My telescope has one motor driven axis: the RA (Right Ascension). This feature enables me to keep a star (or planet etc.) right in the center of my field of view. This is absolutely VITAL when doing astrophotography of Deep Sky Objects, because these usuallly are very dim objects and require long(er) exposure times.

This 'tracking' of a celestial object must be performed in a very smooth manner, without sudden jerks or hiccups, because these destroy the images while capturing.

Poor tracking causes the stars to drift to the left or the right. Either your tracking is too slow (stars moving to the West) or too fast (stars drifting East). Most of the time the culprits are the motor speed or incorrect gears: most likely the worm shaft and the worm gear. Especially the problems originating from the worm gear are called 'Periodic Error', because the - continuous - error repeats itself with each rotation of the worm shaft.

Here is a link explaining how gears operate .

Some time ago I found the following highly interesting information and I saved it on my hard disk.
As the link no longer exists I copy the text here (in yellow and Italics to indicate that I should not be honoured as the author):

In usual amateur telescopes tracking is obtained by the apparently simple worm-screw and gear-wheel system. A high quality worm is still a very demanding mechanical piece that, to reach the precision needed by a professional telescope, must be accurately worked. Well-machined worm-screws are available to order in the U.S.A., Germany and Japan but they are so highly expensive that no commercial telescope maker fancies employing a worm of such high quality. For instance, the cost of a single perfect gearing of this type may exceed the retail price of a complete 8 or 10 inch Schmidt-Cassegrain telescope! Consequently, amateur telescopes moved by common gear and worm systems are all affected by a certain amount of tracking periodic error spanning from as much as 2' - 5' in bad units down to 15" - 20" in the better ones. We can easily check the presence and the extent of this defect in our own scope, at high power and with a reticle eyepiece, by observing how much wandering there is over time taking, for instance, a crater rim on the Moon, or the edge of Jupiter; in some cases, at very high power we see the stars slowly cross the field of view going in and out of sight!

Periodism is caused by eccentricity or non-circularity of the worm: a typical value of this mechanical defect in an average quality worm is 0.001 inch. In recent years the periodic errors of commercial telescopes have been considerably reduced, not facing the classical and very expensive mechanical way but mainly applying electronics. It is practically hopeless to believe that simple mechanical gearing will give a periodic error of less than 1", since the sizes required by a little telescope would need mechanical tolerances comparable to visible light wavelengths, as for optics. Besides, precision mechanics, like fine optics, require first-rate working of every single piece, while mass-produced electronics are quite inexpensive. So in the best modern amateur telescopes periodism is sometimes limited to a mere few arc-seconds by special electronics, as for instance by Celestron "PEC" or Meade "Smart Drive" devices.

The original text continues with an explanation how to use chemical photography to measure the Periodic Error.
Of course I used my webcam as measuring tool (just scroll down to see how I did that).

The motor drive with worm shaft and gear wheel of my telescope proved to be inadequate for elaborate tracking.
For me this was a challenge: would it be possible to adjust the mechanical components of my telescope in such a way, that longer exposure would be possible?

The following pictures speak their own language; I have also added some explanations.

After I had executed the above procedure, the tracking had improved somewhat, but I was not yet satisfied. So I decided to continue my search.
Again (!) I disassembled the worm shaft, but this time I took it out completely. I inspected the ball bearings that support the worm shaft at both ends. BINGO !!! I found a lot of internal friction and 'heavy points' in these (original TAL) ball bearings, one was even worse than the other. Cleaning and lubrication helped only a little bit.

I visited the local car parts shop for an expert opinion (they are supposed to know about ball bearings). They understood my need for precision and they measured the dimensions of the ball bearings: outer diameter 32 mm, inner diameter 15 mm, width 8 mm.
Surprisingly they had replacement ball bearings in stock! I was shocked to feel the difference between the TAL ball bearings and the new ones: like comparing sanding paper with a baby skin ... soooh smoooooth ... :)
I also bought some special ball bearing grease; total costs (ball bearings plus grease): Euro 25,--

Warning: in my search for the cause of my tracking problems I tightened the motor clutch too fast, and ended up with a defective reduction gearbox (the round box between the motor and the motor clutch). Some teeth had broken off, resulting in a total tracking stop after some 4 minutes of tracking :-(
In the meantime the new motor has been installed: all I need now is a clear sky ...

Malcolm Bird (Thank you Malcolm!) of the former TalScopes Canada supplied the following worm shaft adjustment procedure:

The very first thing you want to do is to make sure that there is no sideplay in the wormshaft. Use the threaded collar (with setscrew) on the RH side of the wormshaft (viewed from inside the housing) to take up any play. Do this before loosening the end housings. A snug fit here is desirable. A tell tale sign that you need to make this adjustment is if there is some slight play in RA that you can't adjust out using the bearing housing flanges at either end.

