vlaiv

Well - I don't really count my time or amount of money I spent developing it. Since I plan to release specs to general public - it's more "the budget" needed to complete the project or BOM if you like. I'm really developing this so that anyone who has 3d printer or access to one - can build themselves working star tracker that they can use for DSLR+lens or smart phone astrophotography. Sort of 21st century barn door tracker kind of thing, but instead of going to "dad's workshop" to whip up some sort of contraption out of wood and scrap metal - one would do few clicks online to get needed goods and then its 3d printing and soldering time

I'm working on a 3d printed star tracker, and have been exploring different ways to get speed reduction. In doing so, I came across very interesting video: https://www.youtube.com/watch?v=2SUiwQVWe8w While drive itself proved to be fail for the purpose it was built - it gave me very interesting idea. One of major problems with motorized telescope mounts is how to get required reduction in output speed. Speed reduction goes from several hundred up to few thousands to one - in order to get smooth tracking. Another very big issue is that mechanical means of doing so, due to manufacturing errors introduce two kind of unwanted behavior. First is periodic error and second is backlash. While first is not something we want - it is not as bad as second - at least for imaging as smooth periodic error can be guided out - provided that the mount mechanics is responsive enough. That means minimizing second error - or backlash. Well, above idea solves two issues - large reduction ratios / step precision and removes backlash. It works a bit like differential in a car - which allows for drive wheels to turn at different rate while still being coupled to engine. In above setup - two step motors will be used to drive one mount axis instead of one stepper motor - but they will be used in such configuration that their speeds subtract in order to get resulting speed. If we for example want to have 15"/s sidereal speed - we don't need to drive our motors at that speed - we can simply drive one at 1015"/s and other at 1000"/s in other direction and their difference will give us wanted speed. This also means that we don't need to have very large reduction of our motors RPMs in order to get very slow output speed. Both motors will be constantly running and turning gears, gears will always be engaged - so there won't be backlash as no gear will change direction (not entirely sure on this one - will need to test it) - they will simply slow down or speed up - depending on what is wanted on the output.

That is way more expensive and powerful than it needs to be. DRV8828 can be purchased for as low as 1-2 euro a piece. If one wants 128 or even 256 micro steps then something like TMC2208/2209 is just a bit more expensive - ~4 euro a piece. https://www.ebay.co.uk/itm/275420178213?hash=item4020526725:g:kYAAAOSw63Ni9ggA&amdata=enc%3AAQAHAAAAwN5a%2FWvx2BoXK9nD1CsIBwct65P6VAgZjY98Jn9lnotGFDdDLTAlBVbriWCM%2B2Ex4U3PxT2O7o6wxaNbW5gby2rQIMLH%2BpUE7ttf52hj%2B9BNovnDB0fnWBnGpUZFDI%2BZO3AZjKu5XDum%2BN95LDvoVvUll0xQqQK%2B0F63X2ErC41%2FO3YLdKkQvw3dJuPAXujnnwwZeL7znoBIF%2BaTF1n5wQfOJpsB2g5Cdu9fXVeXC98M5u3OmTeBWwns%2BPDZ3ZU8QQ%3D%3D|tkp%3ABk9SR77x797aYQ One can also save about 5 euro by using 1.8 degree over 0.9 degree stepper. If I'm going to aim to get it done within 50 euro budget - every little saving counts.

Mostly to do with keeping the cost down and with simplicity. There are two cheap / readily available drivers for stepper motors - A4988 and DRV8825. Out of these two - DRV8825 supports 32 micro steps - A4988 supports only 16. On top of that DRV8825 is quite a bit less noisy in operation (not silent but not as noisy either). I've also chosen stepper motor that is the cheapest of the bunch. There are nice smaller units (like Nema 8 ) - but they are often more expensive. Hence 1.8 degrees per step and not 0.9. In final build, people will certainly be able to choose their components as most are drop in replacement - but I wanted to see what is the minimum budget that I could get by with.

