1. The document discusses precession and the gyroscopic effect. It explains how a spinning object like a disc or ship's propeller experiences precession when the axis of spin changes direction.
2. When a spinning object like an airplane propeller or ship's rotor changes the direction of its axis of spin, the gyroscopic effect produces a reactive force perpendicular to the axis of spin. This causes the nose or bow to dip or rise.
3. For a ship, the gyroscopic effect causes the bow to rise and stern to dip when turning left if the rotor spins clockwise, and vice versa if spinning counterclockwise or turning right. This helps explain how gyroscopic forces affect ship and aircraft steering.
- Gyroscopes work based on the principle of angular momentum to maintain orientation. A gyroscope is a spinning wheel or disk whose axis remains fixed in space despite external forces.
- Gyroscopic couples occur due to the vector representation of angular motion and cause precessional motion.
- On airplanes and ships, gyroscopic couples from rotating propellers and rotors help provide stability when turning or pitching and rolling in rough seas.
- On vehicles like motorcycles, the gyroscopic couples from the wheels and engine, along with centrifugal forces, help provide stability and prevent the vehicle from falling over when turning.
1) The document discusses balancing of rotating masses, including static and dynamic balancing of single and multiple rotating masses. Balancing is achieved by adding counteracting masses in the same or different planes to eliminate unbalanced forces and moments.
2) Methods for balancing a single mass include adding a single balancing mass in the same plane or two masses in different planes. Multiple masses can be balanced in the same plane using analytical or graphical methods.
3) Balancing multiple masses in different planes involves transferring masses to a reference plane and satisfying equilibrium of forces and moments in that plane.
The document discusses the physics behind how a gyroscope works. It describes how a gyroscope is able to maintain its orientation due to the principle of conservation of angular momentum. When a force is applied to the axle of a spinning gyroscope, it undergoes precession rather than tilting in the direction of the applied force. This phenomenon occurs because the spinning gyroscope resists changes to its axis of rotation. Gyroscopes have practical applications in navigation systems to help keep airplanes and rockets on their intended course or orbit.
Unit-6: Gyroscope, of Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
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.
A short introduction on the device GYROSCOPE and a brief description on its properties, history, applications, types and future work.
Source:-
1. Theory of Machines by R.S.Khurmi and J.K.Gupta
2. www.google.co.in
2. www.wikipedia.org
The document discusses projectile motion, including that:
1) A projectile's horizontal and vertical motion are independent, with gravity only affecting vertical motion.
2) The path of a projectile is a combination of its horizontal and vertical components - horizontal motion is constant while vertical motion is affected by gravity.
3) Changing the projection angle affects the projectile's altitude and range, with the maximum range occurring at a 45 degree angle.
This document discusses gyroscopes and gyroscopic effects. It begins by defining a gyroscope and explaining that gyroscopes resist changes to the direction of their rotational axis, known as the gyroscopic effect. It then provides examples of applications that utilize gyroscopes, such as gyrocompasses, inertial guidance systems, and precession in bearings. The document goes on to define angular momentum and discuss how gyroscopic couples arise due to a change in the direction of angular momentum. It provides figures to illustrate gyroscopic couples and their effects on aircraft when turning. Finally, it analyzes gyroscopic effects on rotating objects like disks, rods, and propellers mounted on bearings.
- Gyroscopes work based on the principle of angular momentum to maintain orientation. A gyroscope is a spinning wheel or disk whose axis remains fixed in space despite external forces.
- Gyroscopic couples occur due to the vector representation of angular motion and cause precessional motion.
- On airplanes and ships, gyroscopic couples from rotating propellers and rotors help provide stability when turning or pitching and rolling in rough seas.
- On vehicles like motorcycles, the gyroscopic couples from the wheels and engine, along with centrifugal forces, help provide stability and prevent the vehicle from falling over when turning.
1) The document discusses balancing of rotating masses, including static and dynamic balancing of single and multiple rotating masses. Balancing is achieved by adding counteracting masses in the same or different planes to eliminate unbalanced forces and moments.
2) Methods for balancing a single mass include adding a single balancing mass in the same plane or two masses in different planes. Multiple masses can be balanced in the same plane using analytical or graphical methods.
3) Balancing multiple masses in different planes involves transferring masses to a reference plane and satisfying equilibrium of forces and moments in that plane.
