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A four-bar linkage or simply a 4-bar orfour-bar is the simplest movable linkage. Itconsists of four rigid bodies (called bars or links), each attached to two others by singlejoints orpivots to form a closed loop.
Four-bars are simple mechanisms common in mechanical engineeringmachinedesign
and fall under the study ofkinematics.If each joint has one rotationaldegree of freedom(i.e., it is a pivot), then the mechanismis usuallyplanar, and the 4-bar is determinate if the positions of any two bodies areknown (although there may be two solutions). One body typically does not move (calledthe ground link, fixed link, or the frame), so the position of only one other body isneeded to find all positions. The two links connected to the ground link are calledgrounded links. The remaining link, not directly connected to the ground link, is calledthe coupler link. In terms of mechanical action, one of the grounded links is selected tobe the input link, i.e., the link to which an external force is applied to rotate it. Thesecond grounded link is called the follower link, since its motion is completely
determined by the motion of the input link.Planar four-bar linkages perform a wide variety of motions with a few simple parts. Theywere also popular in the past due to the ease of calculations, prior to computers,compared to more complicated mechanisms.
Grashof's law is applied to pinned linkages and states; The sum of the shortest andlongest link of a planar four-bar linkage cannot be greater than the sum of remainingtwo links if there is to be continuous relative motion between the links. Below are thepossible types of pinned, four-bar linkages;
Types of four-bar linkages,s = shortest link,= longest link
Contents
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[hide]
1 Notale four-bar linkages 2 See also 3 References
4 External links
[edit] Notable four-bar linkages
If the input link may rotate full 360 degrees, it is called a crank. The linkage iscalled a crank-rocker if the input link is a crank and the opposite link is a rocker.If the opposite link is also a crank the linkage is called a double-crank.
Pantograph (four-bar, two degrees of freedom, i.e., only one pivot joint is fixed.) Crank-slider, (four-bar, one degree of freedom) Double wishbone suspension Chebyshev linkage (straight-line four-bar linkage) Biological linkages
[edit] See also
Linkage (mechanical) Cognate linkage
Burmester theory
Glider (furniture)
[edit] References
[edit] External links
mechanisms101.com Flash Four-bar Linkages simulator softintegration.com Animated GIF Four-bar linkage with triangular coupler link Kinematic Models for Design Digital Library (KMODDL)
Movies and photos of hundreds of working mechanical-systems models at Cornell
University. Also includes an e-book library of classic texts on mechanical designand engineering.
Retrieved from "http://en.wikipedia.org/wiki/Four-bar_linkage"Categories: Kinematics| Linkages
A mechanical linkage is a series of rigid links connected with joints to form a closedchain, or a series of closed chains. Each link has two or more joints, and the joints have
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constrained to a particular motion, to act as aleverto move the boulder. When more linksare added and joined in various ways their collective motion can be further defined. Verycomplicated and precise motions can be designed into a linkage with only a few parts.
The Industrial Revolution was the golden age of mechanical linkages. Mathematical,
engineering and manufacturing advances provided both the need and the ability to createnew mechanisms. Many simple mechanisms that seem obvious today required some ofthe greatest minds of the era to create.Leonhard Eulerwas one of the firstmathematicians to study linkage synthesis, and James Watt worked very hard to inventthe Watt linkageto support his steam engine's piston. Chebyshev worked on mechanicallinkage design for over thirty years, which led to his work onpolynomials.[1] New linkageinventions, designed by need, were instrumental in cloth making, power conversion andspeed regulation. Even the ability of a mechanism to produce accurate linear motion,without a reference guide way, took years to solve.
Scientists, mostly German, Russian and English, have researched this domain over the
last 200 years, so that today most traditional analysis or synthesis problems (e.g. planarmovement) have been solved (see online libraries under External links). Recently,compliant structures have come to the fore.
Electronic technology has replaced many linkage applications taken for granted today,such as mechanical computation, typewriting and machining. However, modern linkagedesign continues to advance, and designs that used to occupy an engineer for days arenow optimized with a computer in seconds.
Even though servomechanismswith digital control are common, and at first glance easyto use, some motion problems (especially for quick and accurate movements) are still
only soluble using linkages and cams.
