This discussion was contributed by Michael Hart on July 15, 1998 and is reproduced here without editing.  I thought this necessary since this discussion is well thought out and well documented.

In addition, I have reproduced parts of the discussion a second time (at the end) and this time added my rather extensive commentary to it.  This is done not to contradict any of the proposed mechanisms or their solutions, but only to clarify my impression of some of these complex processes and introduce some of my own experiences and solutions.  The original begins immediately below.  To go to the edited and commented version press here.
 

INTRODUCTORY STATEMENT

On July 12 1998, I posted a message stating at 5:05 AM CST, I found, identified and isolated what I believe to be the single cause for retrograde motion.  I had some suspicions that the less than 50% efficiency of a typical self locking worm and worm wheel used for telescope drives was important as was possibly a larger diameter but finer pitch worm such as found on well respected, but rather expensive Byers drives.

Precise measurements proved my suspicions well founded.  As a result, I am prepared to make a rather controversial statement: "Retrograde motion is potentially inherent in any worm and worm-wheel combination".  Except for the word "potentially", you will notice this statement is quite similar what John Piper of Meade has made.  It is not my intent to prove or disprove this, but I believe this summarizes characteristics exhibited by the worm and worm-wheel sets I examined.  Read on to find out why I make this rather bold statement:

Before posting details described elsewhere in this writing, it was necessary to move the scope to a large building exceeding 65 feet or so for precision measurements.  The building was needed to prevent air currents from skewing measurements.  I set my 12" LX-200 up as usual- heavily loaded, but precisely balanced with the aid of the added Dec roller bearings.  I used two 0.0001" graduation dial indicators as a means of measuring deflections in the worm and worm wheel.  A 0.0001" defection is not difficult to produce in even rather thick materials.  I used the stock Meade spring on the worm carriage which loads the worm-wheel a bit and also removes backlash in these components.  I adjusted the worm carriage pivots to just remove lash, but remain rather free to move.
 

THE CAUSE OF RETROGRADE MOTION:

In a word, friction.  At 50% efficiency, just as in similar drive-train, there is a significant amount of friction.  Details as to how friction causes this are outlined later in this report.  Dial indicators were used to measure deflection of the worm and worm-wheel.  I found the worm wheel readily deflects upon application of torque to the worm.  Even finger pressure causes a bit of deflection and only a tiny amount produces problems for autoguiders.  The worm itself also deflects, but to a lessor degree on the LX-200.  The deflection is a result of typical friction between the worm and worm-wheel.

Friction may be minimized considerably by allowing backlash in the worm to worm-wheel combination, however strange things occur at the arc-second level while the drive-train takes up the lash upon reversal.  First, the telescope moves a few arc seconds, then stops while the lash is taken up, then resumes moving. Using electronic backlash compensation is not advised as it causes jerking of the image as the worm disengages the front side of the worm-wheel and hits the back side.  One can here it hammer the worm-wheel.

It appears Meade uses a molybdenum based lubricant noted for anti-friction properties.  How this grease works with typical usage temperatures is likely important, however.  Trying various other lubricants with low friction and temperature properties may be worthwhile, because if friction is lowered, the use of the stock 2-1/4 lb. compression spring to lift the worm into the worm-wheel provides an automatic means for controlling backlash where a bit of run-out exists.

A stock Meade carriage spring has about 2-1/4 lbs. of compression at it's installed working height of 1/2 the uncompressed height. that 2-1/4 lbs. produces enough friction between the well lubricated worm and worm-wheel to deflect the worm-wheel 0.0008" and the worm 0.0002".  That is enough to produce 1 arc second of retrograde (reversed motion from the expected direction) at 85 degrees ambient. One arc second is easily masked by atmospheric turbulence.  A very small increase in carriage spring force will produce a 0.0010 deflection of the worm-wheel resulting in almost a 3 fold increase in retrograde to 2.7 arc seconds.  This is noticeable in a guiding eyepiece in good seeing by those looking for it.
 

HOW RETROGRADE MOTION IS PRODUCED

Friction between the worm and worm-wheel causes the worm to pull the worm-wheel out (or in) and bend the worm in the opposite direction, the direction controlled by the direction of the worm contacting the worm-wheel.  The worm-wheel follows the pitch of the worm until the worm breaks free.  While the worm-wheel is following the pitch of the worm, the worm-wheel travels in a reversed direction, because the pitch direction moves it this way.  The amount of retrograde is determined by the degree of pitch and total deflection. Once the worm breaks free, the normal expected direction resumes.   For a detailed description of this effect with diagrams press here.

