Wow, Dave. You have done some thinking! I don't have an answer to your Q,
but thanks for the mike lesson.

"Dave Martindale" wrote in message
...
I recently bought a used micrometer of a design I've never seen
before. The only manufacturer's identification on it is the Greek
letter "mu" inside a diamond shape. (Mu is the symbol used as the
prefix for "micro" (1e-6) in the metric system. It's like a lower-case
"u" with an added "tail" on the left side). I assume it's Chinese
made, but I don't know for sure.

The micrometer has both the usual scales on the thimble and a
mechanical digital counter display. The thimble reads in mm, the
mechanical display is in inches. The mechanical display is driven by a
V-groove cut into the spindle, like the Mitutoyo mechanical digital
mikes. However, this V-groove is *not* a simple groove parallel to the
spindle axis; it is a slight helix! Does anyone have the comparable
Mitutoyo model, with metric thimble and inch digital display? Is the
groove a helix on it? What are the tooth counts on the internal gears
that drive the counter?

Some background: Mikes with mechanical digital counters drive the
counter with some sort of gearing. The gearing is in turn driven by
the spindle using some mechanism that rotates with the spindle but does
not move left/right as the spindle moves left/right. Mitutoyo uses a
shallow V-groove in the spindle and a pointed setscrew in the gear.
The setscrew rides in the groove so the gear rotates with the spindle,
but the setscrew can slide along the length of the groove. The groove
is visible in the side of the spindle when the micrometer is closed.

Starrett instead uses a long slotted brass sleeve hidden inside the
micrometer's outer graduated stem. A screw that threads into a hole in
the spindle fits in the slot, and rotating the spindle also rotates the
brass sleeve. But as the spindle is extended or retracted by this
rotation, the screw slides within the slot, and the brass sleeve
remains in the same place within the frame. The end of the sleeve is
formed into a gear that drives the mechanical counter. You can't see
any of this mechanism without disassembly.

Now, you need to use the correct gear ratio for the mechanical counter
to indicate correctly. For mikes where both thimble and counter read in
the same units, this is easy. An inch micrometer advances 0.025" per
turn, so the digital counter must increase by 25 counts, which takes 2.5
rotations of the input shaft. Thus, the spindle and counter gears must
have a 5:2 tooth ratio, which is pretty easy. A metric mike advances
0.5 mm per revolution, which is 50 counts, so you need a 5:1 gear ratio.
Any tooth count and tooth pitch that fits this ratio and gives a pair of
gears of the right size to fit in the space available will work.

An inch thimble mike with metric counter is a bit more difficult. The
spindle moves 0.025" per revolution, which is 0.635 mm exactly. Thus,
you need 6.35 revolutions of the counter for every spindle revolution, a
ratio of exactly 127:20. A Mitutoyo Combimike I've looked at actually
uses 127-tooth and 20-tooth gears, with quite fine tooth pitch to keep
the gears small enough to fit.

But making a metric/inch model is worse. One spindle revolution is 0.5
mm,
which is approximately 0.020", but exactly 2.5/127 inch. A metric
thimble moves 0.5 mm per revolution. This is about 0.020, but is
exactly 2.5/127 inch. The digital counter must increment by 2500/127
(about 19.685) counts per turn of the thimble, which requires 250/127
(about 1.9685) revolutions of the counter input gear. This can be done
with a 250:127 tooth count ratio, but getting this many teeth onto a
pair of gears that fits inside the mike frame needs a very fine tooth
pitch. The teeth would be somewhat fragile, and the spacing of the two
gears would be quite fussy to get good mesh without binding.

Probably the most sensible approach is to approximate the gear ratio
needed with smaller gears. The best choice is probably 63- and
32-tooth gears, which gives an error of only 125 parts per million
(0.0125 percent). If the mike is perfectly zeroed (thimble and counter
are exactly zero with the mike closed) then when the thimble reads 25.4
mm the counter would theoretically read 1.000125". Since the counter
only reads to 0.001", that's a maximum error of 1/8 of the spacing
between two least significant digits, pretty negligible in practice.

But the "mu" micrometer uses 59 and 30-tooth gears, which have an error
of -933 PPM, or about 0.1%. With these gears alone, when the thimble
reads 25.4 mm the counter would theoretically read 0.99907" - almost
one full thousandth low. That is a significant error. And that's why
the V-groove on the spindle is a helix. As the spindle is turned 50.8
turns and moves in or out 1 inch, the helical groove causes the spindle
gear to rotate about 17 degrees *relative to the spindle*, at the same
time is is rotating 360*50.8 turns *with the spindle rotation*. The
helix is a left-hand one, so the two rotations add and the counter
rotates about 0.1% faster than it would if the V-groove was straight.
That compensates for the error in the 59:30 gear ratio, and the mike
reads 1.000 at exactly 25.4 mm. Now I understand it, but the helical
groove sure looked strange when I first saw the micrometer.

The V-groove is effectively a helical cam that provides a very small
rotational motion, just enough to compensate for the error in the gear
ratio chosen. It works, but it must be more complex to machine than a
straight groove parallel to the spindle axis. Does anyone else do this?
Why not use 63:32 ratio gears instead?

