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The Sphericon is a geometric solid with a bicone-like shape, but with a twist that allows it to roll in a serpentine line instead of a circle. (See link for a picture of a sphericon.)
When a sphericon rolls, it has periodic points in the path where the curve is very sharp. At these points, the rolling
sphericon tends to slow down, but it will keep rolling. (see link for picture of sphericon path)
If you had a sphericon big enough to stand on (say 18 inches in diameter) then you could hop on top and, with little kicks, get the sphericon rolling and keep it rolling in its peculiar meandering way. This would be fun in the same way learning the hoola hoop or yo-yo is fun. It would be a good form of aerobic exercise, because it is low-impact (unlike running and jumping-rope.)
Balance-walking on the sphericon looks like balance-walking on a ball, but it's easier. A ball is tangent with the ground at a single point, but the sphericon is always tangent with the ground along a line. This makes it more stable than a rolling ball. Deep ridges along the curves give you a good toehold.
The sphericon's tendency to hesitate will help beginners feel safe. The sphericon won't run away with them on flat ground. If the beginner has trouble getting the sphericon moving, he can try gradually sloped ground.
Once the sphericonner has confidence, he should be able to roll a complete revolution of the sphericon in four precisely placed steps. He can participate in sphericon races, or just roll around the neighborhood amazing his friends. With practice, she can go on to freestyle and extreme sphericonning - challenges like steeper slopes, rough terrain, and skate parks.
Sphericon roller toys will be weighted to maximize fun and safety, and covered with soft rubber tread that follows the direction of the rolling surface. Beginners should wear protective gear (as rollerskaters do).
The Sphericon
http://www.pjroberts.com/sphericon
[robinism, Feb 15 2005]
(?) The serpentine path of a sphericon
http://members.cox....m/sphericonpath.jpg
[robinism, Feb 15 2005]
(?) Sphericon roller toy in use
http://members.cox.net/robinism/si1.jpg
[robinism, Feb 15 2005]
Oliod
http://mathworld.wolfram.com/Oloid.html
There are animations on these Mathworld pages [JesusHChrist, Feb 15 2005]
Oloid on a roll
http://www1.ttcn.ne.../oloid/z_ani_2.html
Oh Loid, look at it go! [robinism, Feb 15 2005]
Gigantic Sphericon
http://www.youtube....watch?v=HeSRbfcwqvo
[JesusHChrist, Mar 26 2011]
A beautiful site on round and roundoid things, and much else
http://www.howround.com/
[MaxwellBuchanan, Mar 26 2011]
Rolloids by Kenneth Brecher
https://archive.bri...ridges2023-345.html
Mathematically defined or derived objects that can roll on a flat horizontal surface or down an inclined plane, either in a straight line or with a meandering motion. [robinism, Sep 27 2023]
How Round Is Your Circle? by Bryant and Sangwin
https://www.maths.e...roundcom/front.html
The site that [MaxwellBuchanan] linked to above. [robinism, Sep 27 2023]
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Annotation:
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I suppose this is a stretched out sphericon for better balance? |
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A sphericon axe could be used to chop in two directions (90 degrees) by twisting the handle (180 degrees). |
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I see what you mean about the axe. The shape reminds me of some rounded ceremonial blades from some central or south american culture. But I think the sphericon is most interesting when it's rolling. |
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What do you gain by using the Sphericon as opposed to just walking?
It seems to me that this would be very difficult/uncomfortable. When the left side is flat on the ground the right will be sticking up at a point, and you will need to transfer your right foot backwards over the point to push that side forward to the ground which does not seem to be an easy move. And repeat and repeat and repeat.
but perhaps i'm just missing something. |
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Sphericonifers are few and far between. |
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[brodie], it's supposed to be fun. Kind of like a hoola hoop or a yoyo. A challenge to your balance and coordination. A different sequence of moves than in any other sport. |
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"When the left side is flat on the ground the right will be sticking up at a point" |
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If by "point" you mean the ridgeline, like the peak of a gabled roof, then yes, that is exactly right. And the rider will straddle the ridgeline, with one foot on either side. The ridges of tread give a good foothold. |
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"and you will need to transfer your right foot backwards over the point to push that side forward to the ground" |
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Right, but since the rider was straddling the ridgeline to begin with, it's just a matter of bringing the feet together. You don't need to push hard, because the sphericon tends to move out of the "ridgeline sticking straight up" position. The sphericon is more stable in the "both ridgelines at 45 degrees to ground" position. |
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Nice one Robinism. See link for more sphericon related toys and shapes. Picture entitled "New shapes" has three different sphericons and an oloid. Picture entitled "guy" is supposed to be a stick like fugure that rolls like a sphericon. |
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An Oloid might work too for this roller toy. Google "Oloid". |
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While attending SpheriCon, I fell victim to a professional swindler - A sphericonartist. |
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You know, if you put little rims around the edges of that
rolling oloid, it would hold stocking feet in pretty good. I
imagine it would make for a pretty smooth gait to step
inside the rim before it came in contact with the floor and
put your weight on it as it came in contact and then sort
of ease your weight over to the other side smoothly. |
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Actually, now that I look at it, if you had a really big oloid
you could slollom ski on its surface to make it move in the
opposite direction to the way you were facing. |
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"if you put little rims around the edges of that rolling oloid" |
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I was picturing something similar, only with toe-clips instead of rims. The two toe clips would be mounted to the middle of each arc-edge. With the toe-clips, it becomes a unicycle-type motion. The toe-clips can spin relative to the oloid, so you can keep your feet in the toe clips as the oloid spins. An advantage of the toe-clips is that you don't have to pass your foot over top of the edge of the oloid. |
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Whether it's a rim or a toe cllip, it has to be able to bend or it will interfere with the rolling motion. And if the toe-clip linkage can bend, then I'm not sure it can translate the rider's pumping to the oloid well enough. |
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right -- interfere. One way out of that would be to curve
the surface in but keep the edges where they are. There
is a picture of a "sunken sphericon" like that on Colin
Roberts website. One great thing about sphericons is that
all you need for the rolling motion is the edges -- you can
put whatever you want inbetween to hold the edges
together. |
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I should probably rename this the "Aeroboloid" but I would have to change a lot of details... |
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Don't be afraid, [DF]. The only thing we have to sphere is sphere itself. |
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In keeping with presidential quote/sphericon puns, I offer: |
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Four score and seven spheres ago. - A. Lincoln |
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I am not a sphericon. - R. Nixon |
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Heres my theory on the cold war: we win they sphericon. - R. Reagan |
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To be or not to be, that is the sphericon. |
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//it's supposed to be fun. Kind of like a hoola hoop or a yoyo.//
Ok, I see I was thinking of it more like rollerblades, as a faster more efficient way to get around.
//Whether it's a rim or a toe cllip,//
Something like this might make it easier to use. |
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This idea set me Googling, and let me to the linked site,
which is truly awe-inspiring. |
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So, a [+] is richly deserved. |
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