Q re gyroscope-based toy
Yaakov Eisenberg
I'm trying to figure out how a toy I have works.
I'll describe it but here are some Web pages that
have pictures and videos too:
http://www.ewebservers.com/dynaflexintl/powerball.html
http://www.dynabee.com/main.shtml
It consists of a rotor inside a hollow sphere. Here's
how the two are connected: Inside the sphere, around the
equator, is cut a groove, into which fits a ring that is
free to rotate. The rotor has a shaft through it which
fits into two holes in the ring. So the rotor can spin
around this horizontal shaft, and it can also rotate with
the ring around a vertical axis.
The top of the sphere is cut off, exposing the rotor,
which can be spun by hand around the shaft through it.
Then if a torque is exerted (on the outer sphere)
directed horizontally and perpedicular to the shaft, the
spinning rotor will rotate around a vertical axis. So
far, I understand what's happening: the rotor is just a
gyroscope and is precessing at right angles to the
applied torque.
Now, if the direction of the torque is constantly changed
so that it remains (horizontal and) perpendicular to the
changing direction of the shaft, not only will the rotor
continue to rotate around a vertical axis, but the speed
of its rotation around the horizontal shaft will
increase. Why?
(I should mention that, when applying the torque, the
entire sphere does rotate a bit in the direction of the
torque. If not, there would be no input of energy and so
the rotor couldn't possibly gain speed. So what I've
been describing as a "vertical axis" actually describes
a narrow two-napped cone centered on the sphere.)
--
Yaakov Eisenberg
Christof Pflumm
"Yaakov Eisenberg" <y...@peoplepc.com> writes:
> I'm trying to figure out how a toy I have works.
> I'll describe it but here are some Web pages that
> have pictures and videos too:
>
> http://www.ewebservers.com/dynaflexintl/powerball.html
>
> http://www.dynabee.com/main.shtml
I also have this toy - very fascinating. I don't know how it works,
but I want to add the following, which might be important: If you have
the opening of the hollow sphere facing up and try to rotate the rotor
around the vertical axis, you need quite a lot of force, but if the
opening is facing down, you can easily rotate the rotor by lifting it
a bit. It seems as there's quite a lot of friction between the ring
and the hollow sphere.
Bye,
Christof
DGoncz
the rotor.
Would you describe the hand position a little more clearly? Moving my
outstretched index finger from the wrist only, I am seeing what looks like a 90
degree included angle cone of movement. This cone has an axis. Where is the
axis of the rotor, and where is the axis of the groove in relation to this
axis?
I infer from the web pages given that one holds the device in the hand and
exercises the wrist to its limits, which appear to be this 90 degree included
angle cone. Sorry, I don't know the terms used to describe the muscle movement.
Pronation, extension, flexion -- I've heard some of the terms but don't know
what each means.
This clutch I refer to isn't going to be a plate clutch. I'm thinking of a
centralizing spring keeping the axis of the rotor in away from interaction with
the ring. When torque is applied along any axis other than that of rotation,
such a centralizing spring could yield enough to engage the shaft in a hole in
the ring. Such a shaft might have teeth, and the hole be a ring gear. This is a
dynamic imbalance and if allowed to continue, would drain the angular momentum
of the rotor. But with the right sizes and ratio, and with responsive
engagement, energy could be taken from the sphere, to the ring, into the rotor.
13,000 rpm is claimed. That's "only" about 35 radians per second. I can move my
wrist at around 10 radians per second. The ratio is 3.5, and the planetary
nature of the engagement I propose is in this range, maybe a 1/8 inch pinion in
a 3/8 inch ring gear. I was just tinkering with the planetary on my Derbi moped
starter today.
I'm going over to rec.crafts.metalworking now. The optional accesory for the
Powerball is an accumuating tachometer. At these prices, any of the small lathe
owners there will snap them up. Toys make great tools, sometimes.
>not only will the rotor
>continue to rotate around a vertical axis, but the speed
>of its rotation around the horizontal shaft will
>increase. Why?
>From: "Yaakov Eisenberg" y...@peoplepc.com
>Message-ID: <Y5065.809$ED.4...@news.wenet.net>
>http://www.ewebservers.com/dynaflexintl/powerball.html
I'm taking that link with me. See ya!
Respectfully submitted,
Doug Goncz
Experimental Machinist
Replikon Research, Box 4394, 22044-0394
I sell self-reproducing assemblies of
small machine tools and tooling at 100% retail markup.
http://members.aol.com/DGoncz
Yaakov Eisenberg
Christof Pflumm <lti...@ltihp81.etec.uni-karlsruhe.de> wrote in message news:tpwvjai...@ltihp81.etec.uni-karlsruhe.de...