Dave

In article ,
Dave Martindale wrote:
I recently bought a used micrometer of a design I've never seen
before. The only manufacturer's identification on it is the Greek

[ ... ]

The micrometer has both the usual scales on the thimble and a
mechanical digital counter display. The thimble reads in mm, the
mechanical display is in inches. The mechanical display is driven by a
V-groove cut into the spindle, like the Mitutoyo mechanical digital
mikes. However, this V-groove is *not* a simple groove parallel to the
spindle axis; it is a slight helix! Does anyone have the comparable

[ ... ]

The V-groove is effectively a helical cam that provides a very small
rotational motion, just enough to compensate for the error in the gear
ratio chosen. It works, but it must be more complex to machine than a
straight groove parallel to the spindle axis. Does anyone else do this?
Why not use 63:32 ratio gears instead?

I don't know for micrometers, but I have seen a Gertner (sp?)
travelling microscope (a microscope mounted on a carriage for a
lathe-bed style optical bench) with a long horizontal travel with a
micrometer leadscrew. But the nut is captive end-to-end, but free to
rotate, except for a radial rod which engages a groove in a bronze bar.
That bar has fine setscrews to adjust the angle relative to the axis of
the leadscrew so it introduces very small corrections into the pitch of
the leadscrew. All in all, a very precise bit of metalworking -- and
*very* expensive. :-)

Enjoy,
DoN.
--
Email: | Voice (all times): (703) 938-4564
(too) near Washington D.C. | http://www.d-and-d.com/dnichols/DoN.html
--- Black Holes are where God is dividing by zero ---

" Wow, Dave. You have done some thinking! I don't have an answer to your Q,
but thanks for the mike lesson.".

Yeah! Same here. Kinda makes for more appreciation of the electronics!

Bob Swinney

(Donald Nichols) writes:

I don't know for micrometers, but I have seen a Gertner (sp?)
travelling microscope (a microscope mounted on a carriage for a
lathe-bed style optical bench) with a long horizontal travel with a
micrometer leadscrew. But the nut is captive end-to-end, but free to
rotate, except for a radial rod which engages a groove in a bronze bar.
That bar has fine setscrews to adjust the angle relative to the axis of
the leadscrew so it introduces very small corrections into the pitch of
the leadscrew. All in all, a very precise bit of metalworking -- and
*very* expensive. :-)

Do you know if this was intended to compensate for errors in
manufacturing, or to allow temperature compensation, or something else?

Reminds me of another compensating mechanism, this one in softwa
Astronomical telescopes need to move to stay aligned with a star as the
earth rotates under the telescope. This is usually done by aligning one
of the axes of rotation of the scope mount with the earth's rotation
axis, and then using a motor to rotate that axis continuously at a rate
of one rotation per sideral day (23 hours 56 minutes). The timing
source could be a synchronous motor driven from line AC, or a
synchronous or stepper motor driven by an oscillator.

Just the motor drive is good enough for visual astronomy, but not for
photography where you need to keep the location of stars from drifting
on the image plane during exposures that may last many minutes. The
usual solution to this is having an auxiliary high-power eyepiece that
grabs a bit of light from outside the camera frame. You align a star in
the field of view with the crosshairs in the eyepiece, and then monitor
its location during the exposure. As it drifts away from centre, you
use buttons or switches on a guiding controller to bring the star back
to the centre of the field. Since this eyepiece is operating at a much
higher magnification than the camera, if the wandering motions are kept
small in the eyepiece they will be invisible to the camera.

The corrective motions may be provided by a small motor whose motion is
added to the main tracking motor by a differential (the old way), or
by temporarily increasing or decreasing the frequency of the oscillator
driving the tracking motor (the newer way).

There are several sources of error in all this. One of them is
inaccurately cut gears, which cause the telescope movement to
periodically speed up and slow down. Even if the average speed is
exactly correct, local speed variations cause star image movement. Some
of this error is due to periodic error in worm or plain gear cutting, and
repeats every revolution of the worm or every tooth of the plain gear.

Someone figured out that if you start out an exposure with manual
guiding, and you accurately keep the guide star centred using the hand
controller, then the history of manual corrections you make is actually
a measurement of the error in the drive train. There's a feedback loop
where the instantaneous motor speed is increased and decreased under
human command in order to keep the telescope motion constant, as viewed
by the human operator. If you record the pattern of these corrections
over several cycles of the drive system (e.g. several rotations of the
worm gear), you can estimate the corrections that are necessary *every*
cycle to compensate for mechanical tolerances. At this point, the CPU
inside the telescope controller can "play back" this sequence of corrections
over and over again, without further human help.

Dave

jim rozen writes:

I have recently also found a very curious micrometer, with
mechanical counter display. It has a metric display and
metric screw, but the display is in the form of two lines
of digits in a window. The rightmost digit is simply
printed on the thimble, but the left digits are printed
on pentagonal prisms that are designed to rotate once
for each turn. Each prism has even or odd numbers printed
on it, 1 thru 9 or 0 thru 8. As the thimble turns,
each turn causes the prism to present the next face
to the user.

