Re: [CAD_CAM_EDM_DRO] Differential Threads

Ejay Hire wrote:

> I understand the Math behind the differential threads now, but could
> somebody draw a picture or use small words as to describe how such a
> mechanism would be constructed?
> EjayHire@...

Taking directly from Marvin W. Klotz' webpage at
http://www.geocities.com/mklotz.geo/
article "DIFFTHRD.ZIP" :


For very precise motion or, alternatively, a very high torque
advantage, very fine threads are required. Cutting very fine threads is tricky
at best and the resulting thread tends to be very fragile. A better solution
is to use a differential thread.

What's that? Imagine a cylinder that has one half threaded with a
coarse thread of pitch Pc (tpi - threads per inch). The other half is threaded
with a fine thread Pf (tpi). The coarsely threaded portion of the cylinder is
threaded through a matching nut that is fixed to some unmoving surface. A
"movable" nut is threaded onto the fine threaded portion of the cylinder. This
movable nut is free to move axially along the cylinder but is constrained from
rotating relative to the cylinder. In other words, it can translate but not
rotate. This movable nut is the "output end" of the device that serves to
position or move whatever the differential thread is "driving".

Now, if we turn the cylinder through one revolution it will move
forward (relative to the fixed nut) by a distance 1/Pc. The movable nut will
move in the opposite direction by an amount 1/Pf. The net movement of the
movable nut relative to the fixed nut is then (1/Pc)-(1/Pf). In other words,
the movable nut acts as if it were threaded on a shaft with an effective pitch
of:

Pe = 1/((1/Pc)-(1/Pf))

For example, with the relatively coarse values of:

Pc = 20 tpi
Pf = 25 tpi

we obtain a perfect micrometer thread:

Pe = 1/((1/20) - (1/25)) = 1/(.05-.04) = 1/0.01 = 100 tpi

An attractive application is a leveling screw for a precision level.
Here the fixed nut is a threaded hole in the level base. The movable nut is a
threaded "foot" that is prevented from rotating by friction with the surface
on which the level sits. Turning the threaded cylinder will tilt the base by
minute amounts determined by the geometry of the base and the placement of the
adjusting screw. Obviously, the circumference of the threaded cylinder can be
divided into suitable subdivisions to achieve accurate partial rotations for
an even finer adjustment.

For a given desired range of motion of the movable nut, the computation
of the various dimensions involved can be tricky. DIFFTHRD does all the work
for you.

Moreover, you may not have to hand the required screwcutting gear for
just any thread. (25 tpi isn't easily available on a lathe or via a tap and
die.) The ascii data file supplied (DIFFTHRD.DAT) allows you to specify what
threads you CAN cut (either via a screwcutting lathe or with hand threading
gear) and DIFFTHRD will decide what combination comes closest to producing the
effective pitch you desire.

For a more compact geometry, the entire assembly can be "folded" into
itself. Consider a bolt of pitch Pc threaded into a fixed nut. Bore this
bolt out and thread the hole with a thread of pitch Pf. A second bolt fitted
into this hole and prevented from rotating (say by a spring wire inserted into
a cross-drilled hole) will move with an effective pitch of Pe when the Pc bolt
is rotated.

Update 12/99:

Don't know why I didn't originally include metric threads, since mixes
of Imperial and metric threads offer the possibility of coming closer to a
desired effective pitch. You can now specify metric threads in the data file.
However, the program still operates in Imperial notation.