extreme accuracy for cnc jewelry

thomasm923@... wrote:

> Hello-
>
> This is my first post to this facinating group. I am am jewelry model-
> maker and hope to build a cnc mill sometime in the future. I have
> plenty of questions to ask but I'll keep this post brief.
>
> If I ever learn enough to attemp to build my own machine, I would
> like the machine to have the following qualities: moderate speed,
> high resolution, and accuracy. I have been reading about micro-
> stepping as a way to getting higher resolution, however I am
> concerned that the micro-steps are really not that accurate.

Please consider the use of "differential threads" (see my original
posting 10Aug2000 complete with C source code). This technique
is impractical for large movements (ie over an inch or two) because
of the huge mechanical advantage given. On the other hand, you
can use tiny steppers directly coupled to the shafts.

An exerpt:

I've been playing with different mechanical leveraging ideas
to be used both for direct movement of the table and as a
way to increase the resolution of rotary encoders
( see 11 Apr 2000 "motion-multiplying pulleys: linear to rotary encoder")

.....

Well I came across another VERY interesting page at:
http://www.geocities.com/CapeCanaveral/Hall/4425/ Marvin W. Klotz

which has lots of (DOS) programs (source code & executables)
to aid the machinist. It is well worth your time to look it over.

One of the gems there is a description of "differential threads",
wherein various combinations of course and fine threads acting
together differentially, can create huge mechanical leverages
(or counts/rev for encoders).

This is great for us, because it may give us the capability of having
HUGE number of steps per inch of advancement. For example,
using a 180 step/rev stepper with at 10 microstep driver like the
Geckodrive (ie 1800 steps/rev), then using a 56 TPI course and a
Metric 56.444 TPI (ie 0.45 mm/thread), then you'd get 12,801,539
turns per inch, or an advance ratio of 7.81E-8 inch per step (0.000 000 0781 ").

A more usable example is using a 28 TPI with the above metric thread
to get 100012.493134 steps/inch (or approx 0.000 01" per step).

With such ratio's as these, there should be no requirement to use
pulleys to increase leverage, so the motor can direct drive the shaft.

There are of course some interesting "details", which I leave up to
the "sufficiently curious".

By using some of Marvin Klotz's thread tables and differential thread
formula:

pc = coarse pitch (tpi)
pf = fine pitch (tpi)
pe = effective pitch of differential thread (tpi)

(1/pe) = (1/pc) - (1/pf)

I whipped up a program to compute all the different ratios one could
expect from different thread combinations. The idea is to sort the output
and discover the proper combination to use to achieve a ratio near what
you desire.

Doug Fortune