gyroscope

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Background

The gyroscope is a familiar toy that is deceptively simple in appearance and introduces children to several mechanical principles, although they may not realize it. Something like a complex top made of precisely machined metal, the gyroscope is a spinning wheel that may be set within two or more circular frames, each oriented along a different line or axis. The framework can be tilted at any angle, and the wheel—as long as it is spinning—will maintain its position, or attitude.

But the gyroscope is not just a toy. It is a part of many scientific and transportation-related instruments. These include compasses, the mechanisms that steer torpedoes toward their targets, the equipment that keeps large ships such as aircraft carriers from rolling on the waves, automatic pilots on airplanes and ships, and the systems that guide missiles and spacecraft relative to Earth (that is, inertial guidance systems).

The gyroscope consists of a central wheel or rotor that is mounted in a framework of rings. The rings are properly called gimbals, or gimbal rings. Gimbals are devices that support a wheel or other structure but allow it to move freely. The rings themselves are supported on a spindle or axis at one end that, in turn, can be mounted on a base or inside an instrument. The property of the rotor axle to point toward its original orientation in space is called gyroscopic inertia; inertia is simply the property of a moving object to keep moving until it is stopped. Friction against the air eventually slows the gyroscope's wheel, so its momentum erodes away. The axle then begins to wobble. To maintain its inertia, a gyroscope must spin at a high speed, and its mass must be concentrated toward the rim of the wheel.

History

The gyroscope is a popular children's toy, so it is no surprise that its ancestor is the spinning top, one of the world's oldest toys. A single-frame gyroscope is sometimes called a gyrotop; conversely, a top is a frameless gyroscope. In the sixteenth through eighteenth centuries, scientists including Galileo (1564-1642), Christiaan Huygens (1629-1695), and Sir Isaac Newton (1642-1727) used toy tops to understand rotation and the laws of physics that explain it. In France during the 1800s, the scientist Jean-Bernard-Léon Foucault (1819-1868) studied experimental physics and proved Earth's rotation and explained its effect on the behavior of objects traveling on Earth's surface. In the 1850s, Foucault studied the motions of a rotor mounted in a gimbal frame and proved that the spinning wheel holds its original position, or orientation, in space despite Earth's rotation. Foucault named the rotor and gimbals the gyroscope from the Greek words gyros and skopien meaning "rotation" and "to view."

It was not until the early 1900s that inventors found a use for the gyroscope. Hermann Anschiutz-Kaempfe, a German engineer and inventor, recognized that the stable orientation of the gyroscope could be used in a gyrocompass. He developed the gyrocompass for use in a submersible for undersea exploration where normal navigation and orientation systems are impractical. In 1906, Otto Schlick tested a gyroscope equipped with a rapidly spinning rotor in the German torpedo boat See-bar. The sea caused the torpedo boat to roll 15° to each side, or 30° total; when his gyroscope was operated at full speed, the boat rolled less than 1° total.

In the United States, Elmer Ambrose Sperry (1860-1930)—an inventor noted for his achievements in developing electrical loco-motives and machinery transmissions—introduced a gyrocompass that was installed on the U.S. battleship Delaware in 1911. In 1909, he had developed the first automatic pilot, which uses the gyroscope's sense of direction to maintain the course of an airplane. The Anschiütz Company installed the first automatic pilot—based on a three-frame gyroscope—in a Danish passenger ship in 1916. In that year, the artificial horizon for aircraft was designed as well. The artificial horizon tells the pilot how the airplane is rolling (moving side to side) or pitching (moving front to rear) when the visible horizon vanishes in the clouds or other conditions.

Roll-reduction was needed for ships, too. The Sperry Company had introduced a gyrostabilizer that used a two-frame gyroscope in 1915. The roll of a ship on the ocean makes passengers seasick, causes cargo to shift and suffer damage, and induces stresses in the ship's hull. Sperry's gyrostabilizer was heavy, expensive, and occupied a lot of space on a ship. It was made obsolete in 1925 when the Japanese devised an underwater fin for stabilizing ships.

