Gyroscope 1

Gyroscope

A gyroscope

A gyroscope is a device for measuring or maintainingorientation, based on the principles of conservation ofangular momentum.[1] A mechanical gyroscope isessentially a spinning wheel or disk whose axle is freeto take any orientation. This orientation changes muchless in response to a given external torque than it wouldwithout the large angular momentum associated withthe gyroscope's high rate of spin. Since external torqueis minimized by mounting the device in gimbals, itsorientation remains nearly fixed, regardless of anymotion of the platform on which it is mounted.

Gyroscopes based on other operating principles alsoexist, such as the electronic, microchip-packagedMEMS gyroscope devices found in consumer electronic devices, solid state ring lasers, fibre optic gyroscopes andthe extremely sensitive quantum gyroscope.

Applications of gyroscopes include navigation (INS) when magnetic compasses do not work (as in the Hubbletelescope) or are not precise enough (as in ICBMs) or for the stabilization of flying vehicles like radio-controlledhelicopters or UAVs. Due to higher precision, gyroscopes are also used to maintain direction in tunnel mining.[2]

Description and diagram

Diagram of a gyro wheel. Reaction arrows about theoutput axis (blue) correspond to forces applied about

the input axis (green), and vice versa.

Within mechanical systems or devices, a conventional gyroscopeis a mechanism comprising a rotor journalled to spin about oneaxis, the journals of the rotor being mounted in an inner gimbal orring, the inner gimbal is journalled for oscillation in an outergimbal which is journalled in another gimbal. So basically thereare three gimbals.

The outer gimbal or ring which is the gyroscope frame ismounted so as to pivot about an axis in its own plane determinedby the support. This outer gimbal possesses one degree ofrotational freedom and its axis possesses none. The next innergimbal is mounted in the gyroscope frame (outer gimbal) so as topivot about an axis in its own plane that is always perpendicular tothe pivotal axis of the gyroscope frame (outer gimbal). This innergimbal has two degrees of rotational freedom. Similarly, next innermost gimbal is attached to the inner gimbalwhich has three degree of rotational freedom and its axis posses two.

The axle of the spinning wheel defines the spin axis. The rotor is journaled to spin about an axis which is alwaysperpendicular to the axis of the innermost gimbal. So, the rotor possesses four degrees of rotational freedom and itsaxis possesses three. The wheel responds to a force applied about the input axis by a reaction force about the outputaxis.The behaviour of a gyroscope can be most easily appreciated by consideration of the front wheel of a bicycle. If thewheel is leaned away from the vertical so that the top of the wheel moves to the left, the forward rim of the wheelalso turns to the left. In other words, rotation on one axis of the turning wheel produces rotation of the third axis.

Gyroscope 2

A gyroscope flywheel will roll or resist about the output axis depending upon whether the output gimbals are of afree- or fixed- configuration. Examples of some free-output-gimbal devices would be the attitude referencegyroscopes used to sense or measure the pitch, roll and yaw attitude angles in a spacecraft or aircraft.

Animation of a gyro wheel in action

The centre of gravity of the rotor can be in a fixed position. Therotor simultaneously spins about one axis and is capable ofoscillating about the two other axes, and thus, except for itsinherent resistance due to rotor spin, it is free to turn in anydirection about the fixed point. Some gyroscopes have mechanicalequivalents substituted for one or more of the elements, e.g., thespinning rotor may be suspended in a fluid, instead of beingpivotally mounted in gimbals. A control moment gyroscope(CMG) is an example of a fixed-output-gimbal device that is usedon spacecraft to hold or maintain a desired attitude angle orpointing direction using the gyroscopic resistance force.

In some special cases, the outer gimbal (or its equivalent) may be omitted so that the rotor has only two degrees offreedom. In other cases, the centre of gravity of the rotor may be offset from the axis of oscillation and thus thecentre of gravity of the rotor and the centre of suspension of the rotor may not coincide.