Variations in the coefficient of friction determine the point the worm and worm-wheel break free.  A temperature variation of 20 degrees below 85 degrees produces significantly different (and worse) results.  In colder temperatures,  lower spring pressure is needed to prevent retrograde.  I have tried reducing the spring tension from 2-1/4 to 1-1/4 pounds.  However, in certain situations (such as temperature and worm-wheel run-out),  this is still too much pressure.  To little spring pressure and the worm readily disengages the worm-wheel from a typical imbalance.  As a result, I now use a thumb-screw to replace the existing set-screw and no carriage spring as I described on Doc G's Info Page.
 

HOW TO MINIMIZE OR ELIMINATE RETROGRADE MOTION

1.)  Remove or minimize worm/worm-gear friction.  Without this friction, retrograde is not produced.  The lubricant used and properties of that lubricant at expected use temperatures is very important.

2.)  Precisely adjust the worm and worm-wheel clearances at just short of or barely deflecting the worm wheel or at most- no more than 0.0002".  Too much clearance and almost any amount of electronic backlash compensation slams the worm into the worm-wheel causing jerky motions.  Too much loading that removes all lash may easily produce .0010 deflection and a corresponding 2.7 arc second retrograde.

3.)  Decrease worm (and matching worm-wheel) pitch.

4.)  Increase worm, worm-wheel and optical tube shaft stiffness.

5.)  Use a throated worm wheel design (hobbed type) which will probably prevent or at least minimize worm and worm wheel lockup upon worm reversal.

One and two are user doable on the LX-200.  Three and four are arguably suited for new designs.  Five requires a throated worm wheel design.  See illustration below comparing a throatless (LX style/fly cut type) worm wheel and a throated worm wheel (hobbed type).
 

MAINTAINING OPTIMAL WORM ADJUSTMENTS

For now, eliminating the carriage spring and going with manual carriage adjusting thumbscrew works very well.  Adjust the pressure of the thumbscrew to where resistance is felt (the slewing noise will be similar to, but a bit softer than the RA drive). Back off a bit from this adjustment.  You will likely need to tweak this at different temperatures and optical tube elevations.

Use a dial indicator of modest quality permanently mounted to measure worm-wheel deflection.  A $32 Sears model with 0.001 gradations is adequate as a deflection detector.  <0.0002 deflection virtually eliminates retrograde.  Is this overkill?  Not for precision guiding.  The tiniest bit of deflection indicates all lash is removed, but short of producing noticeable (> 1 sec.) retrograde.

With the LX-200, the lash removal (< 0.0002" deflection but greater than 0) allows a larger backlash compensation adjustment (around 40) yielding a smooth <0.5 second Dec reversal time. This is the optimal balance of friction/backlash adjustment, but requires tweaking to compensate for typical variations.  Above 0.0010" and retrograde starts to appear and Dec reversal times increase to over 2 seconds.
 

CONCLUSION:

At this time, I feel quite comfortable about the subject of retrograde motion, what causes it and why.  In the RA drive that is typically slowed, stopped or sped up, any retrograde if  resent, will not be seen while guiding.  For the Dec drive, it is another story because this drive must be reversed from time to time.  Here, retrograde is seen as quite confusing to the human and worse to the autoguider.

Prudent use of the suggestions outlined here can result in smooth LX-200 Dec drive reversal rates better than 0.5 seconds utilizing electronic backlash settings on a loaded, but well balanced 12" LX-200.  Compare these reversal rates to other drives- they are extraordinary.  They allow a well balanced LX-200 to track at unbelievably precise levels and with high correction rates.

Smaller LX-200 scopes using the same drives should produce equal to or better performance.  Up unto this point, I have obtained excellent results with rather precise adjustments.  Now, I feel I have a better understanding as to why.  Nevertheless, the precise adjustment point needed to achieve the consistent high performance obtained on my 12" LX-200 is a critical one, but when it's dead on, this drive really works well in both RA and declination.
 

Discussion About Retrograde Motion in Worm Gears (Wheels) Caused by Worm Action

In the following discussion, I have selected a few of the most important points made in the above discussion from Michael Hart and added my own comments.  I am in fundamental agreement with Michael on all important points but feel that an additional viewpoint on some points will help readers understand the issues better.   Michael's original commentary is in italics.

The right Ascension and declination drives of a telescope are in general drive by a worm gear engaging a worm wheel (gear).  Other gears will in general be involved as well, but it is the peculiar action of the worm against the worm gear that is sometimes the cause of retro-action or other hesitation or "jerking" of the optical tube.  Retro motion takes place when action in one direction is called for, action in the opposite or retro direction takes place briefly before action in the correct direction takes place.   This problem sometimes manifests itself not as actual retro motion but as hesitation to move in the correct direction briefly.