So they can provide all the needed digits for a 1"
metric micrometer, in one window with only two numbers.

I can't visualize this. Can you find a picture of it somewhere?

Dave

Why not use 63:32 ratio gears instead?



Because 59 is a prime number, and 63 is 3*31, and 32 is 2^5, and 30 is 2*3*5.

I think....



Yours,

Doug Goncz, Replikon Research, Seven Corners, VA
Unequal distribution of apoptotic factors regulates
embryonic neuronal stem cell proliferation

" Doug Goncz " wrote in message
...
Because 59 is a prime number, and 63 is 3*31
^ ^ ^ ^ ^
3*21

and 32 is 2^5, and 30 is 2*3*5.

Tim

--
In the immortal words of Ned Flanders: "No foot longs!"
Website @ http://webpages.charter.net/dawill/tmoranwms

In article ,
Dave Martindale wrote:
(Donald Nichols) writes:

I don't know for micrometers, but I have seen a Gertner (sp?)
traveling microscope (a microscope mounted on a carriage for a
lathe-bed style optical bench) with a long horizontal travel with a
micrometer leadscrew. But the nut is captive end-to-end, but free to
rotate, except for a radial rod which engages a groove in a bronze bar.
That bar has fine setscrews to adjust the angle relative to the axis of
the leadscrew so it introduces very small corrections into the pitch of
the leadscrew. All in all, a very precise bit of metalworking -- and
*very* expensive. :-)

Do you know if this was intended to compensate for errors in
manufacturing, or to allow temperature compensation, or something else?

I think that it was to tune out tiny errors in the leadscrew
pitch. The one I examined was set at a just barely visible angle to the
leadscrew axis over about a 50mm travel. (Or was it 100mm travel?) I
no longer have access to one to examine, so I'm not sure.

But the access to the adjustments was sufficiently restricted
that I think that this was a factory setting and not expected to be
tweaked in the field.

The groove in which the radial arm traveled was straight, giving
only the ability to add to or subtract from the motion on a per turn
basis, somewhat like the micrometer which started this discussion,
except that it was adjustable. IIRC, the readout was in 0.01mm
increments, and the pitch was about 5 T/mm (0.20mm/turn).

Reminds me of another compensating mechanism, this one in softwa
Astronomical telescopes need to move to stay aligned with a star as the
earth rotates under the telescope. This is usually done by aligning one

[ ... ]

Just the motor drive is good enough for visual astronomy, but not for
photography where you need to keep the location of stars from drifting
on the image plane during exposures that may last many minutes. The
usual solution to this is having an auxiliary high-power eyepiece that
grabs a bit of light from outside the camera frame. You align a star in
the field of view with the crosshairs in the eyepiece, and then monitor
its location during the exposure. As it drifts away from centre, you
use buttons or switches on a guiding controller to bring the star back
to the centre of the field. Since this eyepiece is operating at a much
higher magnification than the camera, if the wandering motions are kept
small in the eyepiece they will be invisible to the camera.

Hmm ... instead of projecting the virtual image of the star on
the crosshairs, why not project it on a four-quadrant optical sensor,
(actually two half circles would suffice, I guess) and have it drive the
correction motor (slowly) in the appropriate direction depending on
where the star's light was falling. The ideal is when the star's image
is equally illuminating both halves.

Enjoy,
DoN.
--
Email: | Voice (all times): (703) 938-4564
(too) near Washington D.C. | http://www.d-and-d.com/dnichols/DoN.html
--- Black Holes are where God is dividing by zero ---

In article ,
jim rozen wrote:
In article , Dave Martindale says...

The micrometer has both the usual scales on the thimble and a
mechanical digital counter display.

I have recently also found a very curious micrometer, with
mechanical counter display. It has a metric display and
metric screw, but the display is in the form of two lines
of digits in a window. The rightmost digit is simply
printed on the thimble, but the left digits are printed
on pentagonal prisms that are designed to rotate once
for each turn. Each prism has even or odd numbers printed
on it, 1 thru 9 or 0 thru 8. As the thimble turns,
each turn causes the prism to present the next face
to the user.

So they can provide all the needed digits for a 1"
metric micrometer, in one window with only two numbers.

Clever. I think it's brown and sharp.

TESA -- the Swiss company, sold in this country by B&S. I've
had one since about 1973 or so. In a hard-shell plastic case which
looks sort of like a blue/gray pistol holster. :-)

Enjoy,
DoN.
--
Email: | Voice (all times): (703) 938-4564
(too) near Washington D.C. | http://www.d-and-d.com/dnichols/DoN.html
--- Black Holes are where God is dividing by zero ---

In article , DoN. Nichols says...

TESA -- the Swiss company, sold in this country by B&S. I've
had one since about 1973 or so. In a hard-shell plastic case which
looks sort of like a blue/gray pistol holster. :-)

Yep, that's it! It doesn't say Tesa on it,
but the plastic flip top housing is exactly
as you describe it.

Jim

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