During the intense development of missile systems and flying bombs before and during World War II, two-frame gyroscopes were paired with three-frame instruments to correct roll and pitch motions and to provide automatic steering, respectively. The Germans used this combination on the V-1 flying bomb, the V-2 rocket, and a pilotless airplane. The V-2 is considered an early ballistic missile. Orbiting spacecraft use a small, gyroscope-stabilized platform for their navigation systems. This characteristic of gyroscopes to remain stable and define direction to a very high degree of accuracy has been applied to gunsights, bombsights, and the shipboard platforms that support guns and radar. Many of these mechanisms were greatly improved during World War II, and the inertial navigation systems that use gyroscopes for spacecraft were invented and perfected in the 1950s as space exploration became increasingly important.

Raw Materials

The materials used to manufacture a gyroscope can range from relatively simple to highly complex depending on the design and purpose of the gyroscope. Some are made more precisely than the finest watch. They may spin on tiny ball bearings, polished flecks of precious gemstones, or thin films of air or gas. Some operate entirely in a vacuum suspended by an electrical current so they touch nothing and no friction develops.

A gyroscope with an electrically powered motor and metal gimbals has four basic sets of components. These are the motor, the electrical components, electronic circuit cards for programmed operation, and the axle and gimbal rings. Most manufacturers purchase motors and electrical and electronic components from subcontractors. These may be stock items, or they may be manufactured to a set of specifications provided to the supplier by the gyroscope maker. Typically, gyroscope manufacturers machine their own gimbals and axles. Aluminum is a preferred metal because of its expansion and strength characteristics, but more sophisticated gyroscopes are made of titanium. Metal is purchased in bulk as bar stock and machined.

Design

Using the electrical and mechanical aspects of gyroscopic theory as their guides, engineers choose a wheel design for the gimbals and select metal stock appropriate for the design. The designs for many uses of gyroscopes are fairly standard; that is, redesign or design of a new line is a matter of adapting an existing design to a new use rather than creating a new product from the most basic beginning. Design does, however, involve observing the most fundamental engineering practices. Tolerances, clearances, and electronic applications are very precise. For example, design of the gimbal wheels and design of the machining for them has a very small tolerance for error; the cross section of a gimbal must be uniform throughout or the gyroscope will be out of balance.

The Manufacturing Process

1. The gimbals and gimbal frames are machined from aluminum bar stock using tools developed as part of the design process. They are polished and cleaned and stored in bins until assembly. For assembly, the bins are moved to appropriate locations along the assembly line.
2. Gyroscopes are manufactured in a straight-forward assembly line process that emphasizes the importance of "touch labor" over automation. Gyroscopes are assembled from the inside out. The motor is the heart of the gyroscope and is installed first. A "typical" gyroscope motor is synchronized to spin at 24,000 revolutions per minute (rpm). It must be perfectly synchronized, and the motor is typically bench-tested before assembly. Electrical connections are added to the motor.
3. The gimbals and frames are assembled next, beginning with the inner gimbal and ending with the outer gimbal frame. Bearings are put into place. The "end play" of the bearings (the looseness of fit) typically has a very small tolerance of 0.0002-0.0008 in (0.006-0.024 mm).
4. The outermost electrical connections are attached on the assembly line, and circuit cards are added. Finally, the gyroscope is calibrated at the end of the assembly process. The suspension of the bearings and calibration are hand checked; manufacturers have found that, for even calibration, human observation, testing, and correction are more trustworthy than automated methods.

The gyroscope is an elegant example of an application of simple principles of physics. Because it is simple, manufacturers closely guard any proprietary techniques. Because the gyroscope is a simple device with wideranging uses, some require more manufacturing processes. The manufacturing steps described above take about 10 hours and result in a free gyroscope for an application such as missile guidance. A more exotic gyroscope may require 40 hours of assembly time.