I've come to conclusion that I'm over thinking / over designing the whole thing. As is - this star tracker is supposed to have something like 179.2 * 5 = 896 : 1 reduction ratio or about 0.22"/step resolution. That is probably way to much for simple printed star tracker. EQ5 / HEQ5 / EQ6 class mounts have that sort of resolution - while AzGTI has 0.625"/step and works very well as small portable EQ mount that can even hold small scopes. Here is what are my current thoughts on the matter: 1. Drop resolution to something like 1-2"/step instead of going for sub one arc second per step. With x32 microstepping this equates to total reduction ratios of say 1:100 - 1:200 range (1"/step is 202.5:1 reduction exactly with x32 microstepping). Not sure what would be the best way to do it. It turns out that such arrangement is within reach of simple belted system. Three stages of 1 : 5 will give 1 : 125 and 1 : 6 will give 1 : 216. That does not require complex gearing at all. If I'm to go with any sort of 3d printed gear box - then I'm not sure how to spatially arrange things. I'd like output shaft to be rather rigid and supported by two larger bearings. Then it stands to reason that it will be driven by a belt. I can then either stack gearbox on top of the stepper - like I started - which seems too bulky, or I can add another transmission (belt or gear) between stepper and gearbox - with probably another reduction stage. But what is the point in that - that will give me again 3 stages (two belted and one compound / gearbox) - with too much reduction - and I can simply go with 3 simple belted stages. On the other hand - I really do want to explore the performance of above gearbox (or even greater reduction one) and minimize it further (I have few ideas how to do that and I've found local source of thin bearings so I don't need to wait long time for aliexpress shipments) - but that can be separate project. Your thoughts / ideas on how to proceed with this are welcome of course.

Here is a recording of new gearing system: novel_gearbox_action.mp4 Its not very smooth due to lack of any bearings, but it actually operates/rotates "smoothly" - or no hiccups due to design issues. It is really the same thing as cycloidal disk/gear thing - but using involute gears.

Meanwhile ... (as I'm printing parts for above technology demonstrator) It turns out that I was in proper view in FreeCad and that in fact - gears as I created them - don't mesh properly. When one is making two external spur gears - then, pressure angle and module must match - but when matching external and internal gear - pressure angle changes (and perhaps even module a bit). I've found this extensive resource that I must work thru in order to fully understand math behind all of this: https://www.sdp-si.com/resources/elements-of-metric-gear-technology/index.php#Section1

Here is new reduction gearbox design or rather - this is design of a simple toy prototype that needs to confirm that the thing is working. At least - it's slim: Operation is simple - for every rotation of input shaft - inner gear does one "shuffle" and moves only a few teeth along outer gear (actual number is difference in number of gears - in this example outer is 80 and inner is 75). It is exactly operating like cycloidal gear set - except it is using standard spur gear. I think that it might be better when 3d printed than standard cycloidal disk, because this design allows for herringbone teeth without too much issues.

On a separate note - all this thinking about how to optimize this arrangement - lead to me inventing a new gearbox type At least I think it is novel - I haven't seen it before. It is a cross between planetary gear and cycloidal disk type gear. It consists out of - outer annulus gear, then one large planet that is just a few teeth smaller than outer gear. This large planet sits on excentric circle on driving shaft and has several hole in it where pins from output shaft go. It does not have large reduction ratio but it is slim and can be stacked to get required larger reduction ratios. I'll make a model of it later to test it out and I'll post results.

You are quite right - I thought about it and there is sliding - but not in vertical direction. I will certainly try this. Yes, either that - splitting them into two halves by horizontal cut or splitting them into two half rings vertically, but in either case we need to bolt them down together after assembling.

