Manufacturing options for the very-precise Gilson Atlas circular slide rule? (For the nostalgia-inclined)

Everyone,
I would like feedback regarding design and manufacturing options (in low quantities, and also in a "one-off") for a modernized reproduction
of what is considered by many slide rule collectors (remember slide rules? <smile/>) to be the most precise and aesthetically-pleasing slide rule ever made: The "Gilson Atlas".
What makes the Gilson Atlas unique is its aesthetic simplicity yet relatively high-precision in a small package. For multiplication and division it yields 4-5 digits of precision (100-200 ppm), unlike common slide rules which give about 3-4 digits (>1000 ppm). It also keeps the digit precision more constant across the entire range of the scale, which is the bane of ordinary slide rules.
Unlike ordinary slide rules, however, it is not linear -- it is what is called a circular rule (strictly, the term "slide" should not be used in describing it.) The scale itself is helical-coiled, having either 25 or 30 spirals. Thus, even though the diameter of the Gilson Atlas is a little over 8", it packs a scale over 40 feet long, which is how it achieves its precision.
There are two nice online images of the Gilson Atlas. The first is the earliest Type I (with 30 spirals), while the second one (a very nice image) is the Type III (with 25 spirals) which was manufactured through the 1960's and maybe into the early 70's. The Type III was used by many professionals and students who wanted the higher precision it gave over an ordinary slide rule:
http://sliderules.lovett.com/gilsonsquare/frontnew.jpg (Type I)
http://www.konshak.com/Sliderules/Archive/Gilson_Atlas_Type3_WhiteCollection.jpg
(Type III)
The Gilson Atlases were made from 1/16" coated aluminum. Note that the only moving parts are the two clear cursors (the backside used one cursor but I am focusing here on the high-precision side with the spiral scale.) There are no sliding scales as ordinary slide rules have. This adds to the aesthetic simplicity of the Gilson Atlas. For an overview of how the Gilson Atlas works, the original manual (for the 30-spiral Type I) is online at:
http://www.sphere.bc.ca/test/gilson/gilson-manual2.jpg
http://www.sphere.bc.ca/test/gilson/gilson-manual3.jpg
(The instructions are insufficiently terse, unfortunately.)
Wayne Harrison has produced a Postscript file of the scale layout for the Gilson Atlas Type III (25 spiral), which can be downloaded (along with an explanatory text file) from:
http://www.openreader.org/gilsonatlas/GilsonAtlas3.zip
(The Postscript file probably would not be used for manufacturing purposes, but illustrates how it looks and even works for those inclined to build a "paper" demo. I produced a PDF from Wayne's Postscript, included in the zip file, for easier printing.)
*****
So what are the various design options in a modern replica of the Gilson Atlas? Here are my initial thoughts...
With regard to substrate materials we could consider:
1) Metal: aluminum alloy, titanium, stainless steel, etc. (anything which is corrosion/oxidation resistant). I think it should be a little thicker than the original 1/16" for added stiffness and "solid feel".
2) Plastic: Obviously high quality is desired, having the ivory-like look and feel of the classic slide rules of old, such as Dietzgen, Keufel & Esser, etc. The plastic needs to be very stable (long- lasting and environmentally-resistant), scratch-resistant, able to resolve fine details of inscribed scales, and with the nice surface finish just mentioned.
3) (anything else ???)
Then there's the issue of surface coatings (if any -- coatings can be painted/layered on, or in the case of metal could be electroplated, anodized, nitrided, etc.). And of course how the spiral and marks are placed on the surface with high precision and fineness (e.g., etched, scratched, painted/inked, etc., etc., etc.)
And lastly there's the issue of designing the rotating cursors.
I can't help but think that since the early 1970's (when slide rules were last king), new manufacturing materials and methods could be used to improve the quality and lower the manufacturing cost (including for small runs) for all types of slide rules. But then, maybe I'm wrong here.
Of course, there's no demand for slide rules for practical use, but there's certainly nostalgic interest (witness the large slide rule and vintage scientific instrument collecting communities), so I believe there is a small market there, maybe a few hundred to a thousand.
Your feedback is much appreciated. Let me know if you are interested in being involved with a project to design and build a circular rule similar to the Gilson Atlas.
Thanks!
Jon Noring
(p.s., it is intriguing to consider building a much larger Gilson Atlas, say for a science/technology museum, which can have an even more precise and longer scale. For example, one could etch the spiral and marker lines into a mirror polished stainless steel plate, say 3 to 6 feet diameter. The problem here is making the cursors stiff enough so they don't bend/bow sideways due to their own weight. And maybe there's a clever way to reduce the number of cursors to one and have an alternate method to register intermediate results.)
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Hello Jon,
I read about your project with interest. I'm not particularly familiar with slide rules and the Gilson Atlas since they were really before my time. Nonetheless, the project seems quite interesting.
I would suggest spending some time looking at the economic feasibility of manufacturing the Gilson Atlas. You have clearly thought about the number of potential buyers, but do you know what they would be willing to spend buying this product?
Molding this product would allow you to produce each copy relatively cheaply (maybe $2 to $5), but the initial tooling cost will be quite high (maybe $20K to $30K). Machining them may be a good alternative because you avoid the tooling charge and the result will be very nice (no parting lines, etc.), but the cost for each piece will be much higher. Its hard to estimate the cost of machining without knowing the material, quantity, and design of the moving arms. There are also lots of different qualtity levels when it comes to machining. I'm assuming very good maching would be required to maintain the proper tolerances and cosmetic requirements.
I would be happy to discuss this project further and offer my assistance in exploring the options, etc.
--

