accuracy and resolution is achieved, then add the rotary encoder and research the improvements.

So what motor would you guys suggest to go for in this case?
I'm still biased towards chosing a stepper and gearing it down, however with a DC motor that gives 'smooth' rotation and a rotary encoder to exactly tell the angle of the antenna at a given point, perhaps a higher accuracy can be achieved?
Is there some kind of universal size for such motors, that I can make a pan-tilt head to try different motors for the best result?