Yes, I'm pretty sure the friction plays a role.
Ignoring the package's explicit warning not to, I sprayed some
silicone lubricant inside. Voila, it stopped working. I thoroughly
cleaned it out with soap and water, and it now works again,
though it still doesn't have quite as much friction as before.
(But I don't mind; it's easier to start.)
DGoncz <dgo...@aol.com> wrote in message
news:20000628151910...@ng-md1.aol.com...
> Would you describe the hand position a little more clearly?
> Moving my outstretched index finger from the wrist only,
> I am seeing what looks like a 90 degree included angle cone
> of movement. This cone has an axis. Where is the axis of the
> rotor, and where is the axis of the groove in relation to this
> axis?
Your cone's axis is identical to the axis of the groove. The
rotor's axis is perpendicular to this.
Actually, that's not quite right. The toy moves with the hand,
so the groove's axis is not really the cone's axis; it's the cone's
generator, i.e., it sweeps out the cone's surface.
> 13,000 rpm is claimed. That's "only" about 35 radians per second.
> I can move my wrist at around 10 radians per second. The ratio
> is 3.5, and the planetary nature of the engagement I propose is
> in this range, maybe a 1/8 inch pinion in a 3/8 inch ring gear.
Are you sure? I get 1360 radians per second.
--
Yaakov Eisenberg
[Moderator's note: 13,000 rpm is indeed 1360 rad/s. Perhaps Christof
Pflumm divided by 2 pi rather than multiplying. -TB]
DGoncz
13,000 / 60 / 2 / 3.14 ~= 35
13,000 / 60 * 2 * 3.14 ~= 1360
2 * 2 * 3.14 * 3.14 ~= three dozen
And if it's off by nine or a multiple of nine, it's a digit transposition
error. Courtesy Gloria Newbery, Teri's mom.
There 6.28 radians in a rev. I was wrong and did it twice! The little-big rule.
Got to love that silicone. It's EP and handy. Ruins VCR clutches for the same
reason as it makes the wrist exercise toy stop working. But when I put the VCR
in the dishwasher, the rewind came back but suddenly everything else stopped
working. :)
I understand now that the toy is held with one of the openings in the palm.
Thanks.
Just the friction, then, no gearing?
Yours,
Douglas Dana Edward Edward Goncz
ferrofluid controlled by a pressure pad would add an interesting advantage to
this toy, or even serve as a method of "charging" an angular momentum
accumulator. A simple method would be a hydraulic, pneumatic, or other band
brake.
Could you try pressing in on the spherical sheel to modulate the friction,
Yakov, and let us know how the device behaves?
I don't know of any unidirectional fluids. :) A ratchet molded into the shell
and ring would be unidirectional.
Tom Snyder
There was an article about the DynaBee in The Physics Teacher:
Physics Teach., Vol. 18, No. 2, February 1980 Pages 147 - 148
"The physics of the 'Dyna Bee'"
by J. Higbie, Department of Physics, University of Queensland,
Brisbane, Australia 4067
-----------------------------------------------------------
Got questions? Get answers over the phone at Keen.com.
Up to 100 minutes free!
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George J. Bugh
please? I can pay for slow mail. Is that something amazon.com would
have?
Tom Snyder wrote:
>
> There was an article about the DynaBee in The Physics Teacher:
>
> Physics Teach., Vol. 18, No. 2, February 1980 Pages 147 - 148
> "The physics of the 'Dyna Bee'"
> by J. Higbie, Department of Physics, University of Queensland,
> Brisbane, Australia 4067
[Moderator's note: Replies by e-mail, please. -MM]
Yaakov Eisenberg
Douglas Dana Edward Edward Goncz <dgo...@aol.communicate> wrote in message news:20000703103757...@ng-md1.aol.com...
>
> Could you try pressing in on the spherical sheel to modulate the friction,
> Yakov, and let us know how the device behaves?
This would be a good idea,
but the toy is too rigid for me to deform it.
Yaakov Eisenberg
> Is there anyone in Australia that can send me a copy of that article
> please? I can pay for slow mail. Is that something amazon.com would
> have?
>
> Tom Snyder wrote:
> >
> > There was an article about the DynaBee in The Physics Teacher:
> >
> > Physics Teach., Vol. 18, No. 2, February 1980 Pages 147 - 148
> > "The physics of the 'Dyna Bee'"
> > by J. Higbie, Department of Physics, University of Queensland,
> > Brisbane, Australia 4067
Thanks to Tom Snyder for the reference. I went to the
library and made a copy of the article. Here is its
text. It also contains some diagrams, which I can't
reproduce here, though I've included their captions.