History

Gyroscope invented by Léon Foucault in 1852.Replica built by Dumoulin-Froment for the

Exposition universelle in 1867. NationalConservatory of Arts and Crafts museum, Paris.

The earliest known gyroscope-like instrument was made by GermanJohann Bohnenberger, who first wrote about it in 1817. At first hecalled it the "Machine".[3] [4] Bohnenberger's machine was based on arotating massive sphere.[5] In 1832, American Walter R. Johnsondeveloped a similar device that was based on a rotating disk.[6] [7] TheFrench mathematician Pierre-Simon Laplace, working at the ÉcolePolytechnique in Paris, recommended the machine for use as ateaching aid, and thus it came to the attention of Léon Foucault.[8] In1852, Foucault used it in an experiment involving the rotation of theEarth.[9] [10] It was Foucault who gave the device its modern name, inan experiment to see (Greek skopeein, to see) the Earth's rotation(Greek gyros, circle or rotation), which was visible in the 8 to 10minutes before friction slowed the spinning rotor.

In the 1860s, electric motors made the concept feasible, leading to thefirst prototype gyrocompasses; the first functional marine gyrocompasswas patented in 1908 by German inventor HermannAnschütz-Kaempfe. The American Elmer Sperry followed with hisown design later that year, and other nations soon realized the militaryimportance of the invention—in an age in which naval fight was themost significant measure of military power—and created their owngyroscope industries. The Sperry Gyroscope Company quicklyexpanded to provide aircraft and naval stabilizers as well, and other gyroscope developers followed suit.[11]

In 1917, the Chandler Company of Indianapolis, Indiana, created the "Chandler gyroscope", a toy gyroscope with apull string and pedestal. It has been in continuous production ever since and is considered a classic American toy.In the first several decades of the 20th century, other inventors attempted (unsuccessfully) to use gyroscopes as the basis for early black box navigational systems by creating a stable platform from which accurate acceleration

Gyroscope 3

measurements could be performed (in order to bypass the need for star sightings to calculate position). Similarprinciples were later employed in the development of inertial guidance systems for ballistic missiles.[12]

During World War Two, the gyroscope became the prime component for aircraft and anti-aircraft gun sights.[13]

Properties

A gyroscope in operation with freedom in allthree axes. The rotor will maintain its spin axis

direction regardless of the orientation of the outerframe.

A gyroscope exhibits a number of behaviours including precession andnutation. Gyroscopes can be used to construct gyrocompasses whichcomplement or replace magnetic compasses (in ships, aircraft andspacecraft, vehicles in general), to assist in stability (Hubble SpaceTelescope, bicycles, motorcycles, and ships) or be used as part of aninertial guidance system. Gyroscopic effects are used in tops,boomerangs, yo-yos, and Powerballs. Many other rotating devices,such as flywheels, behave gyroscopically although the gyroscopiceffect is not being used.

The fundamental equation describing the behavior of the gyroscope is:

where the vectors τ and L are, respectively, the torque on the gyroscope and its angular momentum, the scalar I is itsmoment of inertia, the vector ω is its angular velocity, and the vector α is its angular acceleration.It follows from this that a torque τ applied perpendicular to the axis of rotation, and therefore perpendicular to L,results in a rotation about an axis perpendicular to both τ and L. This motion is called precession. The angularvelocity of precession ΩP is given by the cross product:

Precession on a gyroscope

Precession can be demonstrated by placing a spinning gyroscope withits axis horizontal and supported loosely (frictionless towardprecession) at one end. Instead of falling, as might be expected, thegyroscope appears to defy gravity by remaining with its axishorizontal, when the other end of the axis is left unsupported and thefree end of the axis slowly describes a circle in a horizontal plane, theresulting precession turning. This effect is explained by the aboveequations. The torque on the gyroscope is supplied by a couple offorces: gravity acting downwards on the device's centre of mass, andan equal force acting upwards to support one end of the device. Therotation resulting from this torque is not downwards, as might beintuitively expected, causing the device to fall, but perpendicular toboth the gravitational torque (horizontal and perpendicular to the axisof rotation) and the axis of rotation (horizontal and outwards from the point of support), i.e. about a vertical axis,causing the device to rotate slowly about the supporting point.

