Gyroscopic exercise tool: Difference between revisions

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A '''gyroscopic exercise tool''' is a specialized device employed in [[physical therapy]] to enhance [[wrist]] strength, promoting the development of palm, forearm, and finger muscles. It can also be used as a unique demonstration of some aspects of [[dynamics (physics)|rotational dynamics]]. The device consists of a [[tennis ball]]-sized plastic or metal shell surrounding a free-spinning mass, with the inner heavy core being spun up via a short rip string. Once the [[gyroscope]] inside is going fast enough, the person holding the device can accelerate the spinning mass to high rotation rates by moving the wrist in a circular motion. This tool is also used to train the wrist by professional athletes, as for instance climbers.

== History ==

{{empty section|date=May 2020}}

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Since the acceleration of the rotation will occur regardless of the direction of the applied torque, as long as it is large enough, the device will function without any fine-tuning of the driving motion. The tilting of the shell does not have to have a particular phase relationship with the precession or even to have the same frequency. Since sliding (kinetic) friction is usually nearly as strong as static (sticking) friction, it is not necessary to apply precisely the value of torque (which will result in the axle rolling without slipping along the side of the groove). These factors allow beginners to learn to speed up the rotation after only a few minutes of practice.

By applying the proportionality of the force of friction to the normal force, <math>F_\mathrm{f} = \mu_\mathrm{k} F_\mathrm{n}</math>, where <math>\mu_\mathrm{k}</math> is the [[Friction#Coefficient_of_friction|kinetic coefficient of friction]], it can be shown that the torque spinning up the mass is a factor of <math>\mu_\mathrm{k} \left( r_{\mathrm{axle}} / R_{\mathrm{groove}} \right)</math> smaller than the torque applied to the shell. Since frictional force is essential for the device's operation, the groove must not be lubricated.<ref>Articles{{cite onjournal |title=The Physics of the physics''Dyna Bee'' |date=February 1, 1980 |issn=0031-921X |doi=10.1119/1.2340452 |issue=2 |volume=18 |pages=147–8 |journal=The Physics Teacher |first=J. |last=Higbie|bibcode=1980PhTea..18..147H}} {{closed access}}</ref><ref>{{cite journal |title=Roller Ball Dynamics |date=2000 |issue=9 |volume=36 |journal=Mathematics Today |first=P. G. |last=Heyda}}</ref><ref>{{cite journal |title=Roller Ball Dynamics Revisited |date=October 1, 2002 |issn=0002-9505 |doi=10.1119/1.1499508 |issue=10 |volume=70 |pages=1049–51 |journal=American Journal of Physics |first=P. G. |last=Heyda|bibcode=2002AmJPh..70.1049H}}</ref><ref>{{cite journal |title=On the deviceDynamics (inof approximatelythe increasingDynabee order|date=June 1, 2000 |issn=0021-8936 |doi=10.1115/1.1304914 |issue=2 |volume=67 |pages=321–5 |journal=Journal of sophistication)Applied Mechanics |first1=D. W. |last1=Gulick |first2=O. M. |last2=O’Reilly|bibcode=2000JAM....67..321G}}</ref><ref>{{cite journal |title=Modelling of the Robotic Powerball®: A Nonholonomic, Underactuated and Variable Structure-Type System |date=June 1, 2010 |doi=10.1080/13873954.2010.484237 |first1=Tadej |last1=Petrič |first2=Boris |last2=Curk |first3=Peter |last3=Cafuta |first4=Leon |last4=Žlajpah |journal=Mathematical and Computer Modelling of Dynamical Systems|volume=16|issue=4 |pages=327–346 |hdl=10.1080/13873954.2010.484237 |s2cid=120513329 |hdl-access=free}}</ref><!--some of these may be better as external links-->

* {{cite journal |title=The Physics of the ''Dyna Bee'' |date=February 1, 1980 |issn=0031-921X |doi=10.1119/1.2340452 |issue=2 |volume=18 |pages=147–8 |journal=The Physics Teacher |first=J. |last=Higbie|bibcode=1980PhTea..18..147H }} {{closed access}}

* {{cite journal |title=Roller Ball Dynamics |date=2000 |issue=9 |volume=36 |journal=Mathematics Today |first=P. G. |last=Heyda}}

* {{cite journal |title=Roller Ball Dynamics Revisited |date=October 1, 2002 |issn=0002-9505 |doi=10.1119/1.1499508 |issue=10 |volume=70 |pages=1049–51 |journal=American Journal of Physics |first=P. G. |last=Heyda|bibcode=2002AmJPh..70.1049H }}

* {{cite journal |title=On the Dynamics of the Dynabee |date=June 1, 2000 |issn=0021-8936 |doi=10.1115/1.1304914 |issue=2 |volume=67 |pages=321–5 |journal=Journal of Applied Mechanics |first1=D. W. |last1=Gulick |first2=O. M. |last2=O’Reilly|bibcode=2000JAM....67..321G }}

* {{cite journal |title=Modelling of the Robotic Powerball®: A Nonholonomic, Underactuated and Variable Structure-Type System |date=June 1, 2010 |doi=10.1080/13873954.2010.484237 |first1=Tadej |last1=Petrič |first2=Boris |last2=Curk |first3=Peter |last3=Cafuta |first4=Leon |last4=Žlajpah |journal=Mathematical and Computer Modelling of Dynamical Systems|volume = 16|issue=4 |pages=327–346 |hdl=10.1080/13873954.2010.484237 |s2cid=120513329 |hdl-access=free }}

</ref>

As explained, the energy supplied by the external momentum (the hand and arm muscles) can not be directly converted into the rotational energy of the gyroscope around its own axis. Still, it is converted into the energy of precession rotation. Due to the friction between the gyroscope shaft and the sides of the groove, part of this energy is converted into energy of rotation around the gyroscope's axis, accelerating it. This happens when there is friction and a round object, like a bowling ball, is thrown along a horizontal surface. A part of the ball's kinetic energy is converted to rotational energy due to friction.

== References ==

<br />{{Commons category|Gyroscopic exercise tools}}

{{reflist}}

<br />{{Commons category|Gyroscopic exercise tools}}

[[Category:Exercise equipment]]