Gyroscope

A gyroscope

For other uses, see Gyroscope (disambiguation).

A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum^[1]^[2]. This article deals with orientation of reference axes or frames In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position The device is a spinning wheel or disk whose axle is free to take any orientation. A wheel is a circular device that is capable of rotating on its axis facilitating movement or transportation whilst supporting a load ( Mass) or performing labour in machines An axle is a central shaft for a rotating Wheel or Gear. In some cases the axle may be fixed in position with a bearing or Bushing This orientation changes much less in response to a given external torque than it would without the large angular momentum associated with the gyroscope's high rate of spin. A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about Since external torque is minimized by mounting the device in gimbals, its orientation remains nearly fixed, regardless of any motion of the platform on which it is mounted. A gimbal is a pivoted support that allows the rotation of an object about a single axis

1 Description and diagram
2 History
3 Properties
4 Gyrostat
5 U.S. Patents
6 See also
7 References
8 External articles and further readings

Description and diagram

Diagram of a gyro wheel. Reaction arrows about the output axis (blue) correspond to forces applied about the input axis (green), and vice versa.

Within mechanical systems or devices, a conventional gyroscope is a mechanism comprising a rotor journaled to spin about one axis, the journals of the rotor being mounted in an inner gimbal or ring, the inner gimbal being journaled for oscillation in an outer gimbal which in turn is journaled for oscillation relative to a support. In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point A journal bearing is a simple bearing in which a shaft, or "journal" or Crankshaft rotates in the bearing with a layer of Oil or A gimbal is a pivoted support that allows the rotation of an object about a single axis The outer gimbal or ring is mounted so as to pivot about an axis in its own plane determined by the support. The outer gimbal possesses one degree of rotational freedom and its axis possesses none. The inner gimbal is mounted in the outer gimbal so as to pivot about an axis in its own plane, which axis is always perpendicular to the pivotal axis of the outer gimbal. In Geometry, two lines or planes (or a line and a plane are considered perpendicular (or orthogonal) to each other if they form congruent

The axle of the spinning wheel defines the spin axis. An axle is a central shaft for a rotating Wheel or Gear. In some cases the axle may be fixed in position with a bearing or Bushing The inner gimbal possesses two degrees of rotational freedom and its axis possesses one. The rotor is journaled to spin about an axis which is always perpendicular to the axis of the inner gimbal. So, the rotor possesses three degrees of rotational freedom and its axis possesses two. The wheel responds to a force applied about the input axis by a reaction force about the output axis.

The behaviour of a gyroscope can be most easily appreciated by consideration of the front wheel of a bicycle. If the wheel is leaned away from the vertical so that the top of the wheel moves to the left, the forward rim of the wheel also turns to the left. In other words, rotation on one axis of the turning wheel produces rotation of the third axis.

A gyroscope flywheel will roll or resist about the output axis depending upon whether the output gimbals are of a free- or fixed- configuration. A gimbal is a pivoted support that allows the rotation of an object about a single axis Examples of some free-output-gimbal devices would be the attitude reference gyroscopes used to sense or measure the pitch, roll and yaw attitude angles in a spacecraft or aircraft. Flight dynamics is the science of air and space vehicle orientation and control in three dimensions Flight dynamics is the science of air and space vehicle orientation and control in three dimensions Flight dynamics is the science of air and space vehicle orientation and control in three dimensions

Animation of a gyro wheel in action

The center of gravity of the rotor can be in a fixed position. The rotor simultaneously spins about one axis and is capable of oscillating about the two other axes, and thus, except for its inherent resistance due to rotor spin, it is free to turn in any direction about the fixed point. Some gyroscopes have mechanical equivalents substituted for one or more of the elements, e. g. , the spinning rotor may be suspended in a fluid, instead of being pivotally mounted in gimbals. A control moment gyroscope (CMG) is an example of a fixed-output-gimbal device that is used on spacecraft to hold or maintain a desired attitude angle or pointing 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 of freedom. In other cases, the center of gravity of the rotor may be offset from the axis of oscillation, and thus the center of gravity of the rotor and the center of suspension of the rotor may not coincide.