Gyroscope 4

Under a constant torque of magnitude τ, the gyroscope's speed of precession ΩP is inversely proportional to L, themagnitude of its angular momentum:

where θ is the angle between the vectors ΩP and L. Thus if the gyroscope's spin slows down (for example, due tofriction), its angular momentum decreases and so the rate of precession increases. This continues until the device isunable to rotate fast enough to support its own weight, when it stops precessing and falls off its support, mostlybecause friction against precession cause another precession that goes to cause the fall.By convention, these three vectors, torque, spin, and precession, are all oriented with respect to each other accordingto the right-hand rule.To easily ascertain the direction of gyro effect, simply remember that a rolling wheel tends, when it leans to the side,to turn in the direction of the lean.

Variations

GyrostatA gyrostat is a variant of the gyroscope. It consists of a massive flywheel concealed in a solid casing. Its behaviouron a table, or with various modes of suspension or support, serves to illustrate the curious reversal of the ordinarylaws of static equilibrium due to the gyrostatic behaviour of the interior invisible flywheel when rotated rapidly. Thefirst gyrostat was designed by Lord Kelvin to illustrate the more complicated state of motion of a spinning bodywhen free to wander about on a horizontal plane, like a top spun on the pavement, or a hoop or bicycle on the road.

MEMSA MEMS gyroscope takes the idea of the Foucault pendulum and uses a vibrating element, known as a MEMS(Micro Electro-Mechanical System). The MEMS-based gyro was initially made practical and producible by SystronDonner Inertial (SDI). Today, SDI is a large manufacturer of MEMS gyroscopes.

FOGA fiber optic gyroscope (FOG) is a gyroscope that uses the interference of light to detect mechanical rotation. Thesensor is a coil of as much as 5 km of optical fiber. The development of low loss single mode optical fiber in theearly 1970s for the telecommunications industry enabled the development of Sagnac effect fiber optic gyros.

VSG or CVGA vibrating structure gyroscope (VSG), also called a coriolis vibratory gyroscope (CVG),[14] uses a resonator madeof different metallic alloys. It takes a position between the low accuracy, low cost MEMS gyroscope and the higheraccuracy and higher cost fiber optic gyroscope (FOG). Accuracy parameters are increased by using low intrinsicdamping materials, resonator vacuumization, and digital electronics to reduce temperature dependent drift andinstability of control signals.[15]

High-Q Wine-Glass Resonators for precise sensors like HRG [16] or CRG [17] are based on Bryan's "wave inertiaeffect", and they made from high-purity quartz glass or from single-crystalline sapphire.

Gyroscope 5

DTGA dynamically tuned gyroscope (DTG) is a rotor suspended by a universal joint with flexure pivots.[18] The flexurespring stiffness is independent of spin rate. However, the dynamic inertia (from the gyroscopic reaction effect) fromthe gimbal provides negative spring stiffness proportional to the square of the spin speed (Howe and Savet, 1964;Lawrence, 1998). Therefore, at a particular speed, called the tuning speed, the two moments cancel each other,freeing the rotor from torque, a necessary condition for an ideal gyroscope.

See also• Aerotrim• Anti-rolling gyro — Ship gyroscopic roll stabilisers.• Balancing machine• Countersteering• Euler angles• Eric Laithwaite• Flywheel• Gyro monorail• Gyrocar• Gyroscopic exercise tool• Inertial navigation system• Momentum wheel• Precession• Rifling• Top

References[1] " Gyroscope (http:/ / demonstrations. wolfram. com/ Gyroscope/ )" by Sándor Kabai, Wolfram Demonstrations Project.[2] Discover magazine (http:/ / discovermagazine. com/ 2009/ may/ 20-things-you-didnt-know-about-tunnels) 20 things you didn't know about

tunnels (Number 8).[3] Johann G. F. Bohnenberger (1817) "Beschreibung einer Maschine zur Erläuterung der Gesetze der Umdrehung der Erde um ihre Axe, und der

Veränderung der Lage der letzteren" (Description of a machine for the explanation of the laws of rotation of the Earth around its axis, and ofthe change of the orientation of the latter), Tübinger Blätter für Naturwissenschaften und Arzneikunde (http:/ / www. ion. org/ museum/ files/File_1. pdf), vol. 3, pages 72–83.

