
A gyroscope
A
gyroscope is a device for measuring or
maintaining
orientation,
based on the principles of
angular
momentum. 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
[7263].
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".
Bohnenberger's gyroscope was based on a rotating massive sphere. In
1832, American Walter R. Johnson developed a gyroscope that was
based on a rotating disk.
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. In 1852, Foucault
used it in an experiment involving the rotation of the Earth. 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.
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 producible 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.
Properties
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
Powerball. 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:
- \boldsymbol\tau=\over {dt}}={{d(I\boldsymbol\omega)} \over
{dt}}=I\boldsymbol\alpha
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
ΩP is given by the
cross product:
- \boldsymbol\tau=\boldsymbol\Omega_{\mathrm{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. 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
ΩP is inversely
proportional to
L, the magnitude of its angular momentum:
- \tau = \mathit{\Omega}_{\mathrm{P}} L \sin\theta,\!
where
θ is the angle between the vectors
ΩP 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
- , "Steering apparatus for automobile torpedoes".
- , "Gyroscopic control apparatus".
- , "Mechanical speed governor".
- , "Steering mechanism for torpedoes".
- , "Governing mechanism for turbines".
- , "Electrical apparatus".
- , "Meter".
- , "Electric top for gyroscopes".
- , "Gyroscope for torpedo steering mechanism".
- , "Roller bearing car wheel".
- , "Gyroscopic top".
- , "Gyroscope or revolving toy".
- , "Lumber cart".
- , "Vehicle wheel".
- , "Engine-governor and speed-regulator".
- , "Governor for steam engine".
- , "Levelling instrument".
- Reissued
- , "Rate Gyroscope with torsional suspension"
See also
References
- " Gyroscope" by Sándor Kabai, Wolfram Demonstrations
Project.
- " Total Angular Momentum", ScienceWorld
- 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 .
- 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 .
- 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
.
- 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
.
- 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
.
- Wagner JF, "The Machine of Bohnenberger," The
Institute of Navigation
- 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 ..."
- 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
.
- MacKenzie, Donald. 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.
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
- Websites
- Papers
- Lectures