PPT: Gyroscopic Motion | Theory of Machines (TOM) - Mechanical Engineering PDF Download

 Page 1


• Gyroscope is a mechanical system or arrangement having a
rotor(usually heavy) spinning at high speed about its axis and being
free to turn in any direction.
Page 2


• Gyroscope is a mechanical system or arrangement having a
rotor(usually heavy) spinning at high speed about its axis and being
free to turn in any direction.
Principle of Gyroscope :
Whenever a body is rotating in a plane(plane YZ) about an axis(axis
Ox) and a couple is applied on the rotating body across the axis of
rotation or spin in an another perpendicular plane(plane XY), the
rotating or spinning body starts processing in a third mutually
perpendicular plane(plane XZ).
Page 3


• Gyroscope is a mechanical system or arrangement having a
rotor(usually heavy) spinning at high speed about its axis and being
free to turn in any direction.
Principle of Gyroscope :
Whenever a body is rotating in a plane(plane YZ) about an axis(axis
Ox) and a couple is applied on the rotating body across the axis of
rotation or spin in an another perpendicular plane(plane XY), the
rotating or spinning body starts processing in a third mutually
perpendicular plane(plane XZ).
Applications of Gyroscope
? Computer Pointing Devices
? Gyroscopic behaviour is used in the racing car industry.
This is because car engines act just like big gyroscopes.
? Wheels on motorbikes act as gyroscopes and make the
bike easier to balance (stay up right) when moving.
? Ship stabilisers
Page 4


• Gyroscope is a mechanical system or arrangement having a
rotor(usually heavy) spinning at high speed about its axis and being
free to turn in any direction.
Principle of Gyroscope :
Whenever a body is rotating in a plane(plane YZ) about an axis(axis
Ox) and a couple is applied on the rotating body across the axis of
rotation or spin in an another perpendicular plane(plane XY), the
rotating or spinning body starts processing in a third mutually
perpendicular plane(plane XZ).
Applications of Gyroscope
? Computer Pointing Devices
? Gyroscopic behaviour is used in the racing car industry.
This is because car engines act just like big gyroscopes.
? Wheels on motorbikes act as gyroscopes and make the
bike easier to balance (stay up right) when moving.
? Ship stabilisers
Precessional Angular Motion
(Vectorial representation of angular motion)
• We know that the angular acceleration is the rate of change of
angular velocity with respect to time.
• It is a vector quantity and may be represented by drawing a vector
diagram with the help of right hand screw rule.
• Consider a disc, as shown in Fig. (a), revolving or spinning about the
axis OX (known as axis of spin) in anticlockwise when seen from the
front, with an angular velocity in a plane at right angles to the paper .
Page 5


• Gyroscope is a mechanical system or arrangement having a
rotor(usually heavy) spinning at high speed about its axis and being
free to turn in any direction.
Principle of Gyroscope :
Whenever a body is rotating in a plane(plane YZ) about an axis(axis
Ox) and a couple is applied on the rotating body across the axis of
rotation or spin in an another perpendicular plane(plane XY), the
rotating or spinning body starts processing in a third mutually
perpendicular plane(plane XZ).
Applications of Gyroscope
? Computer Pointing Devices
? Gyroscopic behaviour is used in the racing car industry.
This is because car engines act just like big gyroscopes.
? Wheels on motorbikes act as gyroscopes and make the
bike easier to balance (stay up right) when moving.
? Ship stabilisers
Precessional Angular Motion
(Vectorial representation of angular motion)
• We know that the angular acceleration is the rate of change of
angular velocity with respect to time.
• It is a vector quantity and may be represented by drawing a vector
diagram with the help of right hand screw rule.
• Consider a disc, as shown in Fig. (a), revolving or spinning about the
axis OX (known as axis of spin) in anticlockwise when seen from the
front, with an angular velocity in a plane at right angles to the paper .
• After a short interval of time t, let the disc be spinning about the new axis of spin
OX ’ (at an angle d? ) with an angular velocity ( ? + d ?).
• Using the right hand screw rule, initial angular velocity of the disc ? is represented
by vector ox; and the final angular velocity of the disc ( ? +d? ) is represented by
vector ox ’ as shown in Fig. (b).
• The vector xx ’ represents the change of angular velocity in time dt i.e. the angular
acceleration of the disc. This may be resolved into two components, one parallel
to ox and the other perpendicular to ox.