Subject: Re: Rack and Pinions

From: [email-masked]
Date: Fri, 13 Jan 95 20:08:08 -0500

Well this sounds fun. I hope a real gear expert speaks up. In the
meantime how about using two rails, and four wheels grooved to
stay on the rails, four for stability, and if you still need the
rack for traction you can control the backlash as the weight is
the rails. I look forward to your first progress report

---

From: [email-masked] (James Kirkpatrick)
Date: 13 Jan 95 10:55:53 MST

I have a tricky question about gears, gear meshing, and
rack-and-pinions in particular.

With ordinary spur gears, they are held at some particular spacing
by way of fixing the axis of rotation in some sort of bearings.
For example, clock wheels rotate in holes in the plates, keeping
the level of "mesh" constant.  If the meshing is too close or too
distant you get uneven running or perhaps even jamming.

I'm presuming that this is also true for rack and pinions, considering
that a rack is sort of a very large gear.  I'd like to get smooth
operation even if the pinion is actually unconfined and bearing down
upon the rack.  This might dictate tooth forms and other factors
that I am unable to decipher from reading Machiner's Handbook.

Application:  I'm considering building a very strange clock
called an inclined-plane clock.  This is a cylindrical clock
that slowly rolls down an inclined plane (say 20 degrees or so),
picking up power and stability from an offset weight (the clock
face is sort of connected to this offset weight, so the face and
hands do not rotate as the case rolls down the incline).  To assure
no slippage and uniform rolling from front to back, one way to design
it is to put two rack "rails" on the plane, and two circular pinions
around the clock.  I want to make sure that as the clock slowly rolls
down the plane, it follows a smooth path.  It should not do things
like jump over each tooth, both for noise reasons and visual/temporal
stability.

This seems analogous to a simple rack and pinion, but as I mentioned,
the pinion is being forced into the rack rather than rotating a fixed
distance away via a bearing.

I remember as a kid I had an Edmund telescope with a rack-and-pinion
eyepiece, and as you turned the knob it would tend to jump from one
tooth to the next.  They also sold a helical (I think) version with
the teeth on the rack slanted at an angle, to alleviate this.

Another thought I had was to use rails shaped like railroad rails,
and make the contacting edges of the clock like a railroad wheel.
The geometry of these is such that they tend to self center.  But
I don't think I can get reliable adhesion at the needed angles, and
am unconvinced the system would be stable.

I hate to get hung up at the very first step of planning!

I am aware that a British company made a run of these several years
back, as reproductions of earlier clocks.  (Thwaite & Reed?)  So
it can be done, but such details as these are unclear.

Any gear experts here?

Jim

---

From: [email-masked] (Bruce Holder)
Date: Mon, 16 Jan 1995 18:30:25 GMT

James Kirkpatrick ([email-masked]) wrote:
: I have a tricky question about gears, gear meshing, and
: rack-and-pinions in particular.

  [Questions on gear train design, center-to-center distance, smoothness
   of meshing, etc.]

: Any gear experts here?

  I'm no expert, but I've re-read the gear parts of Machinery's 
Handbook (at least the parts on spur gears) enough times that I think
I'm beginning to get a glimmer of understanding.

   One of the good things about the involute tooth gears is that the
center distance is not critical.  For instance, gears are tested by
putting them in a fixture where they are pressed firmly together by a
spring and the center distance is measured as they are rotated.  If
they are properly made (i.e., if there is adequate clearance between
tooth crests and roots), gears can run tight together, as in your clock.
For heat and wear reasons, they usually aren't.

  I suspect that the rack and pinion adjustment on the Edmund telescope
suffered from having the smallest pinion that would do the job, so
there was only one tooth at a time really engaged.  If you choose a
relatively large pinion (if I read your message correctly, you're
thinking about putting the pinion around the outside diameter of the
clock), there are more engaged teeth, so even if only one tooth is
actually carrying the load, the other engaged teeth are not far away
>from  their desired positions and can take the load without much
discontinuity in motion as the rotation continues.  Using a relatively
fine tooth pitch will also increase the number of teeth engaged for a
given diameter.

  I also suspect that the frictional load that the adjuster in the
telescope was working against was at the high end of the service range
for the rack and pinion chosen, and that the axis of the pinion was
too far away from the pitch line of the rack.

  If you can find or make a rack for the helical gears, that would be
the ideal solution.  The smooth running afforded by the multiple
simultaneous teeth meshing is one of the two reasons for using helical
gears.  (The ability to to turn corners without bevel gears is the
other.) 

  If you decide to go with the spur gears, here are a couple of other
ideas to reduce any roughness in the motion.  First, offset the front
and back pinions rotationally by 1/2 of the gear pitch, so that while
one is making the transition from tooth to tooth, the other is solidly
in contact in the pitch line area of the tooth.  Second, think about a
traveler between the racks that would resist any gear roughness trying
to push the axis of the pinions out of its right angle to the racks.

---

From: [email-masked] (Steve Rayner)
Date: Tue, 17 Jan 1995 10:00:38 GMT

In a previous article, [email-masked] (James Kirkpatrick) says:

>imkirk
>Newsgroups: rec.crafts.metalworking
>Subject: Rack and Pinions
>Message-ID: <[email-masked]>
>From: [email-masked] (James Kirkpatrick)
>Date: 13 Jan 95 10:55:53 MST
>Reply-To: [email-masked] (James Kirkpatrick)
>Sender: [email-masked] (James Kirkpatrick)
>Distribution: world
>Organization: University of Wyoming
>Nntp-Posting-Host: mallard.uwyo.edu
>X-Newsreader: mxrn 6.18-24
>Lines: 53
>
>
( snip, hack )
All that you need to do is put two rings around the outside of the clock case
that space it out from the rack as it rolls.  If you use commercial rack
around 32 DP like the Boston Gear product, it is quite narrow.  This may
cause problems, but you can use it as a guide if you use two more rings on
the case with the gear in between to guide it as it rolls down the plane. 
If you cut your own gear try altering the addenum and dedenum to get
proper mesh, and smooth running, also the depth of the rings (easiest).
It is OK for the rack & wheel to be involute, but the wheels and pinions
of the movement should be of the proper cycloidal form as the wheels drive
the pinions, unlike normal gearing.

Hope this helps
-- 
                                Steve Rayner.