--
Yaakov Eisenberg
----
A new "toy" for grown-ups has recently appeared on the
market called the "Dyna-Bee." It is about the size of a
soft ball and has a wheel inside it which can be speeded-up
by appropriate wrist-action when it is held in the hand and
given an initial spin. It is sold as a wrist exerciser but
let's face it, it's a toy.
The real challenge is to get it to work. Only those
with an inborn muscular coordination can make it work right
away. The rest of us need lots of practice. But, like
riding a bicycle, once you get the knack, you never forget.
The interesting question is what makes it work? It turns
out that this is a very handy device for illustrating the
principles of gyroscopic motion since precession actually
drives the internal wheel.
The device consists of an internal weighted wheel
mounted on a small diameter rigid axle. The axle runs in
a U-shaped groove inside the plastic housing. The groove
extends all the way around the inside of the spherical
housing so that the axle can roll through a full circle
(Fig. 1). There is a hole in the bottom of the spherical
housing which exposes part of the wheel's rim so that it
can be given its initial spin by flicking it with the heel
of the hand.
Fig. 1. Schematic of the Dyna Bee.
The internal U-groove extends all the way around and
holds the axle tips. There is also a steel ring with
two holes in it for the axle tips which slides along
the inside of the housing in contact with the groove.
This ring keeps the axle along a diameter of the groove
circle.
Once the wheel is spinning, the housing is twisted so
that the bottom of the U-groove presses upward on one end
of the axle and the top of the groove presses down on the
opposite end. This gives the spinning wheel a torque and
it responds by precessing the axle tips along the length of
the groove. The axle tips move in just the right direction
so that as they roll on the side of the groove, it causes
the wheel to speed-up. That is, the precessional motion
moves the axle tip along in the groove and the friction is
in just the right direction to cause the wheel to spin
faster (Fig. 2).
Fig. 2. The torque applied by the sides of the groove
causes the spinning wheel to precess.
As the axle tips move around, the forcing torque must
move around as well and this is what gives the circular
wrist action needed to make it work. As the wheel gains
speed the precessional velocity decreases and the tangential
velocity of the axle's lateral edge in contact with the
groove increases. These two effects merge together when the
precessional speed of the tip is just sufficient to cause
it to roll without slipping in the groove. At this stage
a dynamical equilibrium is reached where the wheel will no
longer speed up. It just "holds its own." If you want the
Dyna Bee to go faster, you have to increase the precessional
speed by increasing the applied torque.
The precessional speed of the axle tip is V = R d\theta/dt
= R\Omega, where R is the radius of the circular U-groove
(length of half the axle) and \Omega is the angular precession
rate. The tangential speed of the axle's lateral edge is v =
r\omega, where r is the radius of the axle shaft and \omega is
the angular speed of the internal wheel. The angular momentum
of the wheel is L = I\omega, where I is the moment of inertia
of the wheel. The torque causes the angular momentum vector
to precess: \tau = dL/dt = L d\theta/dt = L\Omega (Fig. 2.).
The precessional speed of the axle tip is then:
V = R\Omega = R\tau / L = R\tau / I\omega
The relative velocity between [the] edge of the axle in contact
with the groove and the groove itself is
v_r = V - v = R\tau / I\omega - r\omega
When this becomes zero, the axle rolls in the groove without
slipping. For a constant torque, the maximum angular speed
is then: (Fig. 3)
\omega_0 = \sqrt{R\tau/Ir}
Fig. 3. Graph of V and v versus \omega for constant torque
Unfortunately this device is too small for lecture
demonstrations, but it may be possible to construct a
larger one operating on the same principle for lecture
use. However, for small classes or laboratory groups
it should be quite effective since everyone wants to
"have a go" as we say in Australia.
Yaakov Eisenberg
George J. Bugh
Yaakov Eisenberg wrote:
>
> George J. Bugh <gb...@flash.net> wrote in message news:3963C107...@flash.net...
> > Is there anyone in Australia that can send me a copy of that article
> > please? I can pay for slow mail. Is that something amazon.com would
> > have?
> >
> > Tom Snyder wrote:
> > >
> > > There was an article about the DynaBee in The Physics Teacher:
> > >
> > > Physics Teach., Vol. 18, No. 2, February 1980 Pages 147 - 148
> > > "The physics of the 'Dyna Bee'"
> > > by J. Higbie, Department of Physics, University of Queensland,
> > > Brisbane, Australia 4067
>
> Thanks to Tom Snyder for the reference. I went to the
> library and made a copy of the article. Here is its
> text. It also contains some diagrams, which I can't
> reproduce here, though I've included their captions.
[...]