The document discusses the physics behind how a gyroscope works. It describes how a gyroscope is able to maintain its orientation due to the principle of conservation of angular momentum. When a force is applied to the axle of a spinning gyroscope, it undergoes precession rather than tilting in the direction of the applied force. This phenomenon occurs because the spinning gyroscope resists changes to its axis of rotation. Gyroscopes have practical applications in navigation systems to help keep airplanes and rockets on their intended course or orbit.
Unit-6: Gyroscope, of Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
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.
A short introduction on the device GYROSCOPE and a brief description on its properties, history, applications, types and future work.
Source:-
1. Theory of Machines by R.S.Khurmi and J.K.Gupta
2. www.google.co.in
2. www.wikipedia.org
The document discusses projectile motion, including that:
1) A projectile's horizontal and vertical motion are independent, with gravity only affecting vertical motion.
2) The path of a projectile is a combination of its horizontal and vertical components - horizontal motion is constant while vertical motion is affected by gravity.
3) Changing the projection angle affects the projectile's altitude and range, with the maximum range occurring at a 45 degree angle.
This document discusses gyroscopes and gyroscopic effects. It begins by defining a gyroscope and explaining that gyroscopes resist changes to the direction of their rotational axis, known as the gyroscopic effect. It then provides examples of applications that utilize gyroscopes, such as gyrocompasses, inertial guidance systems, and precession in bearings. The document goes on to define angular momentum and discuss how gyroscopic couples arise due to a change in the direction of angular momentum. It provides figures to illustrate gyroscopic couples and their effects on aircraft when turning. Finally, it analyzes gyroscopic effects on rotating objects like disks, rods, and propellers mounted on bearings.
Unit-3 - Velocity and acceleration of mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
This document describes the design and fabrication of a rocker bogie mechanism. The rocker bogie system is a suspension used on Mars rovers to allow independent wheel movement over obstacles. The design includes two rocker arms that allow the left and right wheels to climb obstacles individually. Calculations are shown for tilt angle, wheel base, link lengths, and motor specifications. Components include shafts, links, wheels, bearings, and motors. The advantages of the rocker bogie system include its ability to climb obstacles twice the wheel diameter and distribute load evenly across independently moving wheels.
The document discusses different types of gear trains used to transmit motion between rotating shafts in machines. It describes simple gear trains which use a single gear on each shaft, compound gear trains which use multiple gears on a shaft, reverted gear trains where the first and last gears share a common axis of rotation, and epicyclic gear trains where gears move in an orbital path relative to a fixed axis. Epicyclic gear trains are useful for achieving high speed ratios within a compact space and are used in applications like lathes, differentials, hoists, and watches.
The document discusses gyroscopic effects in ships. It defines key terms like bow, stern, port, and starboard in relation to a ship. It explains that a ship can pitch, roll, and steer due to gyroscopic effects from the spinning propeller. The direction a ship turns depends on whether the propeller is spinning clockwise or counterclockwise, and whether the observation is made from the bow or stern end. For example, with a clockwise spinning propeller, turning left from the bow end causes the bow to dip and the stern to raise.
This document contains the laboratory manual for Applied Mechanics experiments at a government polytechnic institute. It lists 10 experiments for verifying mechanics laws and principles. The first experiment involves verifying the parallelogram, triangle, and polygon laws of forces using a Gravesand's apparatus. The other experiments include verifying forces in a jib crane, reactions in a simply supported beam, and calculating mechanical advantage, velocity ratio, and efficiency for devices like inclined planes and screw jacks. Procedures, observations tables, and precautions are provided for each experiment.
This document contains information about a study expedition group consisting of 6 members. It discusses key terms related to projectile motion such as velocity, angle, and range of projection. The document explains that a projectile's motion is determined by both vertical and horizontal components. It presents equations to calculate a projectile's maximum height, time of flight, and horizontal range based on its initial velocity and angle of projection.
Transmissions allow engines to operate at optimal RPM for efficiency using gear ratios to reduce RPM and multiply torque. They contain gears that change the speed and direction of rotation. Planetary gears, common in automatic transmissions, use three components - sun gear, planet gears, and ring gear. By holding one component and driving another, different gear ratios are achieved like underdrive, overdrive, and reverse. Ratios are calculated using the number of teeth on each component.