History

The earliest known gyroscope was made by Johann Bohnenberger in 1817, although he called it simply the 'Machine'. Year 1817 ( MDCCCXVII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common The French mathematician Pierre-Simon Laplace, working at the École Polytechnique in Paris, recommended the machine for use as a teaching aid, and thus it came to the attention of Léon Foucault. For other Écoles Polytechniques see École Polytechnique de Montréal and École Polytechnique Fédérale de Lausanne. Jean Bernard Léon Foucault (ʒɑ̃ bɛʁnaʁ leɔ̃ fu'ko ( 18 September 1819 &ndash 11 February 1868) was a French physicist ^[3] In 1852, Foucault used it in an experiment involving the rotation of the Earth. Year 1852 ( MDCCCLII) was a Leap year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Leap year It was Foucault who gave the device its modern name, in an experiment to see (Greek skopeein, to see) the Earth's rotation (Greek gyros, circle or rotation), although the experiment was unsuccessful due to friction, which effectively limited each trial to 8 to 10 minutes, too short a time to observe significant movement.

In the 1860s, electric motors made the concept feasible, leading to the first prototype gyrocompasses; the first functional marine gyrocompass was developed between 1905 and 1908 by German inventor Hermann Anschütz-Kaempfe. A gyrocompass is similar to a Gyroscope. It is a Compass that finds True north by using an (electrically powered fast-spinning wheel and friction Hermann Franz Joseph Hubertus Maria Anschütz-Kaempfe (1872 – 1931 was a German Scientist and Inventor. The American Elmer Sperry followed with his own design in 1910, and other nations soon realized the military importance of the invention— in an age in which naval might was the most significant measure of military power— and created their own gyroscope industries. Elmer Ambrose Sperry ( October 12, 1860 – June 16, 1930) was a prolific Inventor and Entrepreneur, most famous as co-inventor The Sperry Gyroscope Company quickly expanded to provide aircraft and naval stabilizers as well, and other gyroscope developers followed suit. Sperry Corporation (1910-1986 was a major American equipment and Electronics company whose existence spanned more than seven decades of the twentieth century ^[4]

In 1917, the Chandler Company of Indianapolis, Indiana created the "Chandler gyroscope", a toy gyroscope with a pull string and pedestal. It has been in continuous production ever since and is considered a classic American toy.

Some gyroscopes take the idea of the Foucault pendulum and use a vibrating element, known as a MEMS (Micro Electro-Mechanical System). The Foucault pendulum (fuːˈkoʊ "foo-KOH" or Foucault's pendulum, named after the French physicist Léon Foucault, was conceived as Microelectromechanical systems ( MEMS) is the technology of the very small and merges at the nano-scale into Nanoelectromechanical systems (NEMS and Nanotechnology The MEMS based gyro was initially made practical and produceable by Systron Donner Inertial (SDI). Today, SDI is a large manufacturer of MEMS gyroscopes.

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 measurements could be performed (in order to bypass the need for star sightings to calculate position). Black box is a technical term for a device or system or object when it is viewed primarily in terms of its input and output characteristics Similar principles were later employed in the development of inertial guidance systems for ballistic missiles. An Inertial Navigation System (INS is a Navigation aid that uses a Computer and motion sensors to continuously track the position orientation and Velocity A ballistic missile is a Missile that follows a Sub-orbital ballistic flightpath with the objective of delivering a warhead to a predetermined target ^[5]

Properties

A gyroscope in operation with freedom in all three axes. The rotor will maintain its spin axis direction regardless of the orientation of the outer frame.