- John

John Eric Voltin
  Click to see the full signature.
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Jon,
Slide rules are not before my time, but I never used one of this type. Even so, your project is quite interesting, and I might be able to help as well.
I think for the small volume production that you will have, you will be looking at machining each unit, rather than the larger volume methods such as molding. I think that what you will want to do is essentially to "print" the spiral scale on the surface of the plate, rather than to try to scribe it in any form. This requires that the image be developed in detail one time, but then it can be produced as many times as required. I'm pretty sure this was how it was done with the original rule.
If you use a printed image for the scale, there is a potential for error if the arms are not correctly centered with respect to the spiral. This is a kinematic problem, one that I can address if needs be. If you decide to go forward with this project, please let me know how you are going to do this, and let me know if I can be of help.
Jon Noring wrote:

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"Dr. Sam" wrote:

Thanks for your interest! If you know of others who might be interested in this project, tell them about it. John Eric Voltin has graciously offered his help with the 3-D graphics aspects, to develop virtual prototypes and interface with machine shops.

I can't help but believe that with particular substrate materials there can be a cost-effective way in low runs to inscribe/emboss/etch/ whatever the scale markers into the substrate with high precision. But then maybe I'm out to lunch on this.
In terms of the aesthetics, using engraved (and inked where it makes sense) scale markers is visually and tactilly more appealing than printed-on markers -- it speaks of quality. However, printing can look appealing *if* the surface (whether coated or bare) is very smooth and visually non-obtrusive, and the printing is extremely sharp even under significant magnification, and has excellent contrast -- any fuzziness or loss of contrast in different lighting, and it looks cheesy and cheap (engraved/inked markers keep their contrast much better than painted on markers.)
But "printing" the scales is certainly a possibility. At the end of the slide rule era in the 1970's, Pickett (which used aluminum as a substrate) printed the scales using some sort of photographic process, the details of which I'm now trying to obtain from those who research slide rule history. As noted above, Pickett executed this very well because the printing was very sharp and precise, and the background color coating did not interfere with readability. My slide rule of choice at the time was Pickett, which I still have (the surface is painted in an easy-on-the-eyes yellow, with black scales.)
The downside to printing, of course, is durability -- printing is more easily rubbed off by use and by cleaning. Inscribed marks better protect whatever is used to color the mark (if any), so they cannot be rubbed off even with heavy-duty use.
I'd judiciously use color to differentiate some of the scales, as well as the background surface color (if one is applied.) For example, the outermost scale (used to determine the 3-digit answer to the operation before moving to the spiral for the 5 digit answer) should be colored differently from the spiral area (either the background color and/or the scale color.)
(The Atlas 3 used two colors for the background to differentiate the ranges in the spiral, important for usability:
http://www.konshak.com/Sliderules/Archive/Gilson_Atlas_Type3_WhiteCollection.jpg
)
Overuse of color is certainly not good. An aesthetic balance is necessary. Fortunately, with today's realistic 3-D rendering, which can emulate the optical properties of the background surface, we can generate a virtually unlimited number of prototype variations and come up with a coloring scheme which many agree is aesthetically pleasing, functional in various lighting conditions, and which is not expensive or difficult to execute.