Friction arises due to interlocking of minutely projecting particles when two surfaces are in contact and one surface moves relative to the other. There are two main types of friction: static friction and dynamic (kinetic) friction. Static friction acts when a body is at rest, while dynamic friction acts when a body is in motion. Friction can be classified further as dry friction between unlubricated surfaces and fluid friction between lubricated surfaces. The coefficient of friction is defined as the ratio between limiting friction force and normal reaction force. A screw jack uses the principle of an inclined plane to lift loads, with torque required to overcome friction proportional to the load, coefficient of friction, and pitch of the screw.
gyroscope is a chapter of theory of machine. You can easily understand concepts of gyroscope in my ppt. All concepts are with suitable examples and graphics.
saurabh.rana2829@gmail.com
This document discusses cam and follower classification. It describes how cams are machine elements that convert rotating motion to reciprocating or oscillating motion via a follower. Cams and followers make contact along a line and form a higher pair. Cams are usually rotated at a uniform speed to drive the predetermined motion of the follower based on the cam's shape. Followers are classified by the contact surface (knife edge, roller, flat face, spherical face) and motion type (reciprocating, oscillating). Cams are also classified by shape (plate, cylindrical, linear) and motion profile (rise-return-rise, dwell-rise-return-dwell). Key cam concepts discussed include the base circle, trace point,
This document provides an overview of dynamics of machines including:
1. It defines force, applied force, constraint forces, and types of constrained motions like completely, incompletely, and successfully constrained motions.
2. It discusses static force analysis, dynamic force analysis, and conditions for static and dynamic equilibrium.
3. It covers concepts like inertia, inertia force, inertia torque, D'Alembert's principle, and principle of superposition.
4. It derives expressions for forces acting on the reciprocating parts of an engine while neglecting the weight of the connecting rod.
Aerodynamics of a_rotary_wing_type_aircraftdarshakb
This document provides an overview of basic aerodynamic concepts related to rotary wing aircraft, including definitions of key rotorcraft components and terminology. It describes principles such as lift, drag, torque, dissymmetry of lift, and retreating blade stall. Key concepts covered include how rotor blades generate lift via angle of attack and airspeed, how flapping helps compensate for differences in advancing and retreating blade lift, and factors that influence helicopter performance such as ground effect and density altitude.
This document discusses the introduction to gyroscopes. It defines a gyroscope as a spinning device that maintains its orientation. Gyroscopes are used in applications like gyrocompasses, inertial guidance systems, and to provide stability. They can operate using different principles such as MEMS and ring lasers.
Applications include use in spacecraft, ships, tunnels, and consumer electronics. The document discusses gyroscopic effects that occur in vehicles with rotating engine parts. It defines terms like axis of spin, precession, and gyroscopic couple. Diagrams are included to illustrate gyroscope operation and how precession direction depends on the direction of spin and applied torque.
1. Gyroscopes are devices used to control the orientation and angular velocity of rotating bodies. They use the principle of gyroscopic precession to maintain their orientation.
2. Common applications of gyroscopes include their use in inertial navigation systems, gyrocompasses, and to provide stability in vehicles like ships, airplanes, bicycles, and motorcycles.
3. The reactive gyroscopic couple experienced by rotating objects like the engines of airplanes and ships helps provide stability when turning. For example, when an airplane turns left, the reactive couple presses down on the right wing and lifts the left wing, counteracting the turning moment.
The document describes a box transport mechanism created by Jasim Ahraf. It discusses the aims and objectives of designing the mechanism to provide intermittent movement of packages in industries. It reviews different types of linkage mechanisms including simple planar linkages like reverse-motion, push-pull, parallel-motion and bell-crank linkages. It specifically discusses using a crank-rocker mechanism for the box transport mechanism and describes the functions of linkages like converting continuous rotation into continuous or reciprocating motion. It also covers the materials, tools and procedures used to fabricate the box transport mechanism.
This document discusses kinematics of rigid bodies, including:
- Types of rigid body motion such as translation, rotation about a fixed axis, and general plane motion.
- Translation motion is further divided into rectilinear and curvilinear types.
- Key terms related to rotation about a fixed axis like angular position, displacement, velocity, and acceleration.
- Relations between linear and angular velocity and acceleration.
- Two special cases involving rotation of pulleys - a pulley connected to a rotating block, and two coupled pulleys rotating without slip.
- Five sample problems calculating values like angular velocity and acceleration, revolutions, linear velocity and acceleration for rotating bodies.
Cams are used to convert rotary motion to oscillatory motion or vice versa. They are commonly used in internal combustion engines to operate valves. This chapter discusses the fundamentals of cam and follower design including the different types of cams, followers, motions, and cam profiles. The objectives are to understand basic concepts and terminology and learn how to design a cam and follower set to achieve a desired output motion.