[edit] Theory
The most common linkages have one degree of freedom, meaning that there is one inputmotion that produces one output motion. Most linkages are also planar, meaning all themotion takes place in one plane. Spatial linkages (non-planar) are more difficult to designand therefore not as common.
Kutzbach-Gruebler's equation is used to calculate the degrees of freedom of linkages. Thenumber of degrees of freedom of a linkage is also called its mobility.
A simplified version of the Kutzbach-Gruebler's equation for planar linkages :
= mobility = degrees of freedom= number of links (including a single ground link)= number of one-degree-of-freedom kinematic pairs (pin or slider joints)
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A more general form of the Kutzbach-Gruebler equation forplanar linkages involving
more complex joints:
Or, forspatial linkages (linkages involving 3D motion):
= mobility (degrees of freedom)= number of links (including a single ground link)= number of total joints, regardless of connectivity or degree-of-freedom
= sum of each joint's individual degree of freedom
The mobility ofhydraulic machinerycan easily be identified by counting the number ofindependently controlled hydraulic cylinders.
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Simple linkages are capable of producing complicated motion.
Types of commonjoints:
Revolute orpin, one DOF rotation. Examples are; bushings, bearings, bolted
joints, rivets and hinges. Prismatic orslider, one or two DOF linear motion. Examples are; linear
bearings, hydraulic cylinders, rollers and pistons. Spherical orball and socket, three DOF rotation, usually restricted to one DOF
by other joints in the mechanism.
Designers will synthesize a linkage by starting with the required output motion,mechanical advantage, velocity and acceleration. A type of linkage is chosen andmodified to deliver the required performance.
Each link is treated as a vector and the vectors can be combined into a system of
equations because they form a loop. The matrix is solved to create a closed form equationthat relates input motion to output motion. The same is done formechanical advantage, orany other important quantity. The equations of motion are differentiated with respect totime to find velocity and acceleration of the mechanism parts.
[edit] Types of linkages
Four-bar linkages are the simplest closed loop kinematic linkage. They perform a widevariety of motions with a few simple parts. They were also popular in the past due to theease of calculations, prior to computers, compared to more complicated mechanisms.
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Parallel and straight line mechanisms:o James Watt'sparallel motion and Watt's linkageo PeaucellierLipkin linkage, the first planar linkage to create a straight line
output from rotary input; eight-bar, one DOF.o A Scott Russell linkage, which converts linear motion, to (almost) linear
motion in a line perpendicular to the input.o Chebyshev linkage, which provides nearly straight motion of a point with
a four-bar linkage.o Hoekens linkage, which provides nearly straight motion of a point with a
four-bar linkage.o Sarrus linkage, which provides motion of one surface in a direction normal
to another.
[edit] Uses
A spatial 3DOF linkage for joystick applications.
Linkages are primarily used as machine components and tools. Typical examples are
automotive suspensionsandbolt cutters. The internal combustion engine'spiston/rod/crank is a classic four-bar linkage with one degree of freedom. Linkages areoften the simplest, least expensive and most efficient mechanism to perform complicatedmotions.
One highly visible application is thewindshield wiper: a four-bar linkage changes themotor's rotary motion to oscillation. Some wipers also have a second set of four-barlinkages to keep the wiper blades oriented correctly as they sweep. Another visibleapplication is heavy equipment which makes extensive use of four and six bar linkages.
Spatial linkages are becoming more common due tocomputer aided design.
The 4-bar linkageis an adapted mechanical linkage used on bicycles. With a normal full-suspension bike the back wheel moves in a very tight arc shape. This means that morepower is lost when going uphill. With a bike fitted with a 4-bar linkage, the wheel movesin such a large arc that it is moving almost vertically. This way the power loss is reducedby up to 30%.
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Scotch yokeFrom Wikipedia, the free encyclopediaJump to: navigation,search
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Comparison of displacement and acceleration for a Scotch Yoke compared with a crankand slider
The Scotch yoke is a mechanism for converting the linear motion of a slider intorotational motion or vice-versa. Thepistonor other reciprocating part is directly coupledto a slidingyoke with a slot that engages a pin on the rotating part. The shape of themotion of the piston is a pure sine wave over time given a constant rotational speed.
