I know you wanted a physical object, but well-constructed virtual objects can be just as much fun, especially in today's world of touch screens. It's also only a matter of a few years before binocular VR glasses & haptic gloves are available, at which point you will be able to manipulate your virtual objects as if they were real. Also, we should be able to utilize 3D printers today that have the resolution to build our own spirograph, complete with gear teeth that work. At 08:54 AM 6/16/2014, James Propp wrote:
I bought my kids a spirograph (a favorite toy of mine in my youth), and it seems that the manufacturers have had a few fun ideas in the intervening decades. In particular, there's a wider variety of gear-toothed laminae one can now roll inside or outside of a gear-toothed annulus, resulting in a wider variety of pictures.
But one of the basic problems of spirography circa 1970 remains a problem in 2014: slippage. The gear-teeth only serve their stabilizing function if one continually makes sure that one is applying force to the pen (inserted into a hole in the moving lamina) in such a way that the normal component between the lamina and the annulus has the correct sign, while with the other hand steadily pushes down on the annulus to keep it stationary. This is hard work for my five-year-old daughter, who would probably use the spirograph more if slippage weren't such a problem. (One could argue that the main purposes of a spirograph never was mathematical enlightenment but the encouragement of hand-eye coordination, and that the slippage thing is a feature rather than a bug, but I'm going to pretend I didn't say that.)
Has anyone designed a mechanism that permits the spirographer to focus on circumferential force? I'm imagining something like a latchable/unlatchable zipper. Once you've zipped the lamina and the annulus together (making use of the fact that they're in three dimensions), they stick together like the two halves of a zipper, and permit only a single, circumferential degree of freedom.
If someone could solve that problem, then I think the other problem (holding the annulus stationary) wouldn't be as big an issue (though it might still be good to have a wax tray and some pushpins to hold the annulus and the paper to the wax tray, so that one-handed people could do spirographs).
Does anyone know of progress that's been made along these lines, or does anyone have any good ideas for mechanisms that would prevent slippage?
Jim Propp
P.S. Wikipedia tells me that "spirograph" is a registered trademark of Hasbro, so please pretend I capitalized it, etc.
Henry (and others),
I know you wanted a physical object, but well-constructed virtual objects can be just as much fun, especially in today's world of touch screens.
Actually, I'd also be happy with a cool iPhone app, and I was going to post on this subject eventually, if nobody else did, once the subject of physical spirographs had been adequately discussed. More on virtual objects below.
It's also only a matter of a few years before binocular VR glasses & haptic gloves are available, at which point you will be able to manipulate your virtual objects as if they were real.
I look forward to that. (I recently gave an address at a math department's awards ceremonies, in which I told the graduating math majors that it was their generation that would make pure mathematics tangible via virtual reality interfaces, and that I was counting on them.)
Also, we should be able to utilize 3D printers today that have the resolution to build our own spirograph, complete with gear teeth that work.
Well, the gear teeth in Hasbro's spirographs work fine, as long as forces are applied in the right direction, and NO vanilla gear mechanism will work if you pull the gear apart from each other! So the question is, how can we modify the gear mechanism to resist forces that would otherwise pull the gears apart? Getting back to Henry's suggestion, I ask you all: What sort of spirography software exists (or has Hasbro's copyright exerted a dampening effect on people's creativity)? One thing I can imagine is software that lets the user draw two freehand closed curves. The first curve will remain stationary throughout the drawing process; the second curve will roll around the first, maintaining tangency and avoiding slippage. The user also specifies one or more points relative to the second curve that will serve as drawing tips, and associated colors and tip-thicknesses. The computer will perform rescalings of the hand-drawn curves if the user wishes the lengths of the two curves to have a certain specified ratio. And hey, if you prefer a parametric curve, or a curve specified as (a component of) the locus of some two-variable equation over the reals, you can specify that too. Does this exist, or can someone create it? I don't think I'm the only person who'd love a toy like this. Jim
At 08:54 AM 6/16/2014, James Propp wrote:
I bought my kids a spirograph (a favorite toy of mine in my youth), and it seems that the manufacturers have had a few fun ideas in the intervening decades. In particular, there's a wider variety of gear-toothed laminae one can now roll inside or outside of a gear-toothed annulus, resulting in a wider variety of pictures.