Once side play is taken up, make sure your worm is centered on the gear. This is a question of 'feel'. The brass gear has a concave contact face that matches the radius of the worm. With both end housings loose, you can feel when the worm is seated properly on the gear face. It helps to loosen motor mount bracket and move motor out of the way.

Snug down both ends of worm shaft while holding worm against gear with your finger to maintain position. Very small changes in contact pressure can now be made by 'tapping' the end of the worm shaft housing towards or away from the gear. You need enough pressure on the gear to ensure that the teeth are fully meshed with the worm. If this is done, and your side play is eliminated - that should take care of the binding issues.

When you re-position the motor/gear train - make sure that the gear that engages the gear on the worm shaft is aligned and square, and that there is no excess backlash here. There will always be a bit of backlash in any gear train. Just make sure that all your gears are meshing snugly and are aligned with each other, and that should give you a smooth drive.

I wanted to see if all my mechanical efforts had helped (or had made things even worse!).
First I worked hard to reach an almost perfect Polar Alignment.
I used K3CCDTools as imaging tool and Registax and RxPec to make the graph in Excel (Note: the first Registax versions worked very nicely with Carsten Arnholm's RxPec, but no longer. Luckily K3CCDTools version 3 has the full functionality to produce the information you need).
I imaged during 500 seconds (= one worm revolution on my scope) at 1 second intervals.
As you can see in the graph there is almost no drift in RA and DEC.
The Periodic Error is clearly visible and I will try to reduce it even further.

But replacing the 2 worm shaft ball bearings was not enough: the Periodic Error was still far too high, with the result that when I imaged - unguided - with exposure times of 20 seconds, only 10% of the frames was usable.

I sought help from the TAL Yahoo Group of which I am a member.
The group's moderator - Bill Brady - gave me some adjustment hints and encouraged me to press on.
I decided to completely disassemble the RA arm of my TAL-2M and I used the following text from the TAL Yahoo Group:

TAL-2M RA ARM DISASSEMBLY
There are two screws in the "arm assembly" near the RA setting circle on opposite sides. You unscrew these all the way (don't screw them inward), they are actually cap or grub screws and serve as covers. Deeper underneath you will see two more screws, loosen these about 3 turns.

Then stick a screwdriver through one of the holes in the RA plate to stop it rotating and turn the arm assy CCW (unscrew). Just keep right on unscrewing until it comes off. You will then see the end of the RA shaft. Surrounding it is a cover held on by 3 screws. Remove. Then you will see a round nut with two perimeter holes. Unscrew that. If you don't have a spanner you can just grab the nut with a pair of channel locks or other large pliers.

At this point the RA shaft can be pushed out of the motor housing through the back. Drift the bearings out with a wooden dowel or brass punch. The inner bearing is sealed so I just left it alone except for application of a bit of thin gear grease. The outer bearing is the one that collects all the metal chunks despite the cover. It is the most exposed except for the lower Dec bearing which collects everything else that gets loose inside the arm assy. The round nut supplies the pre-load, on reassembly it should be tightened snug only. If you can't pull or push any play in the RA shaft that's tight enough.

I found ... that the large ball bearings inside the RA arm were screaming for grease. And after cleaning I gave them a generous helping of grease.
And lubricating the worm shaft with 'slow' and syrup-like oil - Wynn's Xtend Supreme Friction Proofing, part number 64205, I bought it in a car parts shop - also helped and now I am at +/- 38 arc seconds.

After several months I decided to give it another try and disassembled/assembled the whole mount. I saw to it that the worm shaft made maximum contact with the worm gear wheel.
After that I measured the results of course. I made an astounding discovery: the worm shaft proved to be not true, not straight, but bent. And in such a way that it lifted the RA, which is visible in this graph:

I sought and found help - again - from Malcom Bird of former TalScopes Canada and Malcolm mailed me a replacement worm shaft.
It was installed within 2 hours after arrival and I waited for the first star to appear in order to measure.

I am quite happy with this nice result: this last action halved the periodic error and now I am getting to acceptable values of +23 to -14 arc seconds (peak to valley 37 arc seconds).

I fine tuned the RA clutch and did a final Periodic Error test.
I could not believe my eyes, so I tested twice, on different days. And I double and triple checked to be sure that I had not made an error in measuring ....
I used Regulus as measuring star, with a declination of +11 degrees this is close enough to the equator for a reliable measurement.
Finally convinced that my measurement is the truth I can only be happy.

My periodic Error is now peak-to-valley 14 arc seconds in total: better than I ever expected.
And I started with well over 140 arc seconds ....
In total it took me over 6 months to get where I am now, and I will not try to improve further: enough is enough ...
Finally I can re-install the cover of the motor house, which has been open all that time.

On July 14, 2005 I took the next step: Autoguiding my TAL-2M