Contents
[hide]
1 Advantages 2 Disadvantages 3 Applications 4 References
5 External links
[edit] Advantages
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The advantages compared to a standardcrankshaft and connecting rod setup are:
Fewer moving parts. Smoother operation. Higher percentage of the time spent at top dead center(dwell) improving
theoretical engine efficiency of constant volume combustion cycles, though actualgains have not been demonstrated.[1]
In an engine application, elimination of joint typically served by a wrist pin, andnear elimination of piston skirt and cylinder scuffing, as side loading of piston dueto sine of connecting rod angle is eliminated.
[edit] Disadvantages
The disadvantages are:
Rapid wear of the slot in the yoke caused by sliding friction and high contact
pressures. Increased heat loss during combustion due to extended dwell at top dead center
offsets any constant volume combustion improvements in real engines.[1]
Lesser percentage of the time spent at bottom dead center reducing blowdowntime fortwo stroke engines, when compared with a conventional piston andcrankshaft mechanism.
[edit] Applications
This setup is most commonly used in control valveactuators in high pressureoil and gas
pipelines.It has been used in various internal combustion engines, such as theBourke engine,SyTech engine[2], and many hot air engines and steam engines.
Experiments have shown that extended dwell time will not work well with constantvolume combustion (Otto, Bourke or similar) cycles.[1] Gains might be more apparentusing a stratified direct injection (diesel or similar) cycle to reduce heat losses.[3]
[edit] References
1. ^ abcScience Links Japan | Effect of Piston Speed around Top Dead Center on ThermalEfficiency
2. ^ "The SyTech Scotch Yoke Engine".AutoSpeed.http://www.autospeed.com/cms/A_0948/article.html. Retrieved 2008-07-08.
3. ^ "Effect of the Ratio Between Connecting-rod Length and Crank Radius on ThermalEfficiency".Science Links Japan. http://sciencelinks.jp/j-east/article/200623/000020062306A0851764.php. Retrieved 2008-07-08.
http://en.wikipedia.org/wiki/Crankshafthttp://en.wikipedia.org/wiki/Crankshafthttp://en.wikipedia.org/wiki/Connecting_rodhttp://en.wikipedia.org/wiki/Top_dead_centerhttp://en.wikipedia.org/wiki/Scotch_yoke#cite_note-ref1-0%23cite_note-ref1-0http://en.wikipedia.org/wiki/Scotch_yoke#cite_note-ref1-0%23cite_note-ref1-0http://en.wikipedia.org/w/index.php?title=Scotch_yoke&action=edit§ion=2http://en.wikipedia.org/wiki/Top_dead_centerhttp://en.wikipedia.org/wiki/Scotch_yoke#cite_note-ref1-0%23cite_note-ref1-0http://en.wikipedia.org/wiki/Two_strokehttp://en.wikipedia.org/w/index.php?title=Scotch_yoke&action=edit§ion=3http://en.wikipedia.org/wiki/Actuatorhttp://en.wikipedia.org/wiki/Actuatorhttp://en.wikipedia.org/wiki/Oil_pipeline#Oil_and_natural_gas_pipelineshttp://en.wikipedia.org/wiki/Oil_pipeline#Oil_and_natural_gas_pipelineshttp://en.wikipedia.org/wiki/Oil_pipeline#Oil_and_natural_gas_pipelineshttp://en.wikipedia.org/wiki/Oil_pipeline#Oil_and_natural_gas_pipelineshttp://en.wikipedia.org/wiki/Bourke_enginehttp://en.wikipedia.org/wiki/Bourke_enginehttp://en.wikipedia.org/wiki/Scotch_yoke#cite_note-1%23cite_note-1http://en.wikipedia.org/wiki/Hot_air_enginehttp://en.wikipedia.org/wiki/Steam_enginehttp://en.wikipedia.org/wiki/Scotch_yoke#cite_note-ref1-0%23cite_note-ref1-0http://en.wikipedia.org/wiki/Scotch_yoke#cite_note-2%23cite_note-2http://en.wikipedia.org/w/index.php?title=Scotch_yoke&action=edit§ion=4http://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