g6 Gyroscope 2of2

7/30/2019 g6 Gyroscope 2of2

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M.KHURRAM JAVED

FAHAD BIN WALEED

WAQAS AHMED

GUL HASSAN NIAZI

GROUP MEMBERS


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AN OVERVIEW

Presenter:MUHAMMAD KHURRAM JAVED

2008-EP-17


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WHAT IS A GYROSCOPE?DEFINITION:

A gyroscope is a device for measuring ormaintaining orientation, based on theprinciples of conservation of angularmomentum.


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A mechanical gyroscope is essentially aspinning wheel or disk whose axle is free totake any orientation. This orientation changesmuch less in response to a given externaltorque than it would without the large angular

momentum associated with the gyroscope'shigh rate of spin.


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Gyroscopic effects are also central to things likeyo-yos and Frisbees.

Gyroscopes can be very perplexing objectsbecause they move in peculiar ways and evenseem to defy gravity . These special propertiesmake gyroscopes extremely important ineverything from your bicycle to the advancednavigation system on the space shuttle.


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The essence of this device is a spinning wheel

on an axle. The device once spinning, tends toresist changes to its orientation due to theangular momentum of the wheel.

Balancing the spinning bicycle wheel


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Gyroscopes have two basic properties:Rigidity and Precession

These properties are defined as follows:1. RIGIDITY: The axis of rotation (spin axis) of

the gyro wheel tends to remain in a fixeddirection in space if no force is applied to it.

2. PRECESSION: The axis of rotation has atendency to turn at a right angle to thedirection of an applied force.


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The fundamental equation describing the behavior of thegyroscope is:

where the vectors and L are, respectively, the torque on thegyroscope and its angular momentum, the scalar I is itsmoment of inertia, the vector is its angular velocity, andthe vector is its angular acceleration.

It follows from this that a torque applied perpendicular to theaxis of rotation, and therefore perpendicular to L, results ina rotation about an axis perpendicular to both and L. Thismotion is called precession . The angular velocity ofprecession w P is given by the cross product:

T= w p X l


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Thus if the gyroscope's spin slows down (forexample, due to friction), its angular

momentum decreases and so the rate ofprecession increases. This continues until thedevice is unable to rotate fast enough tosupport its own weight, when it stops

precessing and falls off its support, mostlybecause friction against precession causeanother precession that goes to cause the fall.


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By convention, these three vectors, torque, spin,and precession, are all oriented with respect to

each other according to the right-hand rule.


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Let's look at two small sections of thegyroscope as it is rotating -- the top and thebottom, like this:


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When the force is applied to the axle, thesection at the top of the gyroscope will try tomove to the left, and the section at the bottomof the gyroscope will try to move to the right.By Newton's first law of motion, the top pointon the gyroscope is acted on by the forceapplied to the axle and begins to move towardthe left. It continues trying to move leftwardbecause of Newton's first law of motion, but

the gyro's spinning rotates it, like this:


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This effect is the cause of precession . The

different sections of the gyroscope receiveforces at one point but then rotate to newpositions! When the section at the top of thegyro rotates 90 degrees to the side, it continues

in its desire to move to the left. These forcesrotate the wheel in the precession direction. Asthe identified points continue to rotate 90 moredegrees, their original motions are cancelled. Sothe gyroscope's axle hangs in the air andprecesses.


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When the propeller rotates in anti-clockwisedirection &:

1. The aeroplane takes a right turn, thegyroscope will raise the nose and dip the tail.

2. The aeroplane takes a left turn, the gyroscopewill dip the nose and raise the tail.


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STEERING:Steering is the turning of the complete ship in a curve

towards left or right, while it moves forward.

PITCHING:Pitching is the movement of thecomplete ship up & down in avertical plane.

ROLLING:In rolling, the axis of precision is always parallel to the

axis of spin for all positions.


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PRESENTER:

WAQAS AHMED2008-EP-10


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Consider the four wheels A, B, C and D of anautomobile locomotive taking a turn towards leftin Fig. The wheels A and C are inner wheels, whereasB and D are outer wheels. The centre of gravity (C.G.)

of the vehicle lies vertically above the road surface.


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Let m = Mass of the vehicle in kg,W = Weight of the vehicle in newtons = m.g,r W = Radius of the wheels in metres,R = Radius of curvature in metres(R > r W ),

h = Distance of centre of gravity, verticallyabove the road surface in metres,x = Width of track in metres,I W = Mass moment of inertia of one of the

wheels in kg-m2,W = Angular velocity of the wheels or velocityof spin in rad/s,


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IE = Mass moment of inertia of the rotatingparts of the engine in kg-m2,E = Angular velocity of the rotating parts ofthe engine in rad/s,G = Gear ratio = E / W,v = Linear velocity of the vehicle in m/s =W.rW


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A little consideration will show,that the weight of the vehicle ( W) will beequally distributed over the four wheelswhich will act downwards. The reactionbetween each wheel and the road surface

of the same magnitude will act upwards.ThereforeRoad reaction over each wheel= W/4 = m.g /4 newtons

Let us now consider the effect ofthe gyroscopic couple and centrifugal couple on the

vehicle


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Since the vehicle takes a turn towards left dueto the precession and other rotating parts,therefore a gyroscopic couple will act.