But one of the basic problems of spirography circa 1970 remains a problem in 2014: slippage. The gear-teeth only serve their stabilizing function if one continually makes sure that one is applying force to the pen (inserted into a hole in the moving lamina) in such a way that the normal component between the lamina and the annulus has the correct sign, while with the other hand steadily pushes down on the annulus to keep it stationary. This is hard work for my five-year-old daughter, who would probably use the spirograph more if slippage weren't such a problem. (One could argue that the main purposes of a spirograph never was mathematical enlightenment but the encouragement of hand-eye coordination, and that the slippage thing is a feature rather than a bug, but I'm going to pretend I didn't say that.)
Has anyone designed a mechanism that permits the spirographer to focus on circumferential force? I'm imagining something like a latchable/unlatchable zipper. Once you've zipped the lamina and the annulus together (making use of the fact that they're in three dimensions), they stick together like the two halves of a zipper, and permit only a single, circumferential degree of freedom.
If someone could solve that problem, then I think the other problem (holding the annulus stationary) wouldn't be as big an issue (though it might still be good to have a wax tray and some pushpins to hold the annulus and the paper to the wax tray, so that one-handed people could do spirographs).
Does anyone know of progress that's been made along these lines, or does anyone have any good ideas for mechanisms that would prevent slippage?
Jim Propp
P.S. Wikipedia tells me that "spirograph" is a registered trademark of Hasbro, so please pretend I capitalized it, etc.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The patent office calls similar devices "rose engines". As for locking gears, I have an intuition that the thing is possible with teeth that have concave shanks and a widened head, which can fit between the heads of the opposing teeth when at an angle, but not when straight on. (One would connect them by using the third dimension, dropping a new gear onto the surface to intermesh with one already there.) My intuition also says that the thing becomes much more delicate when there are lots of teeth. On Mon, Jun 16, 2014 at 12:44 PM, James Propp <jamespropp@gmail.com> wrote:
Henry (and others),
I know you wanted a physical object, but well-constructed virtual objects can be just as much fun, especially in today's world of touch screens.
Actually, I'd also be happy with a cool iPhone app, and I was going to post on this subject eventually, if nobody else did, once the subject of physical spirographs had been adequately discussed. More on virtual objects below.
It's also only a matter of a few years before binocular VR glasses & haptic gloves are available, at which point you will be able to manipulate your virtual objects as if they were real.
I look forward to that. (I recently gave an address at a math department's awards ceremonies, in which I told the graduating math majors that it was their generation that would make pure mathematics tangible via virtual reality interfaces, and that I was counting on them.)
Also, we should be able to utilize 3D printers today that have the resolution to build our own spirograph, complete with gear teeth that work.
Well, the gear teeth in Hasbro's spirographs work fine, as long as forces are applied in the right direction, and NO vanilla gear mechanism will work if you pull the gear apart from each other! So the question is, how can we modify the gear mechanism to resist forces that would otherwise pull the gears apart?
Getting back to Henry's suggestion, I ask you all: What sort of spirography software exists (or has Hasbro's copyright exerted a dampening effect on people's creativity)?
One thing I can imagine is software that lets the user draw two freehand closed curves. The first curve will remain stationary throughout the drawing process; the second curve will roll around the first, maintaining tangency and avoiding slippage. The user also specifies one or more points relative to the second curve that will serve as drawing tips, and associated colors and tip-thicknesses. The computer will perform rescalings of the hand-drawn curves if the user wishes the lengths of the two curves to have a certain specified ratio. And hey, if you prefer a parametric curve, or a curve specified as (a component of) the locus of some two-variable equation over the reals, you can specify that too.
