Please
Note: Unfortunately we are no longer in a position to advise about this projects
construction, please do not ask for help.
The SAA 1027 stepper motor control IC is very difficult to find now as it
is no longer being made.
Please do not ask where you can buy one - I DON'T KNOW!
The main tracking error occurs because the screwed rod is straight, unlike the
"thread" on the circumference of a worm wheel. In the simplest version the rod
is fixed at one end at right angles to the lower board and the top end slides
along the top board as the angle increases. The drive slows down as the angle
increases because the distance between the point of contact and the hinge is
getting longer.
However if the screwed rod is pivoted at each end the error is much reduced,
being only due to the fact that the rod forms a chord rather than an arc. In
this case the drive speeds up with time, but for short exposures (e.g. 10 mins)
the error is very small. The deviations from a true drive rate can be expressed
in arc seconds for an elapsed time, assuming the boards are together at the
start.
For example with the improved design the deviation after 10 minutes is only
0.7 arc seconds, increasing to 6 arc seconds after another 10 minutes. These
are quite low values, and in practice there will be other factors which limit
the tracking accuracy. These are estimated and compared later.
The operation of the circuit is as follows. The 4060 IC is a combined oscillator and divider chip. The quartz crystal oscillates at 4.194304 MHz, and this frequency is divided down by 2 in 20 stages to give the 4 Hz rate to drive the stepper motor. As this is a 200 step motor one complete turn takes 50 seconds. (Not one minute as in many traditional designs!). The frequency division is performed partly by the 4060 and completed by the 4024 divider chip. The 4 Hz frequency is taken from output 5 via a switch to the clock input of the SAA 1027 stepper motor control IC. This IC has 4 open collector transistor outputs which send current to the motor windings. The current is limited by the 220 ohm resistor which controls the base current of the output transistors. Since the screwed rod has to be returned to its starting position after each exposure a reversing circuit and stop switch are provided. When the switch SW3 is in the reverse position the motor is driven rapidly back at 8 times the forward rate by using the 32 Hz signal from output 2 of the 4024 IC. At the same time the direction is reversed by switching the M pin of the SAA 1027 IC from ground to 12 volts. When the boards come together again the 32Hz signal is interrupted by the stop switch SW2 which is of the "push to break" type. This can be mounted on the lower board.
Some smoothing and decoupling capacitors are used to reduce noise, and a diode prevents damage if the battery is connected the wrong way round. The IC's should not be subjected to more than 15 volts, so the power source should be a 12 volt lead acid battery, a string of 10 NiCads, or a regulated supply of 12 volts. Unregulated sources such as mains adaptors or battery chargers should not be used to drive the circuit directly.
The battery I use is a 12 v sealed lead acid battery of 6.5 Amp hour capacity. I have used it in freezing conditions without problems. The circuit only draws about 0.25 amps so there is enough capacity to run other things as well. I often use a heater to go around the lens to prevent water condensing on it. That takes another 0.2 amp approximately. This battery is about 100 x 150 x 80 mms in size. The battery can be used in any position. I guess it is the same type you refer to for use in burglar alarms.
Construction of the circuit should be straightforward, e.g. on matrix board. Take precautions against static damage to the two CMOS IC's. The IC's are best mounted in sockets and fitted when the other construction is complete. The whole board can be fitted into a plastic box of small size, with flying leads to the motor and stop switch. The box can be conveniently fixed to the front or underside of the lower board.
The LED shows when the circuit is powered and working. It flashes twice a second. When the circuit has been built this provides a first check that it is operating correctly. In my experience of making ten of these circuits I have found two causes of malfunction. Most common is a mistake in the wiring especially of the components around the crystal, which tend to be crammed together. Once I had a crystal which refused to oscillate. A second one worked perfectly when wired in.
The thread can be chosen to be the same or a different size to the motor shaft, in my case 1/4 inch for both. With the common Whitworth thread the pitch is 20 per inch. Since the rod turns once every 50 seconds the distance from the axis of the hinge to the centre of the rod for the right opening rate can be calculated as 348.3 mm. The calculation is shown in the figure.
Calculation of hinge to rod distance for Scotch drive.
Rotation rate required is one turn per 23 hours 56 minutes
This is 2 pi radians in 1436 minutes Or a rate of 2*pi/1436 radians per minute If the pitch of the screw is x mm and one turn takes place in 50 seconds then the nut is driven along the rod at a rate of (x*60/50)mm per minute If the distance to the hinge is L mm then the angular rate is... (x/L*60/50) radians per minute Setting this equal to the required rate: x/L*60/50 = 2*pi/1436 or L = (x*60/50*1436)/(2*pi)The table below shows some common threads and the hinge to rod distance which is needed.
Threaded rod Pitch Pitch Hinge to pivot distance mm mm 1/4 inch whitworth 20 per inch 1.2700 348.3 3/8 inch Whitworth 16 per inch 1.5875 435.4 M6 metric 10 per cm. 1.0000 274.3 M8 metric 8 per cm. 1.2500 342.8In practice the actual thread can deviate substantially from these correct values. It is worth measuring the pitch, e.g. by counting and marking 100 threads and then measuring the distance. If the thread is not exactly right the hinge to rod distance given above can be modified to suit. E.g. if there are 1% more threads per inch than there should be then reduce the distance by the same amount of 1%. When going to the trouble of providing an accurate quartz drive it is sensible to reduce the other errors as much as possible.
The upper end of the rod runs in a threaded bush which is pivoted in the top board. This could simply be a nut, but having a longer length of thread in contact with the rod will reduce slop in the system and also any errors due to periodic variations in the pitch of the rod.