This indicates to me, provided the printing is sufficiently precise in two dimensions, to drill the center pivot hole after the printing is done. The printing can include the precision guides at the center hole area -- now it's a matter of drilling the hole to precisely align with the center hole marks (probably use a milling machine.) Now, if the printing is not precise enough in a 2-D sense, then some sort of "averaging" process would be necessary to determine the best center point of the spiral -- to do this on a unit-by-unit basis.
*****
Now, with regards to substrate materials, we essentially have three general categories (I've left wood/bamboo off this list):
1) High-quality plastic. (E.g., Cycolac/ABS, which K&E called 'ivorite' and used in its last series of slide rules. It would not surprise me if, since the 1970's, a whole new bunch of much better plastic materials have been developed.)
2) Metal. (Aluminum or titanium looks to be of interest.)
3) Ceramic. (Probably out of the question.)
Aluminum or titanium are of especial interest since they form a fairly stiff and durable substrate with a nice feel to it (e.g., the Pickett slide rule). We can also entertain both hardening and coloring the surface of aluminum using an anodization/dyeing process (don't know if this would be too expensive -- and don't know if it's possible to effect multiple surface background colors -- the scale marks would still have to be inscribed or printed.) Titanium can be nitrided (to form a golden color surface), but again this may be too expensive. (I believe for a given thickness, a titanium alloy is both stiffer and lighter weight than aluminum alloys -- is this so?)
Lots of ways to go.
Jon
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snipped-for-privacy@noring.name says...

For a true engraved scale I'd look into laser engraving or photo-etching for moderate quantities, for example...
http://www.synrad.com/search_apps/process/engraving.htm or <http://www.tech - etch.com/photoetch/photogallery/LaserScale.html>
Presumably the laser engraver could be driven by a CAD file. It shouldn't be too difficult to import coordinates from a spreadsheet into Autocad (probably via .dxf) to generate the spiral, scale points and graduation text. This would give you a very accurate easily modifiable model of the scale. Prototypes would be easy by plotting onto adhesive backed mylar.
I'd be willing to give this a shot if a mathematical representation of the scale is available. I also have access to machine tools for prototype construction.

Off the top of my head, I think you'll find aluminum to be stiffest per unit weight for a solid flat plate among the above materials.
Ned Simmons
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Ned Simmons wrote:

A minute before receiving your message, I sent out an inquiry about laser engraving, so your reply is very timely for sure.
I would suspect (but am not sure) that photo-etching will have a substantial setup cost, but once setup, the per-part manufacturing cost (not counting setup costs) will be lower than laser engraving, which is a one-off process. I don't know about the precision of the photoetching, but it seems like it will compete with laser engraving except for very small sizes (I'm just guessing here.)

Yes, this is how they work, from my online research.

As I noted in my original message, a zip archive of a Postscript rendering (and a PDF conversion) of the Atlas 3 spiral scale is found at:
http://www.openreader.org/gilsonatlas/GilsonAtlas3.zip
Read the text file in that zip archive. The author of the Postscript file, Wayne Harrison, is still active on the 'sliderule' group on Yahoo, so I assume he'd be able to advise us with the mathematics of the spiral and the marks. Also, the authors of the journal article on the Gilson Atlas may also provide advice.
(By and large, I understand the mathematics of the spiral and marks, but I've not reduced it down to formulae that would work with a CAD system -- it depends upon the coordinate system used. Maybe this weekend I'll put something together.)

Wow, great! Two others have offered their help: John Eric Voltin and Dr. Sam. Hopefully others will also step forward to help. If it makes sense, I can start a separate mailing list on Yahoo for more serious discussion of this project. We can also consider a short teleconference (using FreeConference.Com) to help get the project properly launched (we would need to do teleconferences only occasionally -- most of it can be done by online communication, such as the mailing list and AIM or YahooIM.)