Does this exist, or can someone create it? I don't think I'm the only person who'd love a toy like this.
Jim
At 08:54 AM 6/16/2014, James Propp wrote:
I bought my kids a spirograph (a favorite toy of mine in my youth), and it seems that the manufacturers have had a few fun ideas in the intervening decades. In particular, there's a wider variety of gear-toothed laminae one can now roll inside or outside of a gear-toothed annulus, resulting in a wider variety of pictures.
But one of the basic problems of spirography circa 1970 remains a problem in 2014: slippage. The gear-teeth only serve their stabilizing function if one continually makes sure that one is applying force to the pen (inserted into a hole in the moving lamina) in such a way that the normal component between the lamina and the annulus has the correct sign, while with the other hand steadily pushes down on the annulus to keep it stationary. This is hard work for my five-year-old daughter, who would probably use the spirograph more if slippage weren't such a problem. (One could argue that the main purposes of a spirograph never was mathematical enlightenment but the encouragement of hand-eye coordination, and that the slippage thing is a feature rather than a bug, but I'm going to pretend I didn't say that.)
Has anyone designed a mechanism that permits the spirographer to focus on circumferential force? I'm imagining something like a latchable/unlatchable zipper. Once you've zipped the lamina and the annulus together (making use of the fact that they're in three dimensions), they stick together like the two halves of a zipper, and permit only a single, circumferential degree of freedom.
If someone could solve that problem, then I think the other problem (holding the annulus stationary) wouldn't be as big an issue (though it might still be good to have a wax tray and some pushpins to hold the annulus and the paper to the wax tray, so that one-handed people could do spirographs).
Does anyone know of progress that's been made along these lines, or does anyone have any good ideas for mechanisms that would prevent slippage?
Jim Propp
P.S. Wikipedia tells me that "spirograph" is a registered trademark of Hasbro, so please pretend I capitalized it, etc.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The London Science Museum called this one from 1906 a "geometric chuck": https://plus.google.com/+MichaelKleber/posts/YrFMW6eaA2k --Michael On Mon, Jun 16, 2014 at 1:14 PM, Allan Wechsler <acwacw@gmail.com> wrote:
The patent office calls similar devices "rose engines". As for locking gears, I have an intuition that the thing is possible with teeth that have concave shanks and a widened head, which can fit between the heads of the opposing teeth when at an angle, but not when straight on. (One would connect them by using the third dimension, dropping a new gear onto the surface to intermesh with one already there.) My intuition also says that the thing becomes much more delicate when there are lots of teeth.
On Mon, Jun 16, 2014 at 12:44 PM, James Propp <jamespropp@gmail.com> wrote:
Henry (and others),
I know you wanted a physical object, but well-constructed virtual objects can be just as much fun, especially in today's world of touch screens.
Actually, I'd also be happy with a cool iPhone app, and I was going to post on this subject eventually, if nobody else did, once the subject of physical spirographs had been adequately discussed. More on virtual objects below.
It's also only a matter of a few years before binocular VR glasses & haptic gloves are available, at which point you will be able to manipulate your virtual objects as if they were real.
I look forward to that. (I recently gave an address at a math department's awards ceremonies, in which I told the graduating math majors that it was their generation that would make pure mathematics tangible via virtual reality interfaces, and that I was counting on them.)
Also, we should be able to utilize 3D printers today that have the resolution to build our own spirograph, complete with gear teeth that work.
Well, the gear teeth in Hasbro's spirographs work fine, as long as forces are applied in the right direction, and NO vanilla gear mechanism will work if you pull the gear apart from each other! So the question is, how can we modify the gear mechanism to resist forces that would otherwise pull the gears apart?
Getting back to Henry's suggestion, I ask you all: What sort of spirography software exists (or has Hasbro's copyright exerted a dampening effect on people's creativity)?
