The document discusses gyroscopes and their operation. It explains that a gyroscope uses angular momentum to detect or maintain orientation. It consists of a spinning mass mounted on an axle. Mechanical gyroscopes use a spinning mass mounted on gimbals, while electronic gyroscopes use a vibrating proof mass. Common applications include gyrocompasses, guidance systems, bicycles, and more. The document also discusses gyroscopic couples and their effects on ships, airplanes, and vehicles in terms of pitching, rolling, and steering movements.

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2. Gyroscope
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What is a gyroscope?
 Device used to measure or
maintain orientation
 Works on the principals of
angular momentum
 Initial axis of rotation is
conserved
 Consists of a spinning mass
on an axel

4. How Gyroscopes Work
Mechanical Gyroscope
 Spinning mass mounted on gimbals
 Free-output vs. Fixed-output
 Sensors on axis to detect rotation
 Procession
Electronic Gyroscope
 Coriolis vibratory gyroscope
 Proof mass fed oscillating current to induce vibrations
 Vibrating mass tends to oscillate in initial plane of reference
 When rotated, oscillations in orthogonal plane detected by
circuitry
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5. Common Uses
 Gyrocompass
 Used by ships to find true north
 Seeks minimum potential energy
 Stability Assistance
 Hubble Space Telescope
 Bicycles
 Inertial Guidance System
 Guided Missiles
 Measure angular velocity in inertial reference frame
 Detect changes to orientation
 Combined with accelerometer for 6 axis sensor
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6. Angular Momentum
 What is the time derivative of the angular momentum
about the pivot point for the gyroscope?

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7. Gyroscopic couples
Consider a disc spinning
with an angular velocity ω
rad/s about the axis of spin
OX, in anticlockwise
direction when seen from
the front, as shown in Fig.
Since the plane in which
the disc is rotating is
parallel to the plane YOZ,
therefore it is called plane
of spinning.
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8. Gyroscopic stabilization
 Effect of the Gyroscopic Couple on an Aero plane
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9. Continue…
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10. Terms Used in a Naval Ship
 The top and front views of a naval ship are shown in Fig. The
fore end of the ship is
 called bow and the rear end is known as stern or aft. The left
hand and right hand sides of the ship,
 when viewed from the stern are called port and star-board
respectively. We shall now discuss the
effect of gyroscopic couple on the naval ship in the following
three cases:
1. Steering, 2. Pitching, and 3. Rolling.
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11. Continue…
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12. Effect of Gyroscopic Couple on a
Naval Ship during Steering
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Fig - Naval ship taking a left turn.

13. The effect of this reactive gyroscopic couple is
to raise the bow and lower the stern.
1. The effect of this reactive gyroscopic couple is to raise the
bow and lower the stern.
2. When the rotor rates in the anticlockwise direction, when
viewed from the stern and the ship is steering to the left, then
the effect of reactive gyroscopic couple will be to lower the
bow and raise the stern.
3. When the ship is steering to the right under similar conditions
as discussed in note 2 above, then the effect of reactive
gyroscopic couple will be to raise the bow and lower the
stern.
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14. Effect of gyroscopic couple on a
naval ship during pitching
Pitching is the movement of a complete ship up and down in a
vertical plane about transverse axis, as shown in Fig
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Fig- Effect of gyroscopic couple on a naval ship during pitching.

15. Stability of a four wheel drive
moving in a curved path
 Consider the four wheels A, B, C and D of an automobile locomotive
taking a sturn towards left as shown in Fig.
 The wheels A and C are inner wheels, whereas B and D are outer
wheels.
 The centre of gravity (C.G.) of the vehicle lies vertically above
Let m = Mass of the vehicle in kg,
W = Weight of the vehicle in Newton = m.g,
rW = Radius of the wheels in meters,
R = Radius of curvature in metres the road surface.
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16. Continue…
h = Distance of centre of gravity, vertically
above the road surface in metres,
x = Width of track in metres,
IW = Mass moment of inertia of one of the
wheels in kg-m2,
ωW = Angular velocity of the wheels or velocity
of spin in rad/s,
IE = Mass moment of inertia of the rotating
parts of the engine in kg-m2,
ωE = Angular velocity of the rotating parts of
the engine in rad/s,
G = Gear ratio = ωE /ωW,
v = Linear velocity of the vehicle in m/s = ωW.rW
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17. Effect of the gyroscopic couple on
4wheel drive
We know that velocity of precession,
ωP = v/R
∴ Gyroscopic couple due to 4 wheels,
CW = 4 IW.ωW.ωP
and gyroscopic couple due to the rotating parts of the engine,
CE = IE.ωE.ωP = IE.G.ωW.ωP
∴ Net gyroscopic couple,
C = CW ± CE = 4 IW.ωW.ωP ± IE.G.ωW.ωP
= ωW.ωP (4 IW ± G.IE)
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 engine revolves in opposite direction, then
negative sign is used.
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18. Vibration
 Vibration: When elastic bodies such as a spring, a beam
and a shaft are displaced from the equilibrium position by
the application of external forces, and then released, the
execute a vibratory motion.
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19. Types of vibratory motion
 1. Free or natural vibrations. When no external force acts on
the body, after giving it an initial displacement, then the body is
said to be under free or natural vibrations. The frequency of the
free vibrations is called free or natural frequency.
 2. Forced vibrations. When the body vibrates under the
influence of external force, then the body is said to be under
forced vibrations.
 3. Damped vibrations. When there is a reduction in amplitude
over every cycle of vibration,
 the motion is said to be damped vibration.
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20. Types of free vibrations
1. Longitudinal vibrations,
2. Transverse vibrations,
and
3. Torsional vibrations.
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21. Free vibration
 When a system is initially disturbed by a displacement,
velocity or acceleration, the system begins to vibrate with a
constant amplitude and frequency depend on its stiffness and
mass.
 This frequency is called as natural frequency, and the form of
the vibration is called as mode shapes
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Single degree free and damped
vibration.
 Single degree free and
damped vibration. If the
coordinates x and y are used
to describe the motion, it
must be recognized that
these coordinates are not
independent.

23. Two degree of freedom freedom
system
 Some examples of two degree of
freedom systems are shown in the
figure. The first figure shows a two
mass – two spring system that is
described by two linear
coordinates x1 and x2. The second
figure denotes a two rotor system
whose motion can be specified in
terms of θ1 and θ2. The motion of
the system in the third figure can
be described completely either by
X and θ or by x, y and X.
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24. Whirling of shaft
In actual practice, a rotating shaft carries different
mountings and accessories in the form of gears, pulleys,
etc.
When the gears or pulleys are put on the shaft, the centre
of gravity of the pulley or gear does not coincide with the
centre line of the bearings or with the axis of the shaft,
when the shaft is stationary.
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Critical speed.
The speed at which the shaft runs so that the additional
deflection of the shaft from the axis of rotation becomes
infinite, is known as critical or whirling speed.
Fig- Critical or whirling speed of a shaft.

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