-ref1_0-0%23cite_ref-ref1_0-0http://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-ref1_0-1%23cite_ref-ref1_0-1http://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-ref1_0-2%23cite_ref-ref1_0-2http://sciencelinks.jp/j-east/article/200609/000020060906A0236528.phphttp://sciencelinks.jp/j-east/article/200609/000020060906A0236528.phphttp://sciencelinks.jp/j-east/article/200609/000020060906A0236528.phphttp://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-1%23cite_ref-1http://www.autospeed.com/cms/A_0948/article.htmlhttp://www.autospeed.com/cms/A_0948/article.htmlhttp://www.autospeed.com/cms/A_0948/article.htmlhttp://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-2%23cite_ref-2http://sciencelinks.jp/j-east/article/200623/000020062306A0851764.phphttp://sciencelinks.jp/j-east/article/200623/000020062306A0851764.phphttp://sciencelinks.jp/j-east/article/200623/000020062306A0851764.phphttp://sciencelinks.jp/j-east/article/200623/000020062306A0851764.php.%20Retrieved%202008-07-08http://sciencelinks.jp/j-east/article/200623/000020062306A0851764.php.%20Retrieved%202008-07-08http://en.wikipedia.org/wiki/Crankshafthttp://en.wikipedia.org/wiki/Connecting_rodhttp://en.wikipedia.org/wiki/Top_dead_centerhttp://en.wikipedia.org/wiki/Scotch_yoke#cite_note-ref1-0%23cite_note-ref1-0http://en.wikipedia.org/w/index.php?title=Scotch_yoke&action=edit§ion=2http://en.wikipedia.org/wiki/Top_dead_centerhttp://en.wikipedia.org/wiki/Scotch_yoke#cite_note-ref1-0%23cite_note-ref1-0http://en.wikipedia.org/wiki/Two_strokehttp://en.wikipedia.org/w/index.php?title=Scotch_yoke&action=edit§ion=3http://en.wikipedia.org/wiki/Actuatorhttp://en.wikipedia.org/wiki/Oil_pipeline#Oil_and_natural_gas_pipelineshttp://en.wikipedia.org/wiki/Oil_pipeline#Oil_and_natural_gas_pipelineshttp://en.wikipedia.org/wiki/Bourke_enginehttp://en.wikipedia.org/wiki/Scotch_yoke#cite_note-1%23cite_note-1http://en.wikipedia.org/wiki/Hot_air_enginehttp://en.wikipedia.org/wiki/Steam_enginehttp://en.wikipedia.org/wiki/Scotch_yoke#cite_note-ref1-0%23cite_note-ref1-0http://en.wikipedia.org/wiki/Scotch_yoke#cite_note-2%23cite_note-2http://en.wikipedia.org/w/index.php?title=Scotch_yoke&action=edit§ion=4http://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-ref1_0-0%23cite_ref-ref1_0-0http://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-ref1_0-1%23cite_ref-ref1_0-1http://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-ref1_0-2%23cite_ref-ref1_0-2http://sciencelinks.jp/j-east/article/200609/000020060906A0236528.phphttp://sciencelinks.jp/j-east/article/200609/000020060906A0236528.phphttp://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-1%23cite_ref-1http://www.autospeed.com/cms/A_0948/article.htmlhttp://www.autospeed.com/cms/A_0948/article.htmlhttp://en.wikipedia.org/wiki/Scotch_yoke#cite_ref-2%23cite_ref-2http://sciencelinks.jp/j-east/article/200623/000020062306A0851764.phphttp://sciencelinks.jp/j-east/article/200623/000020062306A0851764.phphttp://sciencelinks.jp/j-east/article/200623/000020062306A0851764.php.%20Retrieved%202008-07-08http://sciencelinks.jp/j-east/article/200623/000020062306A0851764.php.%20Retrieved%202008-07-08 -
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Inclined planeFrom Wikipedia, the free encyclopediaJump to: navigation,searchThis article is about thephysicalstructure. For other uses, seeInclined plane(disambiguation).
Inclined plane
Roman soldiers constructed an inclined plane out ofearth to
lay siege to theMasada during the First Jewish-Roman War
in 73CE.