[4] The French mathematician Poisson mentions Bohnenberger's machine as early as 1813: Simeon-Denis Poisson (1813) "Mémoire sur un casparticulier du mouvement de rotation des corps pesans" [Memoir on a special case of rotational movement of massive bodies], Journal del'École Polytechnique, vol. 9, pages 247–262. Available on-line at: http:/ / www. ion. org/ museum/ files/ File_2. pdf .

[5] A photograph of Bohnenberger's instrument is available on-line here: http:/ / www. ion. org/ museum/ item_view. cfm?cid=5& scid=12&iid=24 .

[6] Walter R. Johnson (January 1832). Description of an apparatus called the rotascope for exhibiting several phenomena and illustrating certainlaws of rotary motio (http:/ / books. google. com/ books?id=BjwPAAAAYAAJ), The American Journal of Science and Art, 1st series, vol. 21,no. 2, pages 265–280.

[7] Illustrations of Walter R. Johnson's gyroscope ("rotascope") (http:/ / books. google. com/ books?id=fEyT4sTd7ZkC& pg=PA178&dq=Johnson+ rotascope& ie=ISO-8859-1& output=html), Board of Regents, Tenth Annual Report of the Board of Regents of the SmithsonianInstitution.... (Washington, D.C.: Cornelius Wendell, 1856), pages 177–178.

[8] Wagner JF, "The Machine of Bohnenberger", The Institute of Navigation (http:/ / www. ion. org/ museum/ item_view. cfm?cid=5&scid=12& iid=24)

[9] L. Foucault (1852) "Sur les phénomènes d’orientation des corps tournants entraînés par un axe fixe à la surface de la terre", Comptes rendushebdomadaires des séances de l’Académie des Sciences (Paris), vol. 35, pages 424–427. Available on-line (in French): http:/ / www.bookmine. org/ memoirs/ pendule. html . Scroll down to "Sur les phénomènes d’orientation ..."

[10] Circa 1852, Friedrich Fessel, a German mechanic and former secondary school teacher, independently developed a gyroscope. See: (1) Julius Plücker (September 1853) "Über die Fessel'sche rotationsmachine", Annalen der Physik, vol. 166, no. 9, pages 174–177; (2) Julius Plücker (October 1853) "Noch ein wort über die Fessel'sche rotationsmachine", Annalen der Physik, vol. 166, no. 10, pages 348–351; (3)

Gyroscope 6

Charles Wheatstone (1864) "On Fessel's gyroscope", Proceedings of the Royal Society of London, vol. 7, pages 43–48. Available on-line at:http:/ / books. google. com/ books?id=CtGEAAAAIAAJ& pg=RA1-PA307& lpg=RA1-PA307& dq=Fessel+ gyroscope& source=bl&ots=ZP0mYYrp_d& sig=DGmUeU4MC8hAMuBtDSQn4GpAyWc& hl=en& ei=N4s9SqOaM5vKtgf62vUH& sa=X& oi=book_result&ct=result& resnum=9 .

