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