Re: ATM Correctors and Encoders

[Del Stanton <sdl20@pacificnet.net>]

Dear Carl Brennan

Let me start with drive correctors:

There are two sources of error in a tracking drive that 
has a worm (a helix on a shaft, like the thread on a screw)
driving a worm wheel (the large circular gear with teeth on its
circumference that are engaged by the worm).  The worm 
wheel is connected directly to the polar axis.

The most prominent error is caused by any eccentricity 
in the worm. That means that the thread on the worm is 
not perfectly concentric with the axis of the worms rotation.  
Thus, as the worm rotates the amount that its thread 
engages the worm wheel varies - sometime the thread is 
deeper into the teeth and sometimes the thread is not 
as deep into the teeth.  This variation makes the worm 
wheel turn slightly faster and slower during each revolution 
of the worm.  Since it repeats regularly in time (since the 
worm is rotating at a constant velocity) the error is said to
be periodic.

Now suppose the telescope is set up and correctly aligned.
If it was perfectly aligned and the drive was perfect (here 
I am ignoring atmospheric refraction) then if you pointed 
the telescope at a star and turned on the drive the star 
would remain perfectly centered in the scope.  If the scope 
had a periodic error you would observe that the star would
move ahead and fall behind in a regular pattern.  If the worm
was turning once every thirty seconds the star would move 
ahead slightly for 15 seconds and then fall behind for 15 seconds.

Note that NONE of this matters for visual observation, it is matters
for photography or CCD imaging.

Now - suppose you "guided" the scope.  That is, as the star 
moved ahead you made small corrections to keep it perfectly
centered, and as it moved behind you made small corrections 
the other way.  Next, suppose the telescope remembered all 
those corrections.  That is it remembered them in relationship
to the angle of the driving worm.  Then it could automatically
slow down the worm when it tended to drive the worm wheel
too fast and speed up the worm when it tended to drive the 
worm wheel too slowly.  This is periodic error correction, and
Celestron calls it PEC.  This correction can be stored in 
non-volatile memory (that keeps remembering when the telescope
is turned off) and will compensate for the error from then on.

Encoders are essential "electronic protractors" or setting circles
that are read electronically.  Suppose I had a shaft mounted on 
bearings and I had a thin disk of metal mounted on that shaft.  
The suppose near the edge of the disk I trilled 360 small holes,
evenly spaced. Imagine that the space between the holes is 
equal to the diameter of the holes.

Then imagine I took a small LED and placed it on one side of the 
disk and photo detector on the other side.  As the disk rotates 
the holes would let the light through to the detector once for every 
degree of rotation.  Then I connect a counter to the detector and 
set the count to zero.  Then rotating the shaft clockwise would send 
one pulse of light to the detector for every degree of rotation.  After 
30 degrees of rotation the counter would read 30 - and so forth.  
But if I stopped the rotation and then rotated the disk in the 
OPPOSITE direction the counter would merrily count upwards, 
because it is just counting the number of times the light blinks on.
It has no way of knowing which way the disk is rotating.

Now suppose you fixed up another light/detector pair.  It would
be located about 5 degrees away from the first.  But not exactly
5 degrees, I will mount it 5.25 degrees away.  Remember that the
holes and the spaces between the holes are equal in "width" so
that the signal from the detector when the shaft is uniformly 
rotated is ON one half the time and OFF the other half.  

Ok - we are slowly turning the shaft.  The first detector turns on, 
then 1/4 of a degree later the second detector turns on, 1/4 degree 
later the first detector turns off - and 1/4 degree later the second 
detector turns off.

Below UP means ON and DOWN means OFF.  As you follow the 
trace from left to right that is equivalent to the shaft rotating in
one direction.

First detector
       ---__---__---__---__---__---__---__

Second detector
       _---__---__---__---__---__---__--

Above the length of each segment represents 1/2 degree and the 
lower trace is shifted 1/4 degree to the right compared with the 
upper trace.

Now, if you reverse the rotation it can be detected.  Because the 
overlap time will come in a different sequence.  Suppose the 
two channels are represented by A and B.  And "A" means A just 
turned on and "a" means A just turned off.  The same for B.

For one direction of rotation the sequence of letters will be:

        ABabABab

For the reverse direction of rotation the sequence of letters will be:

       AbaBAbaB

No suppose the shaft stops and the rotation is reversed,  I will 
represent that by a gap in the sequence of letters:

        ABabABab   BAbaBAba 

You see - when you were expecting an "A" (the A channel 
coming ON) you got a "B" (the B channel coming ON). So you 
know the direction of rotation has been reversed.  Therefore 
you will make the counter count down instead of up.

Where ever you reverse the rotation in the sequence you will
be able to detect it, because what the encoder puts out will
be different from what you expected if the rotation continued 
in the same direction.  There are integrated circuits that do this
job automatically.  They watch the sequence of pulses and 
direct the pulses to the UP or DOWN input of a counter to
give you the position of the disk.

What I have just described in an incremental encoder.  It 
can tell you which way it is turning and how far.  But if you
turn off the system and start it up again it always starts with
the counter at zero, thus whatever position the disk is in is 
read out as zero degrees.  Many incremental encoders have 
an auxiliary channel that has a third light/detector pair that 
can detect a single hole in the disk.  When the electronics 
sees that single hole it resets to zero and takes its count from 
there.

Another kind of encoder is an absolute encoder that has many 
more tracks than the single track described above.  It might have 
eight different light/detector pairs looking through different sets of 
holes in the disk.  With such a system the holes and detectors can 
be arranged so that the output is a binary number representing the
rotational position of the disk.  Turn the system off, rotate the disk, 
turn it on.  It reads which detectors are illuminated and tells you 
the new position of the disk.  They are much more expensive and 
are not used in amateur telescopes.

Why we need them should now be obvious.

Del Stanton    (My sig follows the quoted text.)

At 10:44 AM 1/1/97 +0100, you wrote:
>Hi all,
>
>can anybody explain to me what Drive-Correctors and Encoders are
>and why we need them ???
>
>Thanks !
>
>Carl Brennan
>Paderborn, Germany
>carl@pader-online.de
>
Del Stanton  - Burbank, California, USA (Near Los Angeles)

"sdl20@pacificnet.net"  (Lower case "SDL" followed by numeric "20")