[11] MacKenzie, Donald. Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance. Cambridge: MIT Press, 1990. pp. 31–40.ISBN 0-262-13258-3

[12] MacKenzie, pp. 40–42.[13] The Little Top That Aims a Gun (http:/ / www. popsci. com/ archive-viewer?id=PiEDAAAAMBAJ& pg=86& query=destroyer+ escort) by

Gold Sanders, Popular Science July 1945[14] H. Sternberg; C. Schwalm (2007). "Qualification Process for MEMS Gyroscopes for the Use in Navigation Systems" (http:/ / www. isprs.

org/ proceedings/ XXXVI/ 5-C55/ www. cirgeo. unipd. it/ cirgeo/ convegni/ mmt2007/ proceedings/ papers/ sternberg_harald. pdf).International Society for Photogrammetry and Remote Sensing Proceedings. .

[15] Ash, M E; Trainor, C V; Elliott, R D; Borenstein, J T; Kourepenis, A S; Ward, P A; Weinberg, M S (14-15 Sept. 1999). "Micromechanicalinertial sensor development at Draper Laboratory with recent test results" (http:/ / md1. csa. com/ partners/ viewrecord. php?requester=gs&collection=TRD& recid=A0017841AH& q=coriolis+ vibratory+ gyroscope+ CVG& uid=789572486& setcookie=yes). Symposium GyroTechnology Proceedings. .

[16] Lynch D.D. HRG Development at Delco, Litton, and Northrop Grumman //Proceedings of Anniversary Workshop on Solid-State Gyroscopy(19–21 May 2008. Yalta, Ukraine). - Kyiv-Kharkiv. ATS of Ukraine. 2009. - ISBN 978-976-02-5248-6.

[17] Sarapuloff S.A. High-Q Sapphire Resonator of Solid-State Gyroscope CRG-1 http:/ / www. stcu. int/ documents/ reports/ distribution/ tpf/MATERIALS/ Sapphire_Gyro_Sarapuloff_ATSU. pdf

[18] David May (1999). "Modeling the dynamically tuned gyroscope in support of high-bandwidth capture loop design" (http:/ / spiedl. aip. org/getabs/ servlet/ GetabsServlet?prog=normal& id=PSISDG003692000001000101000001& idtype=cvips& gifs=yes& ref=no). Proc. SPIE.doi:10.1117/12.352852. .

Further reading• Felix Klein and Arnold Sommerfeld, "Über die Theorie des Kreisels" (Tr., About the theory of the gyroscope).

Leipzig, Berlin, B.G. Teubner, 1898–1914. 4 v. illus. 25 cm.• Audin, M. Spinning Tops: A Course on Integrable Systems. New York: Cambridge University Press, 1996.• Proceedings of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine). -

Kyiv-Kharkiv. ATS of Ukraine. 2009. ISBN 978-976-02-5248-6.

External links• The Royal Institution’s 1974–75 Christmas Lecture (http:/ / www. gyroscopes. org/ 1974lecture. asp) Professor

Eric Laithwaite• One-Wheeled Robot-Gyrostat (http:/ / demonstrations. wolfram. com/ OneWheeledRobotGyrostat/ ) by Olga

Kapustina and Yuri Martynenko Wolfram Demonstrations Project• The Little Top That Aims a Gun (http:/ / www. popsci. com/ archive-viewer?id=PiEDAAAAMBAJ& pg=86&

query=destroyer+ escort) by Gold Sanders, Popular Science July 1945• Apostolyuk V. Theory and Design of Micromechanical Vibratory Gyroscopes (http:/ / www. astrise. com/

research/ library/ memsgyro. pdf)