Mechanics of Machines (Gyroscopes) as per MGU syllabusbinil babu
1. The document discusses the gyroscopic effect, which is the tendency of a spinning object to resist any change to its axis of rotation. It explains how a gyroscopic couple is generated when a spinning object experiences precession.
2. Key applications of gyroscopic effect discussed include aeroplanes, ships, vehicles. For aeroplanes, the effect of the spinning engine/propeller is to change the plane's attitude during turns. For ships steering or pitching, it causes the bow/stern to raise or lower. There is no effect during ship rolling.
3. Sample calculations are provided to determine the gyroscopic couple generated for different rotating objects like engines, flywheels, and to analyze their effect
1. Gyroscopes and accelerometers are common sensors used to determine the position and orientation of an object. A gyroscope uses Earth's gravity to help determine orientation and consists of a freely rotating disk called a rotor.
2. Gyroscopic motion occurs when the axis of a rotating body changes direction, such as when an airplane takes a turn or the rotor of a ship changes direction. Examples include airplane turns, ship rotors, vehicle wheels turning, and gyroscopic instruments.
3. On ships and vehicles, gyroscopic effects can cause the nose/bow to raise or lower and the stern/tail to correspondingly lower or raise when turning due to interaction between the rotating components and the turning motion.
Unit-3 - Velocity and acceleration of mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
This document describes the design and fabrication of a rocker bogie mechanism. The rocker bogie system is a suspension used on Mars rovers to allow independent wheel movement over obstacles. The design includes two rocker arms that allow the left and right wheels to climb obstacles individually. Calculations are shown for tilt angle, wheel base, link lengths, and motor specifications. Components include shafts, links, wheels, bearings, and motors. The advantages of the rocker bogie system include its ability to climb obstacles twice the wheel diameter and distribute load evenly across independently moving wheels.
The document discusses different types of gear trains used to transmit motion between rotating shafts in machines. It describes simple gear trains which use a single gear on each shaft, compound gear trains which use multiple gears on a shaft, reverted gear trains where the first and last gears share a common axis of rotation, and epicyclic gear trains where gears move in an orbital path relative to a fixed axis. Epicyclic gear trains are useful for achieving high speed ratios within a compact space and are used in applications like lathes, differentials, hoists, and watches.
The document discusses gyroscopic effects in ships. It defines key terms like bow, stern, port, and starboard in relation to a ship. It explains that a ship can pitch, roll, and steer due to gyroscopic effects from the spinning propeller. The direction a ship turns depends on whether the propeller is spinning clockwise or counterclockwise, and whether the observation is made from the bow or stern end. For example, with a clockwise spinning propeller, turning left from the bow end causes the bow to dip and the stern to raise.
This document contains the laboratory manual for Applied Mechanics experiments at a government polytechnic institute. It lists 10 experiments for verifying mechanics laws and principles. The first experiment involves verifying the parallelogram, triangle, and polygon laws of forces using a Gravesand's apparatus. The other experiments include verifying forces in a jib crane, reactions in a simply supported beam, and calculating mechanical advantage, velocity ratio, and efficiency for devices like inclined planes and screw jacks. Procedures, observations tables, and precautions are provided for each experiment.
This document contains information about a study expedition group consisting of 6 members. It discusses key terms related to projectile motion such as velocity, angle, and range of projection. The document explains that a projectile's motion is determined by both vertical and horizontal components. It presents equations to calculate a projectile's maximum height, time of flight, and horizontal range based on its initial velocity and angle of projection.
Transmissions allow engines to operate at optimal RPM for efficiency using gear ratios to reduce RPM and multiply torque. They contain gears that change the speed and direction of rotation. Planetary gears, common in automatic transmissions, use three components - sun gear, planet gears, and ring gear. By holding one component and driving another, different gear ratios are achieved like underdrive, overdrive, and reverse. Ratios are calculated using the number of teeth on each component.