A gyroscope exhibits a number of behaviours including precession and nutation. Precession refers to a change in the direction of the axis of a rotating object Nutation is a slight irregular motion (etymologically a "nodding" in the Axis of rotation of a largely axially symmetric object such as a Gyroscope Gyroscopes can be used to construct gyrocompasses which complement or replace magnetic compasses (in ships, aircraft and spacecraft, vehicles in general), to assist in stability (bicycle, Hubble Space Telescope, ships, vehicles in general) or be used as part of an inertial guidance system. A gyrocompass is similar to a Gyroscope. It is a Compass that finds True north by using an (electrically powered fast-spinning wheel and friction A ship /ʃɪp/ is a large vessel that floats on water Ships are generally distinguished from Boats based on size A spacecraft is a Vehicle or machine designed for Spaceflight. Vehicles, derived from the Latin word vehiculum, are non-living Means of transport. The bicycle, cycle, or bike is a pedal-driven, human-powered vehicle with two wheels attached to a frame, one behind The Hubble Space Telescope ( HST; also known colloquially as "the Hubble" or just "Hubble" is a space telescope that was carried into A ship /ʃɪp/ is a large vessel that floats on water Ships are generally distinguished from Boats based on size Vehicles, derived from the Latin word vehiculum, are non-living Means of transport. An Inertial Navigation System (INS is a Navigation aid that uses a Computer and motion sensors to continuously track the position orientation and Velocity Gyroscopic effects are used in toys like yo-yos and Powerballs. The yo-yo is a Toy consisting of two equally sized and weighted disks of Plastic, Wood, or Metal, connected with an Axle, with a A gyroscopic exercise tool is a device used to exercise the Wrist as part of Physical therapy or in order to build hand and finger strength Many other rotating devices, such as flywheels, behave gyroscopically although the gyroscopic effect is not used. A flywheel is a mechanical device with significant Moment of inertia used as a storage device for Rotational energy.

The fundamental equation describing the behavior of the gyroscope is:

$\boldsymbol\tau={{d \mathbf{L}}\over {dt}}={{d(I\boldsymbol\omega)} \over {dt}}=I\boldsymbol\alpha$

where the vectors $\boldsymbol\tau$ and $\mathbf{L}$ are, respectively, the torque on the gyroscope and its angular momentum, the scalar $I\,$ is its moment of inertia, the vector $\boldsymbol\omega$ is its angular velocity, and the vector $\boldsymbol\alpha$ is its angular acceleration. A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position

It follows from this that a torque $\boldsymbol\tau$ applied perpendicular to the axis of rotation, and therefore perpendicular to $\mathbf{L}$ , results in a motion perpendicular to both $\boldsymbol\tau$ and $\mathbf{L}$ . This motion is called precession. Precession refers to a change in the direction of the axis of a rotating object The angular velocity of precession $\boldsymbol\Omega_P$ is given by the cross product:

$\boldsymbol\tau=\boldsymbol\Omega_P \times \mathbf{L}$

Precession on a gyroscope

Precession can be demonstrated by placing a spinning gyroscope with its axis horizontal and supported loosely (frictionless toward precession) at one end. In Mathematics, the cross product is a Binary operation on two vectors in a three-dimensional Euclidean space that results in another vector which Instead of falling, as might be expected, the gyroscope appears to defy gravity by remaining with its axis horizontal, when the other end of the axis is left unsupported and the free end of the axis slowly describes a circle in a horizontal plane, the resulting precession turning. This effect is explained by the above equations. The torque on the gyroscope is supplied by a couple of forces: gravity acting downwards on the device's centre of mass, and an equal force acting upwards to support one end of the device. The motion resulting from this torque is not downwards, as might be intuitively expected, causing the device to fall, but perpendicular to both the gravitational torque (downwards) and the axis of rotation (outwards from the point of support), i. e. in a forward horizontal direction, causing the device to rotate slowly about the supporting point.

As the second equation shows, under a constant torque, the gyroscope's speed of precession is inversely proportional to its angular momentum. This means that, for instance, if friction causes the gyroscope's spin to slow down, the rate of precession increases. This continues until the device is unable to rotate fast enough to support its own weight, when it stops precessing and falls off its support, mostly because 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 according to the right-hand rule. For the related yet different principle relating to electromagnetic coils see Right hand grip rule.