Yes, I used herringbone gears before - and I really like them, but here it is a no go (or maybe it could be done but assembly would be very difficult) - because planetary system must slide into outer gear on assembly - something not possible with that configuration. Regular helical gears would produce additional force in axial direction, so not sure if that would hamper performance. One thing that worries me about helical gears is sliding action direction. With straight gears all the sliding happens along layer lines of 3d print - which is good sliding direction. As soon as we change the angle - there is additional component of sliding action that happens in "vertical" direction - which is notoriously poor for sliding (layer lines act as teeth on a file and grind against other teeth - so it's as smooth as running two files one against the other and expecting smooth motion ). Here is couple of things that I think improvement can be found in: 1. using lubrication 2. using 0.2mm diameter nozzle to improve accuracy of small features like gear teeth 3. Checking out what happened here: This is FreeCad wire frame view of sun gear and planets: In particular - if we zoom in on any section - we get very nice fit: This is without any printing compensation - just pure geometry. But check this out: same thing with annulus gear - see interference fit for some reason (I know there are more lines in this drawing that it should be for seeing the issue, but I'll point out trouble areas): Although that is very small portion of the tooth and 3D print precision will interfere anyway - I'd be much happier if it was not happening at that level - geometry should align properly at that stage. This is FreeCad Gear workbench - regular involute external gear matching involute spur gear - and teeth don't match properly. Upper teeth in this last image is aligned 100% and somehow profile of it is "thicker" than groove on annulus gear. 4. accepting some amount of backlash in order to make meshing smoother In the end - I must keep in mind. This is supposed to be simple and cheap star tracker. It won't be guided, it won't be slewed around the sky at high speeds. It should meet following things: 1. easy to build 2. cheap 3. good enough for smart phone or DSLR + lens - in essence it is 21st century replacement for barn door tracker Given amount of work I had to put in so far - I think it is failing at being easy to build - at least compared to something like barn door tracker.

Few pics of internals that I promised: base ring attached to stepper with 6002 bearing and sun gear (sun has 15 teeth, base annulus has 81 - both are module 1). Next comes planet system: planet gears with carrier - they have 608 bearings inside and are supported by 6002 at top and bottom. Top and bottom gear in each planet have 33 teeth, and bottom is module 1 while top is 0.94... something something (can't remember it like that as fraction it is 48/51): Planetary set installed: Then comes output annulus with attached output shaft. It has 84 teeth at module 48/51: It is supported by two 6002 on each side - one resting against top planetary carrier and other against gearbox housing. Here it is installed: There is gap between top and bottom annulus - which is where "split ring" in the name of the system comes from. In the end - there is gearbox housing - which is nothing special, just a seating supporting the last bearing (giving rigidity and center to whole assembly) and means to bolt it to base of housing. You can now see where the bulk of assembly comes from: 1. 81 teeth x 1mm module - means at least 90 mm of diameter of the whole thing (81 gear diameter + 3-4mm of outer shell on each side). 2. around 30mm of planetary system - 20mm gears + 2x5mm carriers (4mm thick + 1mm spacing), then 3x 6009 bearing which is 9mm thick - that together is already almost 60mm in height - add few times 3-4 mm of housing and support stuff .... Now, I could design even higher reduction ratio in smaller diameter if I make output and input ring differ by 1 tooth - but that also require additional care when printing planetary gears as top and bottom gears will be offset and there will be overhang tooth from top gear to deal with in printing - which I wanted to avoid for this version. Also - with less teeth in planets - I'll also need smaller bearings to support them in planetary system - at the moment planets are 33mm - which fits nicely on 608 bearings that are 22mm in diameter. If I want to go for say ~23-24 tooth per planet - that would require bearings with 15mm outer diameter - something I plan to source from Ali express at some point. Wider support bearings would also contribute to rigidity. Bearings that I'm using are quite cheap and are not as so good - so there is a bit of "play" in them. This leads to things not staying on axis but rather bending a bit. Wider support bearings would reduce this bending for same amount of play in bearing.