Classification Simple machine
Industry Construction
The inclined plane is one of the original six simple machines; as the name suggests, it isa flat surface whose endpoints are at different heights. By moving an object up aninclined plane rather than completely vertical, the amount of force required is reduced, atthe expense of increasing the distance the object must travel. The mechanical advantageof an inclined plane is the ratio of the length of the sloped surface to the height it spans;this may also be expressed as thecosecant of the angle between the plane and thehorizontal. Note that due to the conservation of energy, the same amount ofmechanicalenergy is required to lift a given object by a given distance, except for losses fromfriction, but the inclined plane allows the same work to be done with a smaller forceexerted over a greater distance
Calculation of forces acting on an object on an inclined
plane
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Key:N =Normal force that is perpendicular to the planem = Mass of objectg = Acceleration due to gravity (theta) = Angle of elevation of the plane, measured from the horizontalf= frictional force of the inclined plane
To calculate the forces on an object placed on an inclined plane, consider the three forcesacting on it.
1. The normal force(N) exerted on the body by the plane due to the force ofgravityi.e. mg cos
2. the force due to gravity (mg, acting vertically downwards) and3. the frictional force(f) acting parallel to the plane.
We can decompose the gravitational force into two vectors, one perpendicular to the
plane and one parallel to the plane. Since there is no movement perpendicular to theplane, the component of the gravitational force in this direction (mgcos ) must be equaland opposite to normal force exerted by the plane,N. If the remaining component of thegravitational force parallel to the surface (mgsin ) is greater than the static frictionalforcefs then the body will slide down the inclined plane with acceleration (gsin fk/m), wherefk is the kinetic friction force otherwise it will remain stationary.
When the slope angle () is zero, sin is also zero so the body does not move.
The MA or Mechanical advantage(ratio of load to effort) of the inclined plane equals tolength of the plane over the height of the plane, in an ideal case where efficiency is
100%.
Learning Objectives / Experiments
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Comparative determination of inertia of rotation byrolling down an inclined plane and by performingpendulum experimentsTechnical Description
This benchtop unit enables basic experiments to be performed ondynamics and is ideal for laboratory experiments. A metal carrier with athree point support is used as an inclined plane for the experiment; thedifferent rotating masses are rolled down this plane. The inclined planecan be precisely aligned using two integrated sprit levels and three bolts.The angle of inclination is adjusted using an adjustment bolt and isindicated by the built-in inclinometer. The inclinometer uses the plumbline principle. A 1000mm ruler is integrated directly into the inclined planefor measuring the travel. The steel rotating masses each have selfcenteringconical pins. Using a separate pendulum block the moment ofinertia of the rotating masses can be determined by swinging.Learning Objectives / Experiments- Demonstration of the law of gravity on an inclined plane- Influence of the mass of a body on its acceleration- Determination of the moment of inertia on rotating masses by
performing a rolling test- Determination of the moment of inertia by performing a pendulum test- Influence of the moment of inertia of a rotating mass on its angularaccelerationScope of Delivery1 inclined plane base, 1 pendulum block, 2 rotating mass discs,1 instruction manualSpecification[1] Experiments on the law of gravity on an inclinedplane and on the angular acceleration of discs[2] Plane 1000mm, adjustable[3] Three spirit levels, three alignment bolts[4] 2 rotating discs with self-centering conical pins
[5] l x w x h 1200x300x280mm
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Summary: Rolling along an incline is an accelerated rolling due to the force of gravityacting through center of mass.
An incline is an ideal arrangement to realize accelerated rolling motion. Force due togravity acts through the center of mass of the rolling body. Component of gravity parallelto incline accelerates the body in translation as it goes down and decelerates the body asit goes up the incline.
We have already discussed the case of force, whose line of action pass through center ofmass. For rolling of the body, the friction between rolling body and surface appears suchthat the condition as laid down by equation of accelerated rolling is satisfied. When abody rolls down, it has linear acceleration in downward direction. The friction, therefore,acts upward to counter sliding tendency as shown in the figure. This friction constitutesan anticlockwise torque providing the corresponding angular acceleration as required formaintaining the condition of rolling (if linear velocity is increasing, then angular velocityshould also increase according to equation of accelerated rolling).
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GyroscopeFrom Wikipedia, the free encyclopediaJump to: navigation,searchFor other uses and non-rotary gyroscopes, see Gyroscope (disambiguation). For theAustralian rock band Gyroscope, see Gyroscope (band).
A gyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principlesofconservation of angular momentum.[1] A mechanical gyroscope is essentially aspinningwheel or disk whose axle is free to take any orientation. This orientationchanges much less in response to a given externaltorquethan it would without the largeangular momentum associated with the gyroscope's high rate of spin. Since externaltorque is minimized by mounting the device in gimbals, its orientation remains nearlyfixed, regardless of any motion of the platform on which it is mounted.
Gyroscopes based on other operating principles also exist, such as the electronic,
microchip-packaged MEMS gyroscope devices found in consumer electronic devices,solid state ring lasers, fibre optic gyroscopes and the extremely sensitivequantumgyroscope.
Applications of gyroscopes include navigation (INS) when magnetic compasses do notwork (as in the Hubble telescope) or are not precise enough (as in ICBMs) or for thestabilization of flying vehicles likeradio-controlled helicopters orUAVs. Due to theirhigh precision, gyroscopes are also used to maintain direction in tunnel mining.[2]
Description and diagram
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Diagram of a gyro wheel. Reaction arrows about the output axis (blue) correspond toforces applied about the input axis (green), and vice versa.
Within mechanical systems or devices, a conventionalgyroscope is a mechanismcomprising a rotorjournalled to spin about oneaxis, thejournalsof the rotor beingmounted in an innergimbal or ring, the inner gimbal is journalled for oscillation in anouter gimbal which is journalled in another gimbal for a total of three gimbals.
The outer gimbal or ring which is the gyroscope frame is mounted so as to pivot aboutan axis in its own plane determined by the support. This outer gimbal possesses onedegree of rotational freedom and its axis possesses none. The next inner gimbal ismounted in the gyroscope frame (outer gimbal) so as to pivot about an axis in its ownplane that is alwaysperpendicularto the pivotal axis of the gyroscope frame (outergimbal). This inner gimbal has two degrees of rotational freedom. Similarly, nextinnermost gimbal is attached to the inner gimbal which has three degrees of rotationalfreedom and its axis possesses two.
The axle of the spinning wheel defines the spin axis. The rotor is journaled to spin aboutan axis which is always perpendicular to the axis of the innermost gimbal. So, the rotorpossesses four degrees of rotational freedom and its axis possesses three. The wheelresponds 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 thefront wheel of a bicycle. If the wheel is leaned away from the vertical so that the top ofthe wheel moves to the left, the forward rim of the wheel also turns to the left. In otherwords, 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 whetherthe 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.
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Animation of a gyro wheel in action
The centre of gravity of the rotor can be in a fixed position. The rotor simultaneouslyspins 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 aboutthe fixed point. Some gyroscopes have mechanical equivalents substituted for one ormore of the elements, e.g., the spinning rotor may be suspended in a fluid, instead ofbeing pivotally mounted in gimbals. A control moment gyroscope (CMG) is an exampleof a fixed-output-gimbal device that is used on spacecraft to hold or maintain a desiredattitude angle or pointing direction using the gyroscopic resistance force.
In some special cases, the outer gimbal (or its equivalent) may be omitted so that therotor has only two degrees of freedom. In other cases, the centre of gravity of the rotormay be offset from the axis of oscillation and thus the centre of gravity of the rotor andthe centre of suspension of the rotor may not coincide.
[edit] History
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Gyroscope invented by Lon Foucault in 1852. Replica built by Dumoulin-Froment forthe Exposition universelle in 1867. National Conservatory of Arts and Crafts museum,Paris.
The earliest known gyroscope-like instrument was made by German Johann
Bohnenberger, who first wrote about it in 1817. At first he called it the "Machine".[3][4]
Bohnenberger's machine was based on a rotating massive sphere.[5]In 1832, AmericanWalter R. Johnson developed a similar device that was based on a rotating disk.[6][7] TheFrench mathematician Pierre-Simon Laplace, working at the cole Polytechnique inParis, recommended the machine for use as a teaching aid, and thus it came to theattention ofLon Foucault.[8] In 1852, Foucault used it in an experiment involving therotation of the Earth.[9][10] It was Foucault who gave the device its modern name, in anexperiment to see (Greekskopeein, to see) the Earth's rotation (Greekgyros, circle orrotation), which was visible in the 8 to 10 minutes before friction slowed the spinningrotor.