To easily ascertain the direction of gyro effect, simply remember that a rolling wheel tends, when entering a corner, to turn over to the inside.

Gyrostat

A gyrostat is a variant of the gyroscope. The first gyrostat was designed by Lord Kelvin to illustrate the more complicated state of motion of a spinning body when free to wander about on a horizontal plane, like a top spun on the pavement, or a hoop or bicycle on the road. William Thomson 1st Baron Kelvin (or Lord Kelvin) OM, GCVO, PC, PRS, FRSE, (26 June 1824 &ndash 17 December 1907 It consists of a massive flywheel concealed in a solid casing. Its behaviour on a table, or with various modes of suspension or support, serves to illustrate the curious reversal of the ordinary laws of static equilibrium due to the gyrostatic behaviour of the interior invisible flywheel when rotated rapidly.

U. S. Patents

In the USPTO classification scheme, the generic locus for gyroscope patents is Class 74, Machine element or mechanism, and Subclass 5R. Every rotating body has gyroscopic action, but such devices are not included unless at least one axis of oscillation is present. The combinations of gyroscopes with other devices are placed in subclass 5. 22.

Numbers

U.S. Patent 839,161 , "Steering apparatus for automobile torpedoes", .
U.S. Patent 795,045 , "Gyroscopic control apparatus", .
U.S. Patent 785,587 , "Mechanical speed governor".
U.S. Patent 785,425 , "Steering mechanism for torpedoes".
U.S. Patent 751,888 , "Governing mechanism for turbines".
U.S. Patent 738,823 , "Electrical apparatus".
U.S. Patent 730,613 , "Meter".
U.S. Patent 662,484 , "Electric top for gyroscopes".
U.S. Patent 648,878 , "Gyroscope for torpedo steering mechanism".
U.S. Patent 642,704 , "Roller bearing car wheel".
U.S. Patent 484,960 , "Gyroscopic top".
U.S. Patent 461,948 , "Gyroscope or revolving toy".
U.S. Patent 365,530 , "Lumber cart".
U.S. Patent 312,692 , "Vehicle wheel".
U.S. Patent 220,867 , "Engine-governor and speed-regulator".
U.S. Patent 162,446 , "Governor for steam engine".
U.S. Patent 34,298 , "Levelling instrument".

Reissued

U.S. Patent RE024,880 , "Rate Gyroscope with torsional suspension"

References

^ "Gyroscope" by Sándor Kabai, The Wolfram Demonstrations Project. A top, or spinning top, is a Toy that can be spun on an axis balancing on a point In Science, a vibrating structure gyroscope is a type of Gyroscope that functions much like the Halteres of insects
^ "Total Angular Momentum", ScienceWorld
^ Wagner JF, "The Machine of Bohnenberger", The Institute of Navigation [1]
^ MacKenzie, Donald. ScienceWorld, also known as Eric Weisstein's World of Science, is a Web site that opened to the general public in January 2002. Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance. Cambridge: MIT Press, 1990. pp 31-40. ISBN 0-262-13258-3
^ MacKenzie, pp 40-42.

External articles and further readings

Books

Felix Klein and Arnold Sommerfeld, "Über die Theorie des Kreisels" (Tr. Felix Christian Klein ( 25 April 1849 &ndash 22 June 1925) was a German Mathematician, known for his work in Group Arnold Johannes Wilhelm Sommerfeld (5 December 1868 &ndash 26 April 1951 was a German theoretical Physicist who pioneered developments in atomic , 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.

Websites

Papers

Theory and Design of Micromechanical Vibratory Gyroscopes Vladislav Apostolyuk

Lectures

The Royal Institution’s 1974-75 Christmas Lecture Professor Eric Laithwaite

Dictionary

-noun

an apparatus composed of a wheel which spins inside of a frame (gimbal) and causes the balancing of the frame in any direction or position. In the form of a gyroscopic stabilizer, used to help keep aircraft and ships steady.

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