One thing I can imagine is software that lets the user draw two freehand closed curves. The first curve will remain stationary throughout the drawing process; the second curve will roll around the first, maintaining tangency and avoiding slippage. The user also specifies one or more points relative to the second curve that will serve as drawing tips, and associated colors and tip-thicknesses. The computer will perform rescalings of the hand-drawn curves if the user wishes the lengths of the two curves to have a certain specified ratio. And hey, if you prefer a parametric curve, or a curve specified as (a component of) the locus of some two-variable equation over the reals, you can specify that too.
Does this exist, or can someone create it? I don't think I'm the only person who'd love a toy like this.
Jim
At 08:54 AM 6/16/2014, James Propp wrote:
I bought my kids a spirograph (a favorite toy of mine in my youth), and it seems that the manufacturers have had a few fun ideas in the intervening decades. In particular, there's a wider variety of gear-toothed laminae one can now roll inside or outside of a gear-toothed annulus, resulting in a wider variety of pictures.
But one of the basic problems of spirography circa 1970 remains a problem in 2014: slippage. The gear-teeth only serve their stabilizing function if one continually makes sure that one is applying force to the pen (inserted into a hole in the moving lamina) in such a way that the normal component between the lamina and the annulus has the correct sign, while with the other hand steadily pushes down on the annulus to keep it stationary. This is hard work for my five-year-old daughter, who would probably use the spirograph more if slippage weren't such a problem. (One could argue that the main purposes of a spirograph never was mathematical enlightenment but the encouragement of hand-eye coordination, and that the slippage thing is a feature rather than a bug, but I'm going to pretend I didn't say that.)
Has anyone designed a mechanism that permits the spirographer to focus on circumferential force? I'm imagining something like a latchable/unlatchable zipper. Once you've zipped the lamina and the annulus together (making use of the fact that they're in three dimensions), they stick together like the two halves of a zipper, and permit only a single, circumferential degree of freedom.
If someone could solve that problem, then I think the other problem (holding the annulus stationary) wouldn't be as big an issue (though it might still be good to have a wax tray and some pushpins to hold the annulus and the paper to the wax tray, so that one-handed people could do spirographs).
Does anyone know of progress that's been made along these lines, or does anyone have any good ideas for mechanisms that would prevent slippage?
Jim Propp
P.S. Wikipedia tells me that "spirograph" is a registered trademark of Hasbro, so please pretend I capitalized it, etc.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
On 6/16/2014 10:14 AM, Allan Wechsler wrote:
The patent office calls similar devices "rose engines". As for locking gears, I have an intuition that the thing is possible with teeth that have concave shanks and a widened head, which can fit between the heads of the opposing teeth when at an angle, but not when straight on. (One would connect them by using the third dimension, dropping a new gear onto the surface to intermesh with one already there.) My intuition also says that the thing becomes much more delicate when there are lots of teeth.
I doubt that can be made to work. As the teeth unmesh they are pulled out almost orthogonally. You could make gears that resisted unmeshing by embedding magnets in the teeth. Brent Meeker
I want Gosper's young friend Julian's opinion on this. I'm still betting that there are locking solutions for moderate numbers of teeth, say, eight. In fact, I suspect there are locking solutions for all numbers of teeth, but that for larger numbers the grip would be extremely tenuous. On Mon, Jun 16, 2014 at 3:57 PM, meekerdb <meekerdb@verizon.net> wrote:
On 6/16/2014 10:14 AM, Allan Wechsler wrote:
The patent office calls similar devices "rose engines". As for locking gears, I have an intuition that the thing is possible with teeth that have concave shanks and a widened head, which can fit between the heads of the opposing teeth when at an angle, but not when straight on. (One would connect them by using the third dimension, dropping a new gear onto the surface to intermesh with one already there.) My intuition also says that the thing becomes much more delicate when there are lots of teeth.
I doubt that can be made to work. As the teeth unmesh they are pulled out almost orthogonally. You could make gears that resisted unmeshing by embedding magnets in the teeth.
Brent Meeker
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (5)
-
Allan Wechsler -
Henry Baker -
James Propp -
meekerdb -
Michael Kleber