Yes, that is my impression. Titanium doesn't appear to offer anything special or unique for this particular project (as far as I can tell) other than it being a "sexy" material (the bare metal is more corrosion-resistant, especially in ocean environments.)
A higher-end aluminum alloy (such as the venerable 6061) appears to offer a good choice as substrate material. The other choice would be a higher-end plastic as noted in prior messages.
With aluminum, we can either keep it bare metal, or anodize it (with choice of color(s) or simply clear), or use some paint-like or plastic coating on it. There's advantages and disadvantages for each option.
With plastic, it will probably have to be thicker to maintain sufficient stiffness and "feel", but this is not a major issue (if it is 8.25" diameter, anything between 0.25 to 0.5" thick seems right to me.) The plastic chosen would have to meet various requirements, some of which are related to how the scale will be placed on it (e.g., if laser engraved, certain plastics cannot be used since they produce poisonous gases, such as PVC.) Some plastics appear to be quite difficult to coat or print on (try coating Teflon or other fluorinated plastic. <smile/>)
Jon
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says...

I printed the pdf and made a crude mylar cursor. It looks very good--I may have been jummping to conclusions about needing a CAD model. When all you have is a hammer, everything looks like a nail...
You were being kind when you said the instructions you pointed to in an earlier post were 'terse'. I assume that choosing on which ring to read the result involves jumping rings based on how far the multiplier/divisor is from the center ring?
If I get a chance this week I'll print a scale on mylar and stick it to some lexan or acrylic and make some real cursors.

One possibility for laser engraving might be black anodized aluminum with a silkscreened overlay to get the color bands. If you can burn thru the overlay without damaging the anodize, you've got your color bands and dark graduations in one shot. Registration and durability of the overlay are things to consider. Time for advice from the engravers, I think.
Ned Simmons
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Ned Simmons wrote:

<laugh/>
Actually, the method to determine which spiral segment to read the answer requires that one first determine the approximate 3-4-digit result using the outer scale (refer to the PDF). It's the one downside to the Atlas approach at high-precision calculation ("high-precision" for a slide rule, at least.) When using the spiral, simply select the spiral segment corresponding to the 3-4-digit answer (one has to redo the whole calculational sequence when using the spiral -- there's no way to transfer results from the outer scale to the spiral since they are of different lengths.)
However, interestingly, one can use the outer scale for most work (and ignore the spiral section), and still get precision equivalent to a 25" linear rule (which were made but are very unwieldly -- most slide rules used by engineers/scientists for rough calculations were 10" long). But the spiral scale is there when an engineer/scientist needs the extra 1-2 digits of precision.
There is another interesting and fairly simple slide rule (a cylindrical type also of very long scale length) which doesn't require a precalculation: the Otis King. (This is another on my "would like a replica" list, but appears to be a step-up in machining complexity.)
Here's a good summary of the Otis King:
http://www.svpal.org/~dickel/OK/OtisKing.html
And since we are talking about high-precision slide rules, the other two which come to mind (in addition to other circular types using a scale like the outer scale of the Atlas), the Thacher:
http://www.sphere.bc.ca/test/unusual/thatcher4.jpg
http://www.mathsyear2000.org/museum/floor3/gallery9/gal2_2p5.html
And the Fuller:
http://sliderules.lovett.com/fullertype2/fullertype2pics.htm
(Try to build one of these, especially the Thacher! Note that the Atlas has as good of a precision as the Thacher/Otis King/Fuller, and in a much simpler and much more compact package. The downside with the Atlas, as noted above, is the need for precalculation to 3-4-digits of the answer, while the cylindrical types give direct read-out of the answer without need for precalculation -- however again, using the outer scale of the Atlas outperforms nearly all linear slide rules.)

Great! Let me know how it works. Hopefully your printer has good XY accuracy (so the printout is a true circle and not slightly elliptical -- with my laser printer I find that one axis of the circle is 0.03" shorter than the other, which works out to about 4 parts per thousand deviation.)