Here are a few videos with sound of the thing in action: Full slew speed at 2 degrees/s: (this is close to limit of resolution offered by micropython that I'm using for simplicity - it is pulse every 30 micro seconds with 6400 steps per revolution - or 200x32 for micro stepping - motor is running at about 300RPM) full_slew.mp4 Next is x10 slower stepping speed - so around 30RPM on input shaft - with almost no noticeable motion on the output shaft. Noise is much more tolerable in this case: tenth_slew.mp4 Third one is equivalent of tracking speed - or sidereal. Input shaft is running at that speed - and output shaft is 1/5 of sidereal (because there is planned x5 belt stage as well). No noise is coming from gears - its all from stepper motor ticking away ... sidereal.mp4 I guess that adding some lube will improve things, so that is next step (and redesign of the thing - trying to make it thinner).

I don't think it will be necessary. It will certainly impact results over large time period - but I'm not looking at that - I'll be looking at deviation from standard speed in minute or half a minute intervals. Besides lens distortion there is also issue of tilt - both camera and laser - paper should be perpendicular to both and if it's not there might be linear speed gradient - but again, that is not something I'm worried about - I want to see jitter / noise in tracking performance rather than smooth changing curve beyond 1 minute.

Idea is very simple - It won't be able to do large section of movement, but rather small one - say 3-4 minutes of tracking. That is plenty enough to get general sense of smoothness of the motion. You can trade resolution for angular section by the way. One places laser on the output shaft. Laser is placed horizontally and aimed at the white wall. In case white wall is not accessible, or is not smooth enough - a piece of white paper / cardboard can do the trick as well. Camera and lens are used to record laser point position and covert that into pixels (centroid on laser point is performed at regular intervals and recorded). With something like ASI1600 - I'll have about 3800px horizontal resolution - then it is only matter of doing some basic math - like distance of laser to paper and camera paper distance / focal length. Say that we use 1 meter of white wall and place laser 30 meters away. That will give us ~6875 arc seconds of working space (so at 15.041"/s - that is 457 seconds of tracking or ~7.6 minutes), and at 3800px - we have something like 2"/px of base resolution. With centroid being sub pixel accurate - we'll probably have tracking on less than 1" precision - which is more than enough for star tracker. (in case of A4 piece of paper - everything is scaled to 1/3 - so 10 meters away vs 30cm of size of paper - and shorter FL lens should be used - or camera placed closer to cover the paper).

I know, but I wanted a budget variant. I also have silent stepper drivers on my ender 3 v2.

Btw, I'll later post some images of internals, so you can see what it looks like (and why it's so huge - one might say "over engineered").

Update: I'm not sure if I'm going to pursue this any further. It looks like I'm hitting the wall, both on budget and on my design skills - at least that is what it seems at the moment. I designed and 3d printed 179.2:1 split ring compound planetary gearbox - and thing is huge. Here is image of it next to RPI pico and drv8825, sitting on top of nema 17 stepper. Yep - there is nema 17 stepper under all that plastic If you don't believe - here is another image from different angle: Now you can appreciate the size of the thing - combined with nema 17 motor - it is already as large as something like AzGTI - and that is only power train - no housing for the tracker itself. Cost is also slowly building up. In that gearbox I have something like 7e worth of bearings, stepper is another 10e, electronics so far are about 10e as well - and that is just on breadboard - no custom PCB or anything like that. I'm still missing 12V to 5V reducer (another say 2e). There might be up to 5e worth of plastic in above gearbox. I'm probably going to need additional 10e of bearings for wedge and tracker case, and when I'm finished - I think that I'll miss the 50e mark by maybe 50% or even more - and the thing is going to be huge by the looks of it Main problem is lack of stock thin bearings that have large bore diameter. I can source them locally - but they start from 10e a piece and run up to 30-40e or even more. I might turn to AliExpress for these - but that is 1-2 months wait on goods - so its going to be slow process (I'm already waiting for few things - like green laser to test the smoothness of this drive and 3/8-16 "blind rivnuts" that I'll use for tripod attachment on the wedge). If I manage to bring it down in size, and if it provides enough smoothness of tracking - I might consider bringing it to a finish, but even so - its not going to be "easy DIY" star tracker for the masses - it really does require skill to print and assemble it, and PCB is going to be additional challenge. As is - it runs at x5 sidereal rate because I envisioned another 5:1 reduction via belt. If I redesign it - then I'll move motor from the bottom and onto a side of the gear box and 5:1 belt reduction will be "first stage" with output from the gearbox directly attached to base of the star tracker. Thing runs and provides that 179.2:1 reduction and makes funny noises . On sidereal or close to sidereal rate - funny noises are down to stepper and at "slew speed" (2 degrees per second - although I don't think star tracker needs slew function) - gears start to be heard and it all sounds like concrete mixer . I still haven't applied any grease to it - must purchase white lithium + ptfe grease and try that.