Friction arises due to interlocking of minutely projecting particles when two surfaces are in contact and one surface moves relative to the other. There are two main types of friction: static friction and dynamic (kinetic) friction. Static friction acts when a body is at rest, while dynamic friction acts when a body is in motion. Friction can be classified further as dry friction between unlubricated surfaces and fluid friction between lubricated surfaces. The coefficient of friction is defined as the ratio between limiting friction force and normal reaction force. A screw jack uses the principle of an inclined plane to lift loads, with torque required to overcome friction proportional to the load, coefficient of friction, and pitch of the screw.
gyroscope is a chapter of theory of machine. You can easily understand concepts of gyroscope in my ppt. All concepts are with suitable examples and graphics.
saurabh.rana2829@gmail.com
This document discusses cam and follower classification. It describes how cams are machine elements that convert rotating motion to reciprocating or oscillating motion via a follower. Cams and followers make contact along a line and form a higher pair. Cams are usually rotated at a uniform speed to drive the predetermined motion of the follower based on the cam's shape. Followers are classified by the contact surface (knife edge, roller, flat face, spherical face) and motion type (reciprocating, oscillating). Cams are also classified by shape (plate, cylindrical, linear) and motion profile (rise-return-rise, dwell-rise-return-dwell). Key cam concepts discussed include the base circle, trace point,
This document provides an overview of dynamics of machines including:
1. It defines force, applied force, constraint forces, and types of constrained motions like completely, incompletely, and successfully constrained motions.
2. It discusses static force analysis, dynamic force analysis, and conditions for static and dynamic equilibrium.
3. It covers concepts like inertia, inertia force, inertia torque, D'Alembert's principle, and principle of superposition.
4. It derives expressions for forces acting on the reciprocating parts of an engine while neglecting the weight of the connecting rod.
Aerodynamics of a_rotary_wing_type_aircraftdarshakb
This document provides an overview of basic aerodynamic concepts related to rotary wing aircraft, including definitions of key rotorcraft components and terminology. It describes principles such as lift, drag, torque, dissymmetry of lift, and retreating blade stall. Key concepts covered include how rotor blades generate lift via angle of attack and airspeed, how flapping helps compensate for differences in advancing and retreating blade lift, and factors that influence helicopter performance such as ground effect and density altitude.
This document discusses the introduction to gyroscopes. It defines a gyroscope as a spinning device that maintains its orientation. Gyroscopes are used in applications like gyrocompasses, inertial guidance systems, and to provide stability. They can operate using different principles such as MEMS and ring lasers.
Applications include use in spacecraft, ships, tunnels, and consumer electronics. The document discusses gyroscopic effects that occur in vehicles with rotating engine parts. It defines terms like axis of spin, precession, and gyroscopic couple. Diagrams are included to illustrate gyroscope operation and how precession direction depends on the direction of spin and applied torque.
1. Gyroscopes are devices used to control the orientation and angular velocity of rotating bodies. They use the principle of gyroscopic precession to maintain their orientation.
2. Common applications of gyroscopes include their use in inertial navigation systems, gyrocompasses, and to provide stability in vehicles like ships, airplanes, bicycles, and motorcycles.
3. The reactive gyroscopic couple experienced by rotating objects like the engines of airplanes and ships helps provide stability when turning. For example, when an airplane turns left, the reactive couple presses down on the right wing and lifts the left wing, counteracting the turning moment.
The document describes a box transport mechanism created by Jasim Ahraf. It discusses the aims and objectives of designing the mechanism to provide intermittent movement of packages in industries. It reviews different types of linkage mechanisms including simple planar linkages like reverse-motion, push-pull, parallel-motion and bell-crank linkages. It specifically discusses using a crank-rocker mechanism for the box transport mechanism and describes the functions of linkages like converting continuous rotation into continuous or reciprocating motion. It also covers the materials, tools and procedures used to fabricate the box transport mechanism.
This document discusses kinematics of rigid bodies, including:
- Types of rigid body motion such as translation, rotation about a fixed axis, and general plane motion.
- Translation motion is further divided into rectilinear and curvilinear types.
- Key terms related to rotation about a fixed axis like angular position, displacement, velocity, and acceleration.
- Relations between linear and angular velocity and acceleration.
- Two special cases involving rotation of pulleys - a pulley connected to a rotating block, and two coupled pulleys rotating without slip.
- Five sample problems calculating values like angular velocity and acceleration, revolutions, linear velocity and acceleration for rotating bodies.
Cams are used to convert rotary motion to oscillatory motion or vice versa. They are commonly used in internal combustion engines to operate valves. This chapter discusses the fundamentals of cam and follower design including the different types of cams, followers, motions, and cam profiles. The objectives are to understand basic concepts and terminology and learn how to design a cam and follower set to achieve a desired output motion.