When very fast motion is called for, the retro motion is often not noticeable.  But at guiding speeds where action between the gears is very slow and precision is paramount, this retro motion can be conspicuous and debilitating.  It is almost impossible to correct for retro motion in automated software guiding implementations.  The retro motion is in many ways equivalent to hysteresis in a servomechanism and thus related to nonlinear action somewhere within the gear contact mechanism.  This is a complex phenomenon which will be examined in detail in the following discussion.

The design of gears of almost all types is well known and well understood.  The smooth transmission of force between gears depends on the shape and contact area of the gears.  The contact surface between spur gears is very tiny and setup as a rolling/sliding action.  Making the transition between teeth in a smooth fashion requires very high precision machining.  In the case of a worn contacting a worm wheel, the requirement for precision is no less complex.  There is, in the worm to worm gear contact an appreciable surface of contact.  The worm can be thought of as a continuous ramp which is spiraling forward steadily with the tooth on the worm gear riding along the surface.  At each turn of the worm, the next tooth is engaged.  Clearly the precision of the spacing of the teeth on the worm gear and on the worm are critical.

The worm used the same surface over and over again as it turns while the worm gear uses tooth after tooth in succession.  Thus there may be a primary error period associated with the worm and the particular single thread of the worm that is used over and over again.  As the worm completes a revolution and the next tooth is engaged there may be a slight discontinuity in the motion of the worm gear if the spacing of the teeth is not perfect.  Any periodicity irregularities will be repeated for each turn of the worm.

I am prepared to make a rather controversial statement: "Retrograde motion is potentially inherent in any worm and worm-wheel combination".  Except for the word "potentially", you will notice this statement is quite similar what John Piper of Meade has made.  It is not my intent to prove or disprove this, but I believe this summarizes characteristics exhibited by the worm and worm-wheel sets I examined.

This is indeed a kind comment.  I would have said that some designs minimize retro problems and some exacerbate it.  I strongly feel that the floating platform design is subject to maladjustment and exacerbates the retro problem.

I set my 12" LX-200 up as usual- heavily loaded, but precisely balanced with the aid of the added Dec roller bearings.  I used two 0.0001" graduation dial indicators as a means of measuring deflections in the worm and worm wheel.  A 0.0001" defection is not difficult to produce in even rather thick materials.

I think it is appropriate to mention at this point just how delicate and how precise the movements of the worm and worm wheel need to be.  If one allows 2 arc-seconds of motion of the optical tube, and uses a worm wheel of the size in the LX200, 5.75 inches (146 mm), the motion at the contact between the worm wheel and the worm is only 0.8 E-6  (0.8 microns)
That is about the wavelength of red light!   (0.0001 inches is 2.54 microns)  These are very tiny mechanical movements.  The worm need turn only 0.1 degrees to give 2 arc seconds of motion of the optical tube in this system.  This should put into perspective not only great accuracy required but give some hints as to how to improve the drives.

THE CAUSE OF RETROGRADE MOTION:   In a word, friction. ... I found the worm wheel readily deflects upon application of torque to the worm. ... The worm itself also deflects, but to a lessor degree on the LX-200.  The deflection is a result of typical friction between the worm and worm-wheel.

This very important point.  Because of the friction between the worm which moves laterally to the worm wheel when it turns, there is a force which tends to bend the worm wheel in the direction of motion of the worm surface.  This friction depends upon the force of the worm against the worm wheel, the condition of the surfaces involved and the properties of the lubricant.   The worm wheel may actually be distorted but it is more likely that the worm bends at the drive shaft or actually shifts the shaft laterally.

Friction may be minimized considerably by allowing backlash in the worm to worm-wheel combination, however strange things occur at the arc-second level while the drive-train takes up the lash upon reversal.

Reducing the friction while still maintaining essential contact between the worm and worm wheel is a very critical adjustment to make.  It is the essence of the adjustment method described elsewhere on this web site.  It is possible to do this, it works, but it is persnickety.

It appears Meade uses a molybdenum based lubricant noted for anti-friction properties.  How this grease works with typical usage temperatures is likely important, however.  Trying various other lubricants with low friction and temperature properties may be worthwhile, because if friction is lowered, the use of the stock 2-1/4 lb. compression spring to lift the worm into the worm-wheel provides an automatic means for controlling backlash where a bit of run-out exists.

Indeed an investigation of lubricants might be helpful, but the lubricant already used is so good that I doubt if this is a very fruitful approach to improvement.

A stock Meade carriage spring has about 2-1/4 lbs. of compression at it's installed working height of 1/2 the uncompressed height. that 2-1/4 lbs. produces enough friction between the well lubricated worm and worm-wheel to deflect the worm-wheel 0.0008" and the worm 0.0002".  That is enough to produce 1 arc second of retrograde (reversed motion from the expected direction) at 85 degrees ambient. One arc second is easily masked by atmospheric turbulence.  A very small increase in carriage spring force will produce a 0.0010 deflection of the worm-wheel resulting in almost a 3 fold increase in retrograde to 2.7 arc seconds.  This is noticeable in a guiding eyepiece in good seeing by those looking for it.

I do not doubt this result, but it is astonishing how nonlinear the result is.  When a tiny change in a variable gives a 3 times change in another it is bad news..

HOW RETROGRADE MOTION IS PRODUCED   Friction between the worm and worm-wheel causes the worm to pull the worm-wheel out (or in) and bend the worm in the opposite direction, the direction controlled by the direction of the worm contacting the worm-wheel.  The worm-wheel follows the pitch of the worm until the worm breaks free.  While the worm-wheel is following the pitch of the worm, the worm-wheel travels in a reversed direction, because the pitch direction moves it this way.  The amount of retrograde is determined by the degree of pitch and total deflection. Once the worm breaks free, the normal expected direction resumes.

This is close to the correct description of the mechanical action that takes place.  Believe it or not!   Michael has made an important, and very perceptive observation.  A slightly more complex action between the worm and worm wheel actually takes place   For a more detailed description of the effect with diagrams, press here.

HOW TO MINIMIZE OR ELIMINATE RETROGRADE MOTION

1.)  Remove or minimize worm/worm-gear friction.  Without this friction, retrograde is not produced.  The lubricant used and properties of that lubricant at expected use temperatures is very important.

I am convinced that this is the main source of retro motion.  I can not name another at the moment.  There are certainly other sources of hesitant,  jerky forward motion and irregular motion.

2.)  Precisely adjust the worm and worm-wheel clearances at just short of or barely deflecting the worm wheel or at most- no more than 0.0002".  Too much clearance and almost any amount of  electronic backlash compensation slams the worm into the worm-wheel causing jerky motions.  Too much loading that removes all lash may easily produce .0010 deflection and a corresponding 2.7 arc second retrograde.

This adjustment requires a mechanism for getting at the platform adjustment screw.  This technique is described elsewhere on this web site.  (Look under Mechanical concerns/LX200 Mechanical Concerns)  I have personally set two LX200s with a critically tight setting on the platform which eliminates retro motion  for most portions of the declination gear.  It is easy to make this setting with a permanently mounted telescope since if the declination clutch is never loosened, only a portion of the declination worm wheel is used.  An out of round wheel is less of a problem in this mode of operation.

3.)  Decrease worm (and matching worm-wheel) pitch.

This is again an important point which deserves further explanation.  Lateral motion of the worm wheel against the worm actually causes a motion that is dependent on the pitch of the worm (actually the lead angle)  This angle is typically 4 or 5 degrees for a 24 pitch gear with a small, 1/2 inch worm.  Thus the motion in the circumferential direction is only about one-tenth that in the lateral direction.  The smaller the lead angle the better.  Finer pitch wheels with larger worms reduce the lead angle.

4.)  Increase worm, worm-wheel and optical tube shaft stiffness.

Also, increase the size of the worm wheel and increase the size of the worm.  The first reduces the precision required at the worm/worm-wheel interface and the second reduces the lead angle.

5.)  Use a throated worm wheel design (hobbed type) which will probably prevent or at least minimize worm and worm wheel lockup upon worm reversal.

One and two are user doable on the LX-200.  Three and four are arguably suited for new designs.  Five requires a throated worm wheel design.  See illustration (above) comparing a throatless (LX style/fly cut type) worm wheel and a throated worm wheel (hobbed type).

As might be expected, Meade takes the cheap way out by providing a fly cut worm wheel instead of the hobbed wheel.  Manufacturers like Byers and others provide the hobbed type worm wheels.

The new drive I have designed and am building uses a 9 inch declination worm wheel, 1/2 inch thick mounted on a 1 inch shaft which is driven by a 1 inch worm mounted on a 1/2 inch shaft.  The RA drive uses a 12" worm wheel, 1 inch thick mounted on a 2 inch shaft which is driven by a 2 3/8 inch worm mounted on a 1 inch shaft.  All worm wheels are of the hobbed type.  This drive is still under construction.
 

MAINTAINING OPTIMAL WORM ADJUSTMENTS AND CONCLUSIONS      See discussion above.

These discussions remain somewhat in a state of flux.  As we learn more about the mechanics of the drives some modifications may come about.  But at this time I feel the above explanations are valid and the improvements suggested very workable.

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