In the 1860s, electric motors made the concept usable, leading to the first prototypegyrocompasses; the first functional marine gyrocompass was patented in 1908 byGerman inventorHermann Anschtz-Kaempfe. The AmericanElmer Sperry followedwith his own design later that year, and other nations soon realized the militaryimportance of the inventionin an age in which naval prowess was the most significantmeasure of military powerand created their own gyroscope industries. The SperryGyroscope Company quickly expanded to provide aircraft and naval stabilizers as well,and other gyroscope developers followed suit.[11]
In 1917, the Chandler Company ofIndianapolis, Indiana, created the "Chandlergyroscope", a toy gyroscope with a pull string and pedestal. Chandler continued to
produce the toy until the company was purchased by TEDCO inc. in 1982. The chandlertoy is still produced by TEDCO today.[12]
In the first several decades of the 20th century, other inventors attempted(unsuccessfully) to use gyroscopes as the basis for earlyblack box navigational systemsby creating a stable platform from which accurate acceleration measurements could beperformed (in order to bypass the need for star sightings to calculate position). Similarprinciples were later employed in the development ofinertial guidance systems forballistic missiles.[13]
During World War Two, the gyroscope became the prime component for aircraft andanti-aircraft gun sights.[14]
[edit] Properties
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A gyroscope in operation with freedom in all three axes. The rotor will maintain its spinaxis direction regardless of the orientation of the outer frame.
A gyroscope exhibits a number of behaviours includingprecession and nutation.
Gyroscopes can be used to construct gyrocompasseswhich complement or replacemagnetic compasses (inships,aircraft and spacecraft, vehiclesin general), to assist instability (Hubble Space Telescope,bicycles,motorcycles, andships) or be used as part ofaninertial guidance system. Gyroscopic effects are used in tops,boomerangs, yo-yos, andPowerballs. Many other rotating devices, such as flywheels, behave gyroscopicallyalthough the gyroscopic effect is not being used.
The fundamental equation describing the behavior of the gyroscope is:
where the vectors and L are, respectively, the torque on the gyroscope and its angularmomentum, the scalarIis its moment of inertia, the vector is its angular velocity, andthe vector is its angular acceleration.
It follows from this that a torque applied perpendicular to the axis of rotation, andtherefore perpendicular to L, results in a rotation about an axis perpendicular to both and L. This motion is calledprecession. The angular velocity of precession P is givenby the cross product:
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Precession on a gyroscope
Precession can be demonstrated by placing a spinning gyroscope with its axis horizontaland 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 axishorizontal, when the other end of the axis is left unsupported and the free end of the axisslowly describes a circle in a horizontal plane, the resulting precession turning. Thiseffect is explained by the above equations. The torque on the gyroscope is supplied by acouple of forces: gravity acting downwards on the device's centre of mass, and an equalforce acting upwards to support one end of the device. The rotation resulting from thistorque is not downwards, as might be intuitively expected, causing the device to fall, butperpendicular to both the gravitational torque (horizontal and perpendicular to the axis ofrotation) 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 , the gyroscope's speed of precession P isinversely proportional toL, the magnitude of its angular momentum:
where is the angle between the vectors P and L. Thus if the gyroscope's spin slowsdown (for example, due to friction), its angular momentum decreases and so the rate ofprecession increases. This continues until the device is unable to rotate fast enough tosupport its own weight, when it stops precessing and falls off its support, mostly becausefriction against precession cause another precession that goes to cause the fall.
By convention, these three vectors, torque, spin, and precession, are all oriented withrespect to each other according to the right-hand rule.
To easily ascertain the direction of gyro effect, simply remember that a rolling wheeltends, when it leans to the side, to turn in the direction of the lean.
[edit] Variations
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[edit] Gyrostat
A gyrostat is a variant of the gyroscope. It consists of a massive flywheel concealed in asolid 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. The firstgyrostat was designed by Lord Kelvin to illustrate the more complicated state of motionof a spinning body when free to wander about on a horizontal plane, like a top spun onthe pavement, or a hoop or bicycle on the road.
[edit] MEMS
A MEMS gyroscopetakes the idea of the Foucault pendulumand uses a vibratingelement, known as a MEMS(Micro Electro-Mechanical System). The MEMS-based gyrowas initially made practical and producible by Systron Donner Inertial(SDI). Today, SDIis a large manufacturer of MEMS gyroscopes.