Mechanics of Machines (Gyroscopes) as per MGU syllabusbinil babu
1. The document discusses the gyroscopic effect, which is the tendency of a spinning object to resist any change to its axis of rotation. It explains how a gyroscopic couple is generated when a spinning object experiences precession.
2. Key applications of gyroscopic effect discussed include aeroplanes, ships, vehicles. For aeroplanes, the effect of the spinning engine/propeller is to change the plane's attitude during turns. For ships steering or pitching, it causes the bow/stern to raise or lower. There is no effect during ship rolling.
3. Sample calculations are provided to determine the gyroscopic couple generated for different rotating objects like engines, flywheels, and to analyze their effect
1. Gyroscopes and accelerometers are common sensors used to determine the position and orientation of an object. A gyroscope uses Earth's gravity to help determine orientation and consists of a freely rotating disk called a rotor.
2. Gyroscopic motion occurs when the axis of a rotating body changes direction, such as when an airplane takes a turn or the rotor of a ship changes direction. Examples include airplane turns, ship rotors, vehicle wheels turning, and gyroscopic instruments.
3. On ships and vehicles, gyroscopic effects can cause the nose/bow to raise or lower and the stern/tail to correspondingly lower or raise when turning due to interaction between the rotating components and the turning motion.
A gyroscope is a device that uses angular momentum to detect orientation and maintain stability. It consists of a spinning wheel or disk whose axis is free to orient in any direction. Gyroscopes are used for navigation and stabilization in ships, airplanes, drones, and other vehicles. They work by producing a gyroscopic effect - as the spinning axis rotates about another axis, conservation of angular momentum causes a reactive torque perpendicular to the plane of rotation. This effect counters external forces and helps maintain the orientation of the device.
1. The document introduces gyroscopic and precessional motion, explaining that when a spinning body moves along a curved path, gyroscopic forces act on it.
2. It defines key terms like gyroscopic couple, precessional motion, and axis of precession. The gyroscopic couple arises due to a change in angular momentum when the axis of spin rotates about the axis of precession.
3. It gives the example of an airplane in a left turn. The reactive gyroscopic couple acts in the anticlockwise direction on the airplane, causing its nose to rise and tail to dip during the left turn.
- A gyroscope is a device that maintains orientation based on angular momentum. It has a spinning wheel or disk mounted on gimbals to minimize external torque and keep its orientation nearly fixed regardless of motion.
- Precession is the change in the axis of spin of a rotating body in response to an external torque. This results in two components of angular acceleration - one parallel and one perpendicular to the original axis of spin.
- A gyroscopic couple is produced on a spinning object when its axis of spin rotates about another axis. This couple depends on angular velocity and moment of inertia and can cause a rotating object like a ship or airplane to tilt when turning or pitching.
1. A gyroscope is a device that uses angular momentum to detect orientation and maintain stability. It consists of a spinning wheel or disk on an axle that is free to take any orientation.
2. Gyroscopes have two key properties - rigidity and precession. Rigidity means the axis of rotation tends to remain fixed in space without external forces. Precession means an applied torque causes the axis to rotate perpendicular to both the torque and angular momentum vectors.
3. Gyroscopes have important applications in navigation, stabilization, and orientation. They are used in ship compasses, aircraft autopilots, navigation systems, and more due to their ability to resist changes in orientation.
1) A marine gyrocompass uses a freely-spinning gyroscope to determine direction based on the principles of angular momentum and the earth's constant rotation.
2) A gyroscope has three degrees of freedom - it can spin about its axis and tilt or turn in horizontal and vertical planes. The earth acts like a giant free gyroscope due to its mass, high-speed rotation, and lack of friction in space.
3) The gyroscope's angular momentum and inertia cause it to resist changes to its axis of spin, allowing it to maintain a fixed direction in space independent of the ship's movements. This gyroscopic property is used to determine true north.
After reading this module, you should be able to . . .
10.01 Identify that if all parts of a body rotate around a fixed
axis locked together, the body is a rigid body. (This chapter
is about the motion of such bodies.)
10.02 Identify that the angular position of a rotating rigid body
is the angle that an internal reference line makes with a
fixed, external reference line.
10.03 Apply the relationship between angular displacement
and the initial and final angular positions.
10.04 Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.
10.05 Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for
that change.
10.06 Identify that counterclockwise motion is in the positive
direction and clockwise motion is in the negative direction.
10.07 Given angular position as a function of time, calculate the
instantaneous angular velocity at any particular time and the
average angular velocity between any two particular times.
10.08 Given a graph of angