DIY Star Tracking with a low end PIC's
Whilst many tripod 'tracking' mounts exist - allowing a DSLR camera to 'track' the stars - these are all (quite literally) astronomically priced ! = even the most 'basic' mount (no tripod, no polar scope) costs about £300, which is more than a basic full GoTo mount (including telescope) !
Like me, you might well feel you are being 'ripped off', for what is basically just a geared motor and a (very) simple controller delivering '1 rev per day' rotation So, can we built it for 1/10th the cost ? (if so, the target price is £30 or less)
What's needed ?
The first thing to sort out is the (battery) power. Since PIC's run at 5v, and a USB 'power bank' (1700mAHr, single LiPO cell) can be had for £1 (from Poundland) there is just no point in using anything else
A PowerBank can be recharged from any USB power source, so no need for a separate 'recharger'
Than you need is a solid box (it has to take the weight of the DSLR camera and be stiff enough to support all the gearing), a gear system and a (PIC controlled) motor. Most likely, to achieve the required accuracy, the DIY approach will need some sort of actual movement 'feed back' system
A 'solid box' means die-cast aluminium - and these are not very cheap (even on eBay). Of course the size will determine the cost, and that will be set by the mechanical gearing and motor, however my usual 'back of the envelope' calculation suggests I'll need something like 150x100x35mmm. A 120x95x34mm die-cast bow can be had for about £10, and a 145x95x49 for about £15 (both eBay). You can also find 'project boxes' in Maplins, however whilst (for once) the price is not excessive they only offer a 'thin wall' box - and what we need to support gears and axles is 'thick walls' .. so once again they fail to 'make the grade'. Using a old cheap PIC that requires an external crystal OSC is actually an advantage, as using a crystal means we can measure the actual movement to a much higher (by some orders of magnitude) accuracy than one with an internal OSC. The cheapest motor is a simple DC servo motor. To drive this with maximum efficiency, Pulse-Code-Modulation (PCM) must be used - so 'all' you need to drive the motor is one PIC i/o pin (plus a MOSFET or similar, if the motor current requirement exceeds 25mA). NB. With the 5v supply, if your use a 6v motor you need to 'de-rate' it's stated speed (by 5/6), so I recommend sticking to a 3v motor which gives you a lot more 'head room' to 'catch up' in the event the system is found to be running slower than it should. To ensure accuracy, some sort of feedback system will be needed (ideally the movement of the actual output shaft should be monitored and 'fed back' into the PWM drive system)
The Gearing Problem
The DSLR mount has to be moved through 360 degrees in one Sidereal day (23 hours, 56 minutes, 4.0916 seconds) i.e. 1436.07 minutes - so all we need is a '1/1436 rpm motor' :-)
The problem is that the 'average' servo motor runs at 10,00 rpm+ and whilst you get motor+reduction gear box cobo's, those that are generally available limit at about 1,000:1 It is (just) possible to find a geared DC motor that runs as slow as 1 rev. per minute (although 6-10 rpm is a more typical 'slowest speed' for a cheap motor). Even a 1rpm motor thus needs another 1436:1 reduction = and a 10rpm motor, 14,361:1 ! Hence the problem = where to find the extra gearing ...
About the only 'off the shelf' gears are those found in the Meccano constructor set. Of course Meccano gears don't all 'mesh' with each other. Restrictions can be found here
The mainstream Meccano spur gear pitch size is 12 teeth to the inch. Gear wheels and pinions from Meccano and (licensed their Argentina mfg. Exacto) are all compatible. Gear wheels may be had with 45, 50, 55, 57, 60, 65, 95, 133, and 152 (rare = expensive) teeth. These gear wheels all have a 1/16" face (a 38 tooth gear wheel is available with a 1/4" face). Pinions are available with 10, 11, 15, 19, 20, 22, 25, and 30 teeth. Most pinions have a 1/4" face but a few may also be had with a 1/2" or 3/4" face. Two sizes of crown (contrate) gears are available to mesh with the pinions, 25 and 50 tooth. A 1/2" diameter single-cut worm is available, so an alternative to using a pinion is to use the worm gear (which moves the spur by 1 tooth per rev) The standard Worm Gear (part (32 32a LH, 32c Short) will mesh with :- 19 tooth gear (Part 26, 26a, 26b or 25u) at ½" pitch to give 19:1 ratio. 57 tooth gear (Part 27a) at 1" pitch to give 57:1 ratio 95 tooth gear (Part 27c) at 1½" (4 Holes) = 95:1 133 tooth gear (Part 27b) = 133:1 (the 152 tooth gear is too expensive to be casually 'used' - if you have one, you can exchange it for a box full of other gears) For completeness, the 60 tooth gear (Part 27d) can be used with the Narrow Worm (Part 32b), which will mesh at 1" (3 Holes) = 60:1 Meccano shaft (axle) diameter is almost precisely 4mm (the hub hole diameter is a bit larger than this). Meccano actually used British 8 SWG (Standard Wire Gauge) 'round bar' (rod) which is 4.064mm in diameter (don't get confused with the American 8 AWG, which is 3.26mm and would be a really sloppy fit :-) ). Whilst it's possible to find 'original' Meccano axle rods, these were made from a (very) mild steel material that was rather (very) easily bent by the average kid = indeed, you will be very lucky to find an original axle that's NOT been bent ! Fortunately, 4mm 'round bar' stainless steel can be found (on eBay) in various lengths. An alternative, easier to mount (especially as a 'stub axle'), is to use M4 'Partial Thread' Allen Bolts (although the 'un-threaded' length is limited, with only 10,15,20 and 25mm being common (with 20mm of thread))
The maximum practical reduction we can get is with Part 27b (133 teeth) together with the standard Worm Gear. If thi si used for the 'final drive', this gives a 133:1 reduction, so requires a (1436/133) = (about) 1/10th rpm drive
Motors geared down to 1/10th rpm just don't exist (at least, not on eBay). About the slowest motor you can get is 1 rpm (cost about £5) which still requires another 10:1 reduction (or 0.5rpm, cost about £12, + another 5:1) I have found a 0.6rpm geared motor on eBay (best price 5.75), however these are all rated at 12v - if we are using a Powerbank, all we have is 5v, so a 3v motor will be required. The slowest I could find was 3rpm (for £12 !). A 3v motor at a more reasonable price delivers 6rpm.
So at least one more pair of gears will be required and this makes everything more mechanically complicated.
Using a second standard worm gear with 27a gets us another 57:1, which would allow a '6rpm' motor to be used at slightly less than it's max. speed (the total reduction is 1/133 * 1/57, which means the motor speed will need to be 1/(1436.07/133/57) = 5.28 rpm) On eBay, for 3v operation, there are two choices = the "3V DC Reduction Geared Motor 6 RPM" for £1.82 and "Metal Gear Reducer Motor DC 3V-6V 6RPM 100mA Large Torque Low Speed Gearbox" for £4.79 Note that the gearing is so high that the motors will be running at almost 'no load' i.e. at the 'headline' speed
Practical gearing
Using 2 sets of worm gears makes things mechanically complicated (worms have to be mounted at 90 degress to the main shaft) = better would be a simple 'stack' gear train that can be arranged on the box lid.
However the smallest Meccano pinion has 10 teeth = so even with the 133 spur this only gets us 13.3 reduction - and, for a 3 stage gear stack, for a 6rpm motor, we need something like 20/20/22. That means a 4 stage gear stack (using 4x Part 27c with 10 tooth pinion = 9.5/9.5/9.5/9.5) !
Using Meccano gears is, to say the least, rather an 'extravagance' = each pinioon costs over £5 and each spur over £10, so a 4 stage reduction means we immediatly blow the budget, as 4x£5 + 4x£10 = £60 !! If we end with a worm gear and a 95/133 tooth spur gear, we can get back to 3 stages, but that's still way too expensive for my taste.
So, off to ebay
Can we get a suitable gear box ? Well, despite spending some time on eBay, I was unable to find a 'DC motor gear box' on it's own. I even considered purchasing two geared motors and removing the gears from one to use on the other, however every example I found (including the 'open gear box' stype) has a drive motor that's 'rivited' into place and with a tiny shaft, making it almost impossoble to use the gears from one assembly on another. However I did find an open construction frame that looked as if it could be taken apart and modified = the "DC 3V 1250RPM 130 Reduction Gear Motor Box 1:12" (cost £2.06). Plainly if I was going to change anything I would need some replacement gears = so I invested £10 in a collection of a few hundred gear wheels from China, my hope being that this collection would include enough parts to build my own 'gear train' .. The ratios available with the various '.. Types Plastic Assorted Gear Set .. ' and '.. Kinds Plastic Motor Shaft Gear Rack Pulley Belt Worm Gears Kit ..' sets are limited. The typical 'dual sprocket' wheels have hubs with a minimium of 8/10/12 teeth and outer rims of 30-50 (so about 6:1 max). Larger 80/100 tooth rim gears have hubs with 32 teeth (so no more than 3:1), although the 100 outer will mate with the 10 tooth hub of a second gear, giving 10:1. Some kits - such as the "78pieces Set Assorted Plastic Shaft Single Double Crown Worm Gears DIY Kit" (£2.80) include axel shaft rods which you might find of some use. Some of kits also have some rather 'solid looking' (blue nylon) gears designed to fit an axle with a standard 'flat' (these are typ. 16 teeth). These can be used with a larger wheel of 64 or 100 teeth (however they have 'square cut outs' instead of a hub) One 'easy' method is to 'stack' 4 of 5 same size (= intermeshing) dual gear wheels on a single pair of axles = except (of cousre) the 'kits' typically only contain one of each type :-) Whatever approach taken, building a 4 stage reduction chain with these parts will be a 'challenge' :-)
Building the gear chain
If the gears are assembled onto the lid, then we can use both sides (spare pully wheels can be used to provide axle support hubs 'through the lid' if necessary).
Starting with a 'long shaft' geared 6rpm 3v motor, I used a worm gear with a 100 tooth gear to get the first 100x reduction. I found a cheap 334 line grating/encoder assembly on eBay for £2.68 - mating this to the end of the 6rpm motor shaft gives 2004 ppm, or about 33.4Hz (at the rated speed) The target speed is 1/1436.07 rpm, and 6/100 = 1/16.77 so we have 'only' 1/86.16 to go ! If the final reduction is a 20 tooth hub driving a 100 tooth wheel (so 1/5), the remaining gears only have to achieve approx 1/17. If the 64 tooth whell can be shaft mounted, and driven by another 16 tooth shaft-mount (so 1/4) this gets us down to 1/4.3 = a 10 tooth wheel driving a 43 tooth.