[edit] FOG
A fiber optic gyroscope (FOG) is a gyroscope that uses the interference of light to detectmechanical rotation. The sensor is a coil of as much as 5 km of optical fiber. Thedevelopment of low loss single mode optical fiber in the early 1970s for thetelecommunications industry enabled the development ofSagnac effect fiber optic gyros.
[edit] VSG or CVG
A vibrating structure gyroscope(VSG), also called a coriolis vibratory gyroscope
(CVG),[15] uses a resonator made of different metallic alloys. It takes a position betweenthe low accuracy, low costMEMS gyroscopeand the higher accuracy and higher costfiber optic gyroscope (FOG). Accuracy parameters are increased by using low intrinsicdamping materials, resonator vacuumization, and digital electronics to reducetemperature dependent drift and instability of control signals.[16]
High-Q Wine-Glass Resonators for precise sensors like HRG [17] or CRG[18] are based onBryan's "wave inertia effect". They are made from high-purity quartz glass or fromsingle-crystalline sapphire.
[edit] DTG
A dynamically tuned gyroscope (DTG) is a rotor suspended by a universal joint withflexure pivots.[19] The flexure spring stiffness is independent of spin rate. However, thedynamic inertia (from the gyroscopic reaction effect) from the gimbal provides negativespring 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 twomoments cancel each other, freeing the rotor from torque, a necessary condition for anideal gyroscope.
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[edit] London moment
A London momentgyroscope relies on the quantum-mechanicalphenomenon whereby aspinningsuperconductorgenerates a magnetic field whoseaxis lines up exactly with thespin axis of the gyroscopic rotor. A magnetometerdetermines the orientation of thegenerated field, which is interpolatedto determine the axis of rotation. Gyroscopes of this
type can be extremely accurate and stable, for example those used in the Gravity Probe Bexperiment measured changes in gyroscope spin axis orientation to better than 0.5milliarcseconds(1.4107degrees) over a one-year period.[20] This is equivalent to anangular separationthe width of ahuman hairviewed from 32 kilometers (20 miles) away.[21]
The GP-B gyro consists of a nearly-perfectsphericalrotating massmade offused quartzwhich provides a dielectric support for a thin layer ofniobiumsuperconducting material.To eliminate friction found in conventional mechanical bearings, the rotor assembly issuspended by six electromagnets that form a magnetic bearing. After the initial spin-upby ajet ofhelium brings the rotor to 4,000 RPM, the polished gyroscope housing is
evacuated to aultra-high vacuum to further reduce dragon the rotor. Provided thesuspension electronics remain powered, the extremerotational symmetry, lack of friction,and low drag will allow the angular momentumof the rotor to keep it spinning for about15,000 years. [22]
A sensitive DC SQUID magnetometer able to discriminate changes as small as onequantum, or about 2 1015Wb, is used to monitor the gyroscope. A precesses, or tilt, inthe orientation of the rotor causes the London moment magnetic fieldto shift relative tothe housing. The moving field passes through a superconductingpickup loop fixed to thehousing, inducing a small electric current. The current produces a voltage across ashuntresistance, which is resolved tospherical coordinatesby amicroprocessor. The system is
designed to minimize Lorentztorqueon the rotor.[23]
[edit] Modern uses
In addition to being used in compasses, aircraft, computer pointing devices, etc.,gyroscopes have been introduced into consumer electronics. Since the gyroscope allowsthe calculation of orientation and rotation, designers have incorporated them into moderntechnology. The integration of the gyroscope has allowed for more accurate recognitionof movement within a 3D space than the previous lone accelerometer within a number ofsmartphones. Scott Steinberg, known for his critiques on newly released technology, saysthat the new addition of the gyroscope in the iPhone 4may "completely redefine the waywe interact with downloadable apps".[24]
Nintendo also has integrated the gyroscope into the Wiiconsole's Wii Remote device byan additional piece of hardware called "Wii MotionPlus". With the ability to simulate amore precise 1:1 representation in 3D space in relation to the simulation within the game,the added gyroscope has allowed Nintendo to create more motion intensive games. [25]
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