[math-fun] helical slide rule
It seems to me (fulfilling my role as Great Improver of obsolete past technologies) that the most compact way to make a high precision slide rule would be helical. Circular? Linear? Garbage.
On 8/30/12, Warren Smith <warren.wds@gmail.com> wrote:
It seems to me (fulfilling my role as Great Improver of obsolete past technologies) that the most compact way to make a high precision slide rule would be helical. Circular? Linear? Garbage.
There are the Fullers ( http://www.utsic.org/2010/11/fullers-spiral-slide-rule-more-than.html ) and Otis King ( http://retrocalculators.com/otis-king.htm ) designs but they require cursors. I've always imagined something different: Start with a hollow cylinder (like a cardboard tube as used to ship a rolled-up blueprint) and cut it into a double helix, then place a C scale on one helix and a D scale on the other. (There are 2 available edges so you could actually have a total of 4 scales.) To operate, one helix would rotate with respect to the other. The trouble is, it's a bit of a challenge to enforce the constant diameter of the helices. If you just apply a bit of twisting force on one end of a helix, any resistance will tend to just make the helix curl up (or uncurl) a bit. So the C scale would need to be glued to a smaller concentric cylinder that is inside it, while the D scale would need to be glued to a larger concentric cylinder, which of course needs to be transparent. To keep things aligned one needs tight tolerances so everything fits snugly. The worst challenge is probably getting the scales printed and mounted accurately on the scale surfaces. I almost think it would require a machine-driven lathe. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
Don't cut the pieces out of a hollow cylinder. Cut them out of a solid cylinder. I bet George Hart can just print out the pieces for you. (Is George on this list? He should be. His daughter Vi, too.) On 8/31/12, Robert Munafo <mrob27@gmail.com> wrote:
On 8/30/12, Warren Smith <warren.wds@gmail.com> wrote:
It seems to me (fulfilling my role as Great Improver of obsolete past technologies) that the most compact way to make a high precision slide rule would be helical. Circular? Linear? Garbage.
There are the Fullers ( http://www.utsic.org/2010/11/fullers-spiral-slide-rule-more-than.html ) and Otis King ( http://retrocalculators.com/otis-king.htm ) designs but they require cursors. I've always imagined something different:
Start with a hollow cylinder (like a cardboard tube as used to ship a rolled-up blueprint) and cut it into a double helix, then place a C scale on one helix and a D scale on the other. (There are 2 available edges so you could actually have a total of 4 scales.) To operate, one helix would rotate with respect to the other.
The trouble is, it's a bit of a challenge to enforce the constant diameter of the helices. If you just apply a bit of twisting force on one end of a helix, any resistance will tend to just make the helix curl up (or uncurl) a bit.
So the C scale would need to be glued to a smaller concentric cylinder that is inside it, while the D scale would need to be glued to a larger concentric cylinder, which of course needs to be transparent. To keep things aligned one needs tight tolerances so everything fits snugly.
The worst challenge is probably getting the scales printed and mounted accurately on the scale surfaces. I almost think it would require a machine-driven lathe.
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
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On 8/31/2012 10:53 AM, Allan Wechsler wrote:
Don't cut the pieces out of a hollow cylinder. Cut them out of a solid cylinder. I bet George Hart can just print out the pieces for you...
Allan, Yes, and I have a large slide-rule collection, including the "Otis King Pocket Calculator", whose spiral C and D scales would unwind to 66 inches each. So I've thought about making all kinds of slide rules by 3D printing. A cursorless helical slide rule that doesn't "spring" could be designed using a two-color process to make the inner cylinder solid with the scale of a contrasting color, and the outer (hollow) cylinder using a clear material for its background color. (The scale markings could be above the line for one and below the line for the other.) However, the technology is not yet as accurate and inexpensive as one would like for two-color 3D-printing processes. George http://georgehart.com/
On 8/31/2012 10:53 AM, Allan Wechsler wrote: Don't cut the pieces out of a hollow cylinder. Cut them out of a solid cylinder. I bet George Hart can just print out the pieces for you...
You still get two helices, with no solid core because the "C scale" and "D scale" pieces meet each other at the axis. I think it would still be springy enough to cause excessive error, unless it were solid diamond or tungsten (-:, and you still have to solve the axis alignment problem (making sure the two helices remain co-axial) which is much more easily solved by the transparent concentric hollow cylinder solution that I mentioned at the end. On 8/31/12, George Hart <george@georgehart.com> wrote:
[...] A cursorless helical slide rule that doesn't "spring" could be designed using a two-color process to make the inner cylinder solid with the scale of a contrasting color, and the outer (hollow) cylinder using a clear material for its background color. (The scale markings could be above the line for one and below the line for the other.) However, the technology is not yet as accurate and inexpensive as one would like for two-color 3D-printing processes.
Wow, 3-D printing the whole thing, that's an approach I wasn't willing to consider. I'd be asking how we make the end product snug enough to keep the two helices co-axial. Clearly you'd print them as two pieces, smooth off the mating surfaces, then screw then together -- but how do you smooth the inner surface of the transparent outer piece, whilst keeping it transparent? I guess I'm getting rather far afield of math-fun here, unless we start citing relevant formulas. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
participants (4)
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Allan Wechsler -
George Hart -
Robert Munafo -
Warren Smith