I saw on one of the laser engraving sites that they can burn through paint coatings to expose the metal underneath, so this certainly looks like an option.
Yes, consulting with one or more experts in laser engraving/etching is a good idea. The most important thing to ask is how much time it will take to burn the long spiral scale and associated tick marks and lettering --> time == $$$. Fortunately we don't have to burn deep or wide. The substrate material undoubtedly affects burn time (based on its optical and thermophysical properties), so again feedback from the experts in laser engraving will assist with material selection.
Jon
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I've been investigating laser engraving as a means to place the scales on the Atlas circular slide rule replica.
As I peruse the various online information sources on laser engraving (just do a Google search), it appears this may be a viable option. Many places do this commercially -- just give them a CAD file and the parts to inscribe, and away they burn. Many will do custom jobs of even one part.
I'm not sure of the cost of such laser engraving services, but I don't see it particularly expensive considering the type of jobs they advertise doing in small runs. Many claim being able to put down lettering as small as 0.01" in size, so it appears they can do the fineness required (I assume the XY precision will also be sufficient).
(Who knows, maybe a company with idle engraver machine time will donate engraving service as a way of advertising their company. We'll let them burn their logo and name somewhere on the dial or edge.)
The only issues with this option are with regards to substrate materials (one can engrave just about anything, though), whether the materials are coated (maybe with various background surface colors) and how to "color" the engraved lines and lettering (it appears there are various techniques depending upon substrate material, coating (if any), etc.) Maybe the engraved areas can be "inked" by some clever inexpensive process?
(It would not surprise me if the cost of laser engraving is strongly proportional to the extent of engraving needed to be done, and clearly with the Atlas replica there will be a need for a *lot* of intricate engraving which probably will take a lot of time -- we are talking about engraving a 40 foot long spiral, with ten thousand tick marks and lots of lettering along the way. Fortunately the needed depth is quite small, so that probably lowers the burn time, especially when using the right substrate.)
Anyone here an expert on laser engraving care to respond? Is this a viable option, or something to cross off our manufacturing options list?
Thanks.
Jon Noring
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Consider screen printing a negative then chem milling the lines, the swabbing the ink into the chem milled slots. This is not as far fetched as you may think. Look at how they make microprocessors with chem milled lines only microns wide and deep. Once you have the basic shape sliding nicely, then do the printing. You can't do it any cheaper nor better any other way that I know of except possibly laser marking.
Wayne www.rcsailcars.com
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[snippage]
You can use metal substrate materials however I don't think they give you much you can't get with good old plastic at fairly minimal charge ... More on that later in this post ...

[this is later in the post] If you will find yourself a good graphics shop that makes printed plastic sheet for backlit signage you will basically have your problems largely solved. I have some good experience with polycarbonate. Many fabricators/graphics shops can screen your graphic onto a 4' x 8' sheet of polycarbonate, cut your holes apply a film on one or both surfaces and then cut the plastic into it's finished shape to ~.005" or less reliably. The most variable part will be that your holes will probably not be completely cylindrical ... I would caution you however that few processes do produce completely cylindrical holes.
For your film I would recommend an anti-glare film that would both protect your polycarbonate from UV and chemicals (again see your supplier) and protect your graphics from abrasion. The cursors could be made of the same/similar material. btw ... polycarbonate is not the only material you can uses ... acrylic and polyethylene will probably meet your needs as well.
The advantages of the process I am advocating are as follows: 1 - The requirements on you are pretty minimal as long as you find a competent shop and there are plenty. 2 - Many shops that produce back-lit signs or at least the graphics for back-lit signs will have a CNC router or can get access to a laser cutter (leaves a slight yellowing at the edge of the cut on Lexan but I don't find it objectionable). This is good because CNC milling will cost you a whole lot more and you will not likely get better results. 3 - There is a wealth of experience in this type of work. I haven't been involved in signage lately but I can tell you that if you go to any department store and find out where they get their signs made you will get useful feedback. I would recommend a local (to me) fabricator except the ones I know have gone out of business. 4 - Entry level pricing is pretty low. You can expect up to ~$2,000 or so for artwork charges and die work depending on colors and the amount of work they have to do. If you provide a DXF file you can probably cut that down to considerably less as in more like $400-500.
If you will be satisfied with general graphics and the precision that can be had you can go to many local graphics/print/sign shops and they will get you what you need. Be explicit on your precision requirements.
If you still aren't satisfied with the precision I can probably put you in touch with one or two precision plastics suppliers that can do the work you need but I have confidence that with a little work you can probably develop your own locally.
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