Some adjustment of the direction of the scope is needed so that it can be aligned
with the hinge. The alignment can then be made by clamping the lower board and
viewing a small very distant object. The object is first centred on the cross
hair or reticle by moving the boards together with the top board in the down
position. Then when the top board is hinged upwards the object should remain
centred in the cross hair. If it moves the scope position should be adjusted
left/right, or up/down, until the movement during this test is eliminated.
The Pole star is not located exactly at the celestial pole, so for good tracking the cross hairs should be offset by 44 minutes, i.e. about 3/4 of a degree from the star. This distance can be set on a reticle, or simply judged from the field of view of the scope. For example if the field is a total of three degrees then placing the star half way between the edge and the cross hairs will give the right offset of 3/4 of a degree.
The direction of the Pole Star away from the true pole is Right Ascension 2 hours 31.8 minutes. However this direction is not obvious! An easy way to fix the direction uses the fact that the next brightest star of Ursa Minor, Kochab or Beta Ursa Minoris, lies almost exactly in the opposite direction. By alternately looking at the positon of this star and the view through the scope Polaris can be offset from the centre in the right direction.
If the scope is a direct viewing type like a rifle scope, Polaris should be
on the other side of the cross hairs to Kochab. However if the scope is an astronomical
type which gives an upside down image then Polaris should be placed on the same
side as Kochab.
Polar Misalignment Tracking time in minutes in minutes of arc 0 10 20 30 40 50 60 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 10 0.00 0.44 0.87 1.31 1.75 2.18 2.62 20 0.00 0.87 1.75 2.62 3.49 4.36 5.24 30 0.00 1.31 2.62 3.93 5.24 6.54 7.85 40 0.00 1.75 3.49 5.24 6.98 8.73 10.47 50 0.00 2.18 4.36 6.54 8.73 10.91 13.09 60 0.00 2.62 5.24 7.85 10.47 13.09 15.71 70 0.00 3.05 6.11 9.16 12.22 15.27 18.33 80 0.00 3.49 6.98 10.47 13.96 17.45 20.94 90 0.00 3.93 7.85 11.78 15.71 19.63 25.56 100 0.00 4.36 8.73 13.09 17.45 21.82 26.18The quartz crystal clock controlling the drive rate of the motor should be accurate to 100 parts per million (ppm) or better. The table shows what effect this clock rate error, and some larger ones, would have. So for our 10 minute exposure example a clock accurate to 100 ppm gives a problem of only 0.9 arc seconds (the least of our worries!).
Drive rate accuracy Total angle Drive rate error(arcsecs)
time (arcsecs) 1% 0.1% 100ppm
10 9000 90 9 0.9
20 18000 180 18 1.8
30 27000 270 27 2.7
The pitch of the screw can be obtained manually by the method described above.
For example if we could measure to 0.5 mm over the length needed i.e. 5 inches
or 125 mm that would be 0.4%. Let's suppose that we can do rather better than
that and measure the actual pitch to 0.1%. Then the tracking error resulting can
be read from the previous table, i.e. 9 arc seconds for a 10 minute exposure.
The mechanical stabilty of the system will obviously affect the tracking. The best situation would be a permanent set up on a solid base as for a telescope. In that case the alignment could also be refined until it was spot on. Most users will probably want to have a portable system though, mounted on a camera tripod for example. Unless this is particularly rigid it will have some movement, e.g. from gusts of wind or from flexure from the weight of camera and lens. This is difficult to estimate, but experience from the design and use of tripods for telescopes is very relevant - the more rigid the better.
A summary of the errors that have been calculated are shown in the table. In order to assess the importance of these we need to know what is tolerable. If we use a short exposure with a normal 50mm lens we don't need nearly as much accuracy as a long time with a telephoto. Let's suppose that we would like a resolution of 40 lines per mm on our film. This corresponds to features that are 25 microns in size in the emulsion. We want to limit any trailing of the stars to 25 microns or less.
The diagram then shows what this trailing corresponds to in seconds of arc for lenses of different focal lengths. So for a 50 mm. standard lens the movement allowed would be 103 arc seconds. But when we go to a 500 mm telephoto we can only tolerate 10 arc seconds of deviation if we are to keep the trailing to 25 microns.
Accuracy of tracking required
A = r / F x 360 / (2 x pi) x 60 x 60
A good resolution is 40 lines per mm on the film. This means a movement of
0.025 mm or less.
For a lens of focal lenght F:
F A 50 103 135 38 300 17 500 10When we put all these figures together we can estimate the exposures that our simple Scotch mount is capable of making. The biggest error turns out to be due to the Polar alignment (or lack of it). With a 10 minute exposure we would get about 26 arc seconds trailing, which would allow us to use a lens of about 200 mm focal length. But if we go to a half hour shot we would have to limit ourselves to a standard lens.
Summary of errors Exposure time in arc seconds 10 20 30 mins Scotch mount(pivoted) 0.7 6 20 Polar alignment (10 arcmins) 26 52 79 Drive rate/pitch (0.1%) 9 18 27 Mechanical stability ? ? ? Usable lens 200 80 50 mm Usable lens (non-critical) 500 200 135 mmThese figures are for the worst case of objects near the celestial equator. Objects near the pole are more forgiving. Also in some situations a bit of trailing would not matter much, e.g. if trying to catch meteors. In these "non-critical" cases the lens could be a longer focal length.
Example with enlarged insert, showing no trailing. The "Coathanger" in Vulpecula.
Taken with 135mm f3.5 lens at f5.6 for 10 min exposure.