Net gyroscopic couple,C = C W C E = 4 I W . W . P I E.G. W . P= W. P (4 I W G.I e )


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The positive sign is used when the wheels and rotating parts of the engine rotate in the same

direction. If the rotating parts of the enginerevolves in opposite direction, then negativesign is used.

When C E > C W , then C will be ve. Thus the reactionwill be vertically downwards on the outer wheels

and vertically upwards on the inner wheels


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Since the vehicle moves along a curved path,therefore centrifugal force will act outwardly at

the centre of gravity of the vehicle. The effect of

this centrifugal force is also to overturn thevehicle.

We know that centrifugal force,

Fc = (m x v2

) / R


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Total vertical reaction at each of the outer wheel

And total vertical reaction at each of the innerwheel


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Presenter:

MUHAMMAD FAHAD BIN WALEED2008-EP-18


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Letm = Mass of the vehicle and its

rider in kg,

W = Weight of the vehicle and its rider in newtons = m.g,h = Height of the centre of gravity of the vehicle and rider,r W = Radius of the wheels,R = Radius of track or curvature,

I W = Mass moment of inertia of each wheel,I E = Mass moment of inertia of the rotating parts of the engine,W = Angular velocity of the wheels,E = Angular velocity of the engine,

G = Gear ratio = E / W ,v = Linear velocity of the vehicle = W r W , = Angle of heel. It is inclination of the vehicle to thevertical for equilibrium.


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We know that

And


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Total

and velocity of precession ,

When the wheels move over the curved path, the vehicle is

always inclined at an angle with the vertical plane asshown in Fig. This angle is known as

angle of heel.


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Notes :(a) When the engine is rotating in the same direction as that of wheels,then the positive sign is used in the above expression and if the enginerotates in opposite direction, then negative sign is used.

(b) The gyroscopic couple will act over the vehicle outwards i.e. in theanticlockwise direction when seen from the front of the vehicle. Thetendency of this couple is to overturn the vehicle in outwarddirection.

Gyroscopic couple


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Centrifugal force ,

Centrifugal Couple ,


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Total overturning couple,

C O = Gyroscopic couple + Centrifugal couple

We know that balancing couple = m.g.h sin

As the stability, the overturning couple must be equal to thebalancing couple, i.e

From this expression, the value of the angle of heel () may be

determined.


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Example

Find the angle of inclination with respect to thevertical of a two wheeler negotiating a turn.Given : combined mass of the vehicle with itsrider 250 kg ; moment of inertia of the engineflywheel 0.3 kg-m2 ; moment of inertia of eachroad wheel 1 kg-m2 ; speed of engine flywheel 5times that of road wheels and in the same

direction ; height of centre of gravity of rider withvehicle 0.6 m ; two wheeler speed 90 km/h ; wheelradius 300 mm ; radius of turn 50 m.


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Presented by Gul Hassan Khan2008-EPK-19


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Gyroscopic effects are also central to things likeyo-yos and Frisbees.


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A gyrocompass is similar to a gyroscope. It is acompass that finds true north by using an(electrically powered) fast-spinning wheel andfriction forces in order to exploit the rotation of theEarth. Gyrocompasses are widely used on ships.They have two main advantages over magneticcompasses:

1. They find true north, i.e., the direction of Earth'srotational axis, as opposed to magnetic north.2. They are far less susceptible to external magnetic

fields, e.g. those created by ferrous metal in a

ship's hull.


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Applications of gyroscopes include navigation(INS) when magnetic compasses do not work, forthe stabilization of flying vehicles like Radio-controlled helicopters or UAVs.

In an INS, sensors on the gimbals axles detectwhen the platform rotates. The INS uses thosesignals to understand the vehicle's rotationsrelative to the platform. If you add to the platforma set of three sensitive accelerometers, you can tell

exactly where the vehicle is heading and how itsmotion is changing in all three directions. With thisinformation, an airplane's autopilot can keep theplane on course, and a rocket's guidance systemcan insert the rocket into a desired orbit.


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A typical airplane uses gyroscopes ineverything from its compass to its autopilot.

The Russian Mir space station used 11gyroscopes to keep its orientation to the sun,and the Hubble Space Telescope has a batch ofnavigational gyros as well.


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g6 Gyroscope 2of2