Quality Control

Quality control is essential throughout the design and assembly processes in manufacturing gyroscopes because the instruments are part of manned aircraft, unmanned missiles, and other transportation and weapons devices that could cause catastrophes if they fail. Engineers, scientists, and designers are highly educated and trained before they are hired and while on the job. Assembly-line workers must pass initial training to be hired, and they have regularly scheduled, ongoing training sessions. Many of the quality standards that must be met in gyroscope manufacture can be measured, so in-process inspection is performed throughout manufacture. Quality control at the highest level is performed by inspectors from outside the company and includes government inspectors. Customers also perform their own inspections and acceptance testing; if the manufacturer's product fails the customers' tests, the failed gyroscopes are returned.

Byproducts/Waste

Gyroscope manufacturers do not produce byproducts, but they tend to make full lines of gyroscopes for a wide variety of applications. They also do not produce much waste. Machining the gimbals and rings produces some aluminum chips, but these are collected and returned to the aluminum supplier for recycling.

Safety Concerns

Manufacturers observe the mandates of the Occupational Safety and Health Administration (OSHA) for light, ventilation, and ergonomics (comfortable seating and work benches that reduce the likelihood of repetitive stress injuries). Humidity must be maintained in the plant to prevent electrostatic discharge. Minor quantities of cleaning solvents are required, but citrus-based cleaners that are benign (harmless) are used.

The Future

Uses for gyroscopes are increasing with the number of devices that require guidance and control. Although the basics of the gyroscope are grounded in the laws of physics and can never change, the technology is evolving. Mechanical and electrical methods for providing the spinning mass that makes the gyroscope work are gradually being replaced by ring lasers and microtechnology. Coils of thin optical fibers hold the key to compact, lightweight gyroscopes that might have applications in navigation systems for automobiles. The gyroscope is such a simple but sophisticated instrument for keeping so many tools in transportation, exploration, and industry in balance that, seen or unseen, it certainly has a place in the future.

Where to Learn More

Books

Campbell, R. W. Tops and Gyroscopes. New York: Thomas Y. Crowell Company, 1959.

Langone, John. National Geographic's How Things Work: Everyday Technology Explained. Washington, DC: National Geographic Society, 1999.

Sparks, James C., Jr. Gyroscopes: What They Are and How They Work. New York: E. P. Dutton & Co., Inc., 1963.

Walton, Harry. The How and Why of Mechanical Movements. New York: Popular Science Publishing Company, E. P. Dutton & Co., Inc., 1968.

Periodicals

"A Gyroscope's Gravity-defying Feat." Science News 137, no. 1 (January 6, 1990): 15.

Scott, David. "Optical-fiber Gyro." Popular Science 230 (June 1987): 25.

Other

Gyroscopes as Propulsion Devices. http://www.gyro-scope.co.uk (July 2000).

Gyroscope Study Guide. http://clubknowledge.com/study/gyro.html(July 2000).

How a gyroscope works. http://www.accs.net/users/cefpearson/gyro.htm (July 2000).

[Article by: Gillian S. Holmes]

A device that is used to define a fixed direction in space or to determine the changein angle or the angular rate of its carrying vehicle with respect to a reference frame. Gyroscopes (also called gyros) respond to vehicle angular rates, that is, rates of change of angles between vehicle axes and reference axes, from which these angles can be computed. Gyros are used for guidance, navigation, and stabilization. See also Gyrocompass; Inertial guidance system; Navigation.

Gyros can be utilized either mounted on a stabilized platform, whose orientation in a movingvehicle remains fixed in space by a means of two, three, or four gimbals, or directly attached to the vehicle's body, so that the gyro experiences the same maneuvering as the vehicle, an operating mode referred to as strapdown. Strapdown operation is desirable because it enables a much less expensive system; it became feasible only in the 1970s and 1980s, when the very high digital computing speed required for the strapdown algorithms became available.

Gyros can be operated closed-loop or open-loop. Closed-loop means that a feedback loop from the gyro output introduces a restoring mechanism either inside the gyro (for example, torquing in mechanical gyros) or counterrotating platform motions to maintain the gyro at its null (initial) setting. In open-loop operation, the gyro is allowed to operate off its null position as it responds to the input angular rates. See also Control systems; Servomechanism.