Article Sources and Contributors 7

Article Sources and ContributorsGyroscope  Source: http://en.wikipedia.org/w/index.php?oldid=393080831  Contributors: .:Ajvol:., 5 albert square, AGToth, Abhilashharpale, Ahoerstemeier, Airdoo0, Ale jrb, Alexmcfire,Amir198332, Anclation, Andres, AndrewDressel, Andy Dingley, Angellcruz, Antonbarabashov, Apostolyuk, Arnero, Ars17, Art Carlson, Arydberg, Attilios, Audriusa, AxelBoldt, BarretBonden,Bigbluefish, Blanchardb, Bob, Bovineone, Brenont, Bryan Derksen, Capitalistroadster, Chuunen Baka, Ckatz, Cleonis, Clicketyclack, Clt13, CoolHand77, Crevox, Crum375, Cwkmail, DMacks,Dancter, Dark Mage, David Haslam, Deagels, Dekisugi, Dmitrek, DonPMitchell, Dori, Dr Dec, Edgar v. Hinüber, Edison, Edoe, Eliyak, Eteq, Falcon8765, Fapertl, Fixentries, Foxtrot RomeoIndia Zulu Echo, Frebel93, FuturedOrange, GTGUSD, GVasil, GeeJo, Giftlite, Glenn, Glennturner, GliderMaven, Gordon Vigurs, Gregorydavid, Gyroscopic, Hackwrench, Hadal, Hahamhanuka, Hailey C. Shannon, Hairy Dude, Harryzilber, Headbomb, Hephaestos, Heron, Hoo man, Hooperbloob, Hraefen, Hughhunt, II MusLiM HyBRiD II, Imsome, Isis4563, Jackehammond,Jamymc, JarrodWood, Jary, Jboyles, Jimp, Jitse Niesen, Jjjsixsix, Johnjohuy23, Jok2000, Jorfer, JustinWick, Karada, Keenan Pepper, Kenny56, Kevins8, Kieff, Kirchsw, Light current, Limideen,Linas, MONESTIER, MSGJ, MacGyver07, Macaddct1984, Magnus Manske, Mandarax, Mani1, Mare, MartinDK, Mayooranathan, Mboverload, Mhss, Michael Hardy, Michal Jurosz, Micru, Mr.Lefty, Muhends, NawlinWiki, NeilN, Nergaal, Nick Pisarro, Jr., Nuno Tavares, O123456782, P0mbal, Patrick, Pepper, Peripitus, Petri Krohn, Pleasantville, Pol098, Pvercello, Ragesoss, Rama,Raven in Orbit, RedKnight7, Rich Farmbrough, Rjwilmsi, Roberta F., Robth, Ronz, Rracecarr, S3000, Sammy0001, Sarah, SchuminWeb, Selkem, Sergii Sarapuloff, Sneg123, Spitfire, Spliced,SpookyMulder, Stephane.magnenat, StradivariusTV, Svdmolen, Symane, Tabletop, TakuyaMurata, The Anome, The Great Apple, The Singularity, Thelardking, Themfromspace, Thumperward,Tiburon, Tide rolls, Timotheus Canens II, Tony Sidaway, Trusilver, Tuspm, U04617, Uncle Milty, Unyoyega, Uorden, Vaceituno, W T L, WikHead, Wolfkeeper, XJamRastafire, Xenonice,Yamamoto Ichiro, Yintan, Zandperl, Zazou25, Zowie, Zr40, Zunaid, 362 anonymous edits

Image Sources, Licenses and ContributorsImage:3D Gyroscope.png  Source: http://en.wikipedia.org/w/index.php?title=File:3D_Gyroscope.png  License: Public Domain  Contributors: Bensin, Kieff, Snaily, 1 anonymous editsImage:Gyroscope wheel-text.png  Source: http://en.wikipedia.org/w/index.php?title=File:Gyroscope_wheel-text.png  License: Public Domain  Contributors: Glenn, Kieff, SharkDImage:Gyroscope wheel animation.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Gyroscope_wheel_animation.gif  License: Public Domain  Contributors: Kieff, SharkD,WikipediaMasterImage:Foucault's gyroscope.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Foucault's_gyroscope.jpg  License: Public Domain  Contributors: User:NctImage:Gyroscope operation.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Gyroscope_operation.gif  License: Public Domain  Contributors: Bensin, Juiced lemon, Kieff, Roomba,Santosga, SharkD, Wst, 9 anonymous editsImage:Gyroscope precession.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Gyroscope_precession.gif  License: Public Domain  Contributors: Hu Totya, Kieff, Newone, SharkD,Thire, WikipediaMaster

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