Imagine the blast ...

Use smileys for that As for the question - don't know the answer. I guess it's combination of join date and number of posts.

Yep, going after galaxies does require good mount for both resolution and longer exposures. Above 5-10 minute is correct for darker skies SQM 21 and higher, but for Bortle 4-5 for example (SQM ~20), exposures in 3-4 minute are ok. In heavier LP - you can get by with even shorter. I used 1 minute exposures on my F/8 scope in Bortle 7 skies (SQM 18.5) with 1600mm FL and 3.8um pixel size.

You don't have to bin - just use camera with larger pixels. Adding x16 read noise is not as bad as it might seem. It only increases read noise by factor of x4 over regular read noise, so if you have camera with say - 1.4e of read noise - it will act as camera with 6.4e of read noise - but here is the thing - you don't have to do anything about it (many old CCD cameras had read noise that was double that - like 12e-13e of read noise). Read noise needs to be swamped by background signal right? When you sum your pixels - you also sum background signal as well as read noise (and everything else) - so ratio of read noise to LP signal / background signal remains the same. If you exposed properly for your sky conditions - binning won't change anything. Advantage is that it is easier to get aperture / faster system at those focal length. Faster in terms of light gathering and not F/ratio. With shorter FL - you need to use F/ratio "faster" system - and that means better optics and more careful collimation - corrective optics must be very good not to add aberrations of their own and so on. For galaxies - it really does not matter. M101 and Leo triplet are just two targets - but there are like thousands of galaxies that are very small, so FOV is not very important (if one really wants to have "galaxy" scope).

I also liked that - but I was not overly fond of being called the brown dwarf all the time (or whatever moniker it was at that time)

Here is the thing - let's look at it from different perspective. Some of the largest galaxies are say - like M101 - less than half a degree x half a degree - but most are sub 10 arc minutes in extent. But for the sake of argument - let's go with 40 arc minutes as the width of the fov (to have some room around the target). 40' = 40 * 60 = 2400" If we want to image at say 1.5"/px - that is 1600px across. IMX571 has 6000+ pixels in width - that leaves us with option to bin at least x4 the data and have 1500+ px across. That is the path I would take - I'd take that EdgeHD 8" - sort out any collimation issues and tilt to get good star shapes across the sensor. According to Celestron spec sheet - spot diagram should be good for 40mm so 28mm should not be a problem: here is spot diagram out to 28mm for EdgeHD. While not perfect - it is not disaster either. I'd expect round stars in regular or even good seeing conditions. I don't think scope would be capable of 1"/px - as combined spot diagram (across all colors) seems to be bigger than airy disk size - so I'd limit it to say 1.5"/px for very good sharp results if mount / guiding and seeing allows. I would do split debayering on the data and additional x2 bin on top of that (or just bin x4 regularly debayered data)

1600mm also gives 1"/px, so does 2400mm and 3200mm. I agree that one should not aim for higher than 1"/px, and in reality, most of the time 1.5"/px is enough (which is by the way - what 2000mm gives if one properly treats the data).