Although my knowledge of electronics was and still is zero, I do have a lot of experience in building telescope mountings. I used this together with a quart-controlled motor built by Ray to construct the heavy duty mounting described here.
In January 1994, I bought a second hand Pentacon 300mm f4 lens. Mine was one of four available for less than £100 ($150) each from a local binocular and telescope dealer in Stockport, near Manchester. The other three were bought by other MAS members including Ray. These are very fine lenses with low off-axis distortion and are eminently suited to low power astrometric work on comets and asteroids. Unfortunately they are also heavy, weighing-in at some 4kg (9lbs) apiece. Normal camera mountings cannot cope with this weight unless they are designed to carry telescopes. Ray Grover uses a Super Polaris mounting and gets excellent results, but such mountings are expensive. I wanted to build a cheap tangent arm drive for mine.
For a long time I have believed that it you can go into your local DIY store and buy off-the-shelf components to make serviceable astronomical equipment. Indeed, it should be possible to over-engineer such one-off equipment to improve on that commercially available. I also hold that any telescope or camera mount should be capable of being constructed so that it doesn't vibrate or move detectably if touched or even lightly knocked during an exposure. My aim was to make a heavy-duty tangent arm drive that would allow 15-20 minute exposures ( typically the limit under suburban or even semi-rural conditions) with 1000 ISO film, giving minimal trailing under poor field conditions of moderate wind buffeting, yet transportable and cheap to build.
I already had two square iron castings holding self-centering double-race ball bearings capable of carrying a 38mm (1.5") shaft. These were salvaged from an engineer's scrap box about ten years ago with the intention of making a small telescope mounting. The castings are 136mm (5.35") square and I fabricated them into a rigid, roughly cubical unit by separating them with 105mm (4.22) lengths of 25mm (1") aluminium tubing through which runs 10mm (3/8") threaded rods. These bolt the bearing assembly solidly together.
This assembly is held at approximately the correct equatorial angle for Manchester, 53.5deg North, by the incorporation of appropriate lengths of 25x40mm aluminium channel under the top casting so that the bearing unit can be inclined and bolted firmly at the correct angle to the upper surface of a triangular box assembly fabricated from 3mm (1/8") aluminium plate and 25x40mm aluminium channel. From above, the plan of this box assembly is that of a truncated equilateral triangle. This stands on and can be bolted to the triangular top plate of a heavy duty tripod that I made using similar kinematic principles, incorporating lots of rigid triangles.
The polar axis is a 300mm (12") length of 38mm (1.5") OD stainless steel tube. An L - shaped declination arm (really a half-fork) was constructed from 65mm (2.6") square-section extruded uPVC rainwater downspouting and two right-angle mouldings, bought for a few pounds at a local DIY store. The arm was initially built using UPVC glue before being held onto the polar axis by the judicious use of hose clamps around the polar axis, inside the UPVC tube, while the hollow plastic was filled with a sloppy cement mixture. When set, this gave a rock-solid polar axis / dec. arm assembly.
The beauty of using cement or concrete in a plastic tube is that the rigid but brittle filling is protected by the aesthetically pleasing black UPVC tube whilst giving the whole a deadening, vibration damping, effect. Although heavy initially, cement eventually dries to give a very rigid, but not too heavy structure. Before filling, the UPVC tube was drilled for the attachment of a 12mm (0.5") thick aluminium-angle camera mounting plate and a slightly smaller secondary camera mounting. These are attached to the declination arm with 8mm (1/3") zinc plated bolts and wing nuts.
The polar axis and declination arm assembly slides smoothly into the bearings and in so doing traps the tangent drive arm. This is a composite structure made from 25x25mm aluminium channel and a piece of scrap, 1" thick oak. The expanded upper end of the tangent arm fits around the polar axis and is held by the downward force of the heavy declination arm. The drive arm is trapped between the top of the upper bearing and a rough plywood disk which acts as a friction clutch beneath the declination arm. I can manually slew the mounting in RA to any part of the sky and then start the stepper motor drive to give good tracking motion with nothing other than this friction. The tangent arm can be clamped to the polar axis if needed but in practice it has been found that the friction disk is sufficient.
The quartz controlled stepper motor is driven by a 12 volt automobile battery bought from a scrap dealer for £5 ($8). The motor drives the mounting at approximately sidereal rate and after the desired exposure is finished, a reversing switch on the control box allows the motor to rewind the screw at x8 sidereal rate. The stepper motor and electronics control box containing the quartz oscillator, an on-off switch and the motor reversing switch are mounted on a piece of 6mm (1/4") aluminium angle, which also carries a small limit switch, mounted on a stalk, to stop the motor after rewinding.
Ray Grover described the geometry of the Scotch tangent arm drive in his article. The 1rev per 50 second motor is attached to a tangent arm of about 348mm ( 13.71") radius driven by a 20 TPI threaded steel rod. A reasonably accurate sidereal rate results. Pivoted at one end, as in the classic Scotch drive, the 'tangent error' causes a rapid loss of drive accuracy as the drive slows down compared to the uniform motion of the sky. However in Ray's mounting, the drive screw is pivoted at both ends to minimise this effect. This results in the drive rate speeding up slightly due to a reversed, but minimised, residual tangent error. I have included an Excel spreadsheet showing the calculations involved. It is also reproduced below.
Motor rev = 50 seconds 180/Pi = 57.29577951 deg/radian 360degs = 1436.068 minutes = 1723.282(1436.068*60/50) Motor revs per mean sidereal day 20TPI = 0.05 inch/rev = 1.269mm = 1.5228mm/min. 1436.068*1.5228 = 2186.844858mm drive diam/2Pi = 348.0471689 calculated NB: In both cases, 1 and 2, AB = AC. This is the tangent arm as it rotates clockwise. Case 1. With no offset of motor from arm on reset to time zero. (fig.1 ) Angle BAC = 2*asin((a/2)/c)*180/Pi (NB: c = b) a BAC Sky actual rotation. Error 0 min.driven 0 mm 0.000000 0.000000 degrees 0 arc secs. 5 " 7.614 " 1.253447244 1.25342254 " 0.09 " 10 " 15.228 " 2.507044 2.50684508 " 0.72 " 15 " 22.842 " 3.760941912 3.76026762 " 2.43 " 20 " 30.456 " 5.015290 5.013690 " 5.76 " 25 " 38.070 " 6.270240 6.267112699 " 11.26 " 30 " 45.684 " 7.525942688 7.520535239 " 19.47 " Case 2. With Xmm offset of motor and variable arm radius.(fig.2) Input x =60.00000 x + a =a' b'=Sqrt(cSqr+xSqr) = 353.430177 mm (b' not equal to c) Input c = 348.3 mm arm radius (c) c Sqr = 121312.89 b'Sqr = 124912.89 2bc = 246199.4613 Angle BAC = acos((b'Sqr+cSqr-a'Sqr)/2bc)*180/Pi - CAD CAD = atan(x/c)*180/Pi = 9.774143774 a' BAC Sky actual rotation. Error 0 min.driven 60.000 0.000000 0.00000 degrees 0 arc secs. 5 " 67.614 mm 1.25260374 1.25342254 " -2.95 " 10 " 75.228 " 2.505702163 2.50684508 " -4.11 " 15 " 82.842 " 3.759676784 3.76026762 " -2.13 " 20 " 90.456 " 5.014833534 5.013690 " 4.12 " 25 " 98.070 " 6.271433065 6.267113 " 15.55 " 30 " 105.684 " 7.529707965 7.520535239 " 33.02 "
My mounting differs somewhat from the standard Scotch drive, and Ray's, in that at commencement of the exposure, with the drive screw fully rewound, the motor drive point is offset some 60mm (2.36") from the threaded brass pivot at the end of the tangent arm. Note that a brass pivot, through which passes the steel screw, was chosen because dissimilar metals tend not to bind. The pivot at the motor end is affected by connecting the drive screw to the motor spindle with a short length of silicone rubber tubing fastened on with twisted wire ties. The effect of the aforementioned offset (which should be reduced if possible) is that the camera moves rather faster, and increasingly so, than the sky rotates. This can be compensated by slightly increasing the length of the tangent arm - my arm is ajustable - so that the drive initially runs slow and then fast so that the overall effect is a modest drive inaccuracy over the duration of the exposure. Appendix 1, calculated in a Microsoft Excel spreadsheet, shows the effect of this residual error. In practice, even the 300mm f4 lens is insensitive to it; halation in the film's emulsion masks the driving error.
Polar alignment is very important, as with any equatorial mounting, and time should be spent to give the best overall accuracy. Polar alignment is aided in my mounting by the incorporation of a x4 telescopic rifle sight in the tubular polar axis. Using short focal length lenses alignment is not critical and even with the 300mm I have found that sighting Polaris through the alignment telescope and offsetting appropriately is sufficiently accurate to allow 20 minute exposures without any noticeable trailing. Polaris is found in the telescope by the trial and error manoeuvring of the tripod facilitated by the adjustable south leg that allows about ten degrees of latitude to be accommodated.
To date, apart from minor problems with the battery holding its charge, the drive has performed very well. The cost excluding the bearings was about £60 ($100) in 1995. The design, illustrated in the pictures supplied by Mike Oates, can be recommended. Please let me know if you want further information. Conversely, how did you build a cheap camera drive?