Gyroscopes use different physical phenomena to respond to input angular rates; for example, spinning-mass gyros sense changes in angular momentum from Coriolis acceleration; resonator gyroscopes sense deflections from Coriolis acceleration; and optical gyros sense phase shifts (theSagnac effect) between counterpropagating beams of light. Instruments that do not have spinning masses are not technically gyros but angular rate sensors. However, the term “gyro” is commonly used for all rate-sensing devices. See also Coriolis acceleration.

The classical spinning-mass gyroscope is based upon the phenomenon that the spin axis of a spinning mass points in a fixed direction in space unless acted upon by an external influence. However, the spin axis can be made to rotate if a torque (or rotational rate) is applied at right angles to the spin vector. The spin vector then begins to rotate (precess) about a third axis, perpendicular to the spin axis and the applied torque; that is, the spin axis tries to align itself with the applied torque. This is the law of gyroscopic precession; measurement of precession is what makes the spinning-mass gyro useful for knowing the changes in direction of the carrying vehicle.

The free gyroscope's spinning mass is isolated from the rotations of the case or the carrying vehicle so that it remains fixed in space. The relative position of the spinning mass tothe gyro case is proportional to the vehicle's angle of rotation.

The rate gyro's spinning mass is forced to rotate with the vehicle rotation rate about one particular axis (for example, pitch or roll). The output torque causing the spinning mass to turn (precess) is opposed by an elastic restraint. The angle, measured by pickoffs, that the spinning mass turns through is proportional to the vehicle rotation rate. Rate gyros are used in applications in which stable errors can be tolerated.

The floated, single-degree-of-freedom, rate-integrating gyro, or floated gyro as it is commonly known, is basically a rate gyro in which the spring restraint is replaced by viscous damping. The spinning mass is contained inside a “float” which is isolated from the case by means of the viscous flotation fluid, low-restraint electromagnetic suspensions, pickoffs, and torque generators. Floated, integrating gyros went from revolutionizing military aircraft navigation in the 1950s to enabling strategic missile guidance, submarine navigation, space flight (for example, the Apollo spacecraft), and satellite stabilization (for example, the Hubble Space Telescope).

In the electrostatically suspended gyroscope (ESG), a spherical rotor is suspended in a spherical chamber in vacuum by electrostatic forces. External motor windings spin the rotor to the desired speed and are then turned off. The rotor will spin for days before requiring motor excitation. Optical or electrical techniques are used to pick off rotor position. The ESG is basically a free gyroscope and does not require a torquer to keep the rotor and case aligned. ESGs are very accurate and are used for long-term navigation of submarines and aircraft and for land surveying. A similar concept is the magnetically suspended gyro (MSG), which uses a magnetic field to suspend the rotor. See also Electrostatics; Magnetism; Relativity.

Optical gyros use the Sagnac effect to detect rotation. The Sagnac effect pertains to the postulate of the theory of relativity that the speed of light is constant, and independent of themotion of the source. If two identical light waves circulate in opposite directions along a closed path undergoing a rotation, then the light beam traveling in the same direction as the rotation takes longer to travel around the path than the other beam, resulting in a changed interference pattern. Optical gyroscopes include the ring laser gyro (RLG) and fiber-optic gyros (FOGs).

The ring laser gyro is widely used in tactical and navigation systems. It comprises a closedoptical cavity (usually a three- or four-sided block of low-expansion-coefficient material), whose light path is defined by mirrors mounted at the corners. The light travels through holes bored in the block containing a low-pressure gas, usually a helium-neon mixture which lases when the anode and cathode are excited. Thus, the RLG is itself actually a laser (that is, it does not require an external light source), and is thus said to be an active device. See also Laser.

The lased light propagates clockwise and counterclockwise so that there are two optical beams, each maintained in resonance (that is, each beam contains an integral number of wavelengths). Under a rotation rate about the gyro input axis, the resonant frequencies of the clockwise and counterclockwise beams change. Some light from both beams is transmitted through one of the mirrors to impinge on a detector. Because the beams have different frequencies, a changing interference pattern (fringes) appears. Measurement of the fringe pattern changes determines the external rotation rate and direction.

Fiber-optic gyros use optical fibers, in place of a lasing block, to define the optical path. The light source is external, and its light is split by a beam splitter or optical coupler to produce clockwise and counterclockwise light beams in the fiber-optic coil. FOGs are called passive devices because the optical source (a laser) is external. There are two principal types: interferometric and resonant. The interferometric fiber-optic gyro (IFOG) has up to 1 km (0.6 mi) of optical fiber wound into a coil with both ends brought into a coupler. The resonant fiber-optic gyro (RFOG) maintains the counterpropagating light beams in resonance, recirculating them in a short fiber-optic coil.

Vibrating gyroscopes use an oscillating mass in place of a spinning mass to sense rates. The mass oscillates (sinusoidally) back and forth through a fixed angle; the amplitude of the oscillation is restrained by the elastic (spring) stiffness of the vibrating structure. Nearly all such gyros oscillate at the resonant frequency of the mass-spring system since the gyro output is maximized at this frequency; hence these gyroscopes are also called resonator gyros. See also Resonance (acoustics and mechanics); Vibration.

n. a device consisting of a wheel or disc mounted so that it can spin rapidly about an axis that is itself free to alter in direction. The orientation of the axis is not affected by tilting of the mounting; so gyroscopes can be used to provide stability or maintain a reference direction in navigation systems, automatic pilots, and stabilizers.

gyroscopic adj. gyroscopically adv.

See the Introduction, Abbreviations and Pronunciation for further details.

A gyroscope

For other uses and non rotary gyroscopes, see Gyroscope (disambiguation).

A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum.^[1][2] A mechanical gyroscope is essentially a spinning wheel or disk whose axle is free to take any orientation. 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. 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. Solid state gyroscopes also exist.

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

Contents 1 Description and diagram 2 History 3 Properties 4 Gyrostat 5 US patents 6 See also 7 References 8 Further reading 9 External links

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. 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 that is always perpendicular to the pivotal axis of the outer gimbal.

The axle of the spinning wheel defines the spin axis. 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. 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.

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

Gyroscope invented by Léon Foucault, and built by Dumoulin-Froment, 1852. National Conservatory of Arts and Crafts museum, Paris.

The earliest known gyroscope was made by German Johann Bohnenberger, who first wrote about it in 1817. At first he called it the "Machine".^[3][4] Bohnenberger's gyroscope was based on a rotating massive sphere.^[5] In 1832, American Walter R. Johnson developed a gyroscope that was based on a rotating disk.^[6][7] 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.^[8] In 1852, Foucault used it in an experiment involving the rotation of the Earth.^[9][10] 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. 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. The Sperry Gyroscope Company quickly expanded 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 a pull string and pedestal. It has been in continuous production ever since and is considered a classic American toy.

MEMS gyroscopes take the idea of the Foucault pendulum and use a vibrating element, known as a MEMS (Micro Electro-Mechanical System). 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). Similar principles were later employed in the development of inertial guidance systems for ballistic missiles.^[12]

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. 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. Gyroscopic effects are used in toys like tops,boomerangs,yo-yos, and Powerballs. Many other rotating devices, such as flywheels, behave gyroscopically although the gyroscopic effect is not 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 its moment 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 angular velocity of precession Ω_P is given by the cross product:

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. 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 rotation resulting from this torque is not downwards, as might be intuitively expected, causing the device to fall, but perpendicular to both the gravitational torque (horizontal and perpendicular to the axis of 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.

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

where θ is the angle between the vectors Ω_P and L. Thus if the gyroscope's spin slows down (for example, due to friction), its angular momentum decreases and so 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.

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. 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.

US 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"

See also

Wikibooks has a book on the topic of Rotational Motion

• Aerotrim
• Anti-rolling gyro — Ship gyroscopic roll stabilisers.
• Balancing machine
• Control moment gyroscope
• Countersteering
• Euler angles
• Eric Laithwaite
• Fibre optic gyroscope
• Gimbal lock
• Gyro monorail
• Gyrocar
• Gyrocompass
• Gyroscopic exercise tool
• Inertial navigation system
• Momentum wheel
• Precession
• Quantum gyroscope
• Rate integrating gyroscope
• Rifling
• Ring laser gyroscope
• Segway
• Top
• Vibrating structure gyroscope

References

1. ^ "Gyroscope" by Sándor Kabai, Wolfram Demonstrations Project.
2. ^ "Total Angular Momentum", ScienceWorld
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 of the change of the orientation of the latter] Tübinger Blätter für Naturwissenschaften und Arzneikunde, vol. 3, pages 72-83. Available on-line at: http://www.ion.org/museum/files/File_1.pdf .
4. ^ The French mathematician Poisson mentions Bohnenberger's gyroscope as early as 1813: Simeon-Denis Poisson (1813) "Mémoire sur un cas particulier du mouvement de rotation des corps pesans" [Memoir on a special case of rotational movement of massive bodies], Journal de l'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 gyroscope 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 certain laws of rotary motion," The American Journal of Science and Art, 1st series, vol. 21, no. 2, pages 265-280. Available on-line at: http://books.google.com/books?id=BjwPAAAAYAAJ&pg=PA265&lpg=PR5&dq=Johnson+rotascope&ie=ISO-8859-1&output=html .
7. ^ Illustrations of Walter R. Johnson's gyroscope ("rotascope") appear in: Board of Regents, Tenth Annual Report of the Board of Regents of the Smithsonian Institution.... (Washington, D.C.: Cornelius Wendell, 1856), pages 177-178. Available on-line at: http://books.google.com/books?id=fEyT4sTd7ZkC&pg=PA178&dq=Johnson+rotascope&ie=ISO-8859-1&output=html .
8. ^ Wagner JF, "The Machine of Bohnenberger," The Institute of Navigation [1]
9. ^ L. Foucault (1852) "Sur les phénomènes d’orientation des corps tournants entraînés par un axe fixe à la surface de la terre," Comptes rendus hebdomadaires 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) 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.

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.

External links

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Websites

• U.S. Dynamics Long Life Gyroscopes
• Technical White Papers on Gyroscopes
• Description of the Systron Donner Inertial MEMS gyroscope
• The Precession and Nutation of a Gyroscope
• Everything you needed to know about gyroscopes
• Project in which gyroscopes are used to drive a robotic arm
• Examples of gyroscopes
• An explanation of gyroscopes

Papers

• Theory and Design of Micromechanical Vibratory Gyroscopes Vladislav Apostolyuk

Lectures

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

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Dansk (Danish)
n. - gyroskop

Nederlands (Dutch)
gyroscoop

Français (French)
n. - gyroscope

Deutsch (German)
n. - Kreisel, Gyroskop , (Meßgerät zum Nachweis der Erdachsendrehung)

Ελληνική (Greek)
n. - γυροσκόπιο

Italiano (Italian)
giroscopio

Português (Portuguese)
n. - giroscópio (m) (Fís.)

Русский (Russian)
гироскоп

Español (Spanish)
n. - giroscopio

Svenska (Swedish)
n. - gyroskop (tekn.)

中文（简体）(Chinese (Simplified))
陀螺仪, 回转仪, 回旋装置

中文（繁體）(Chinese (Traditional))
n. - 陀螺儀, 回轉儀, 迴旋裝置

한국어 (Korean)
n. - 회전의, (어뢰의) 종타 조정기, 회전 운동을 하는 물체

日本語 (Japanese)
n. - ジャイロスコープ, 回転儀

العربيه (Arabic)
‏(الاسم) اداة تستخدم لحفظ توازن الطائرة الخ‏

עברית (Hebrew)
n. - ‮גירוסקופ, גלגל מסתובב על ציר ומשמש כבסיס יציב למצפן בגופים נעים: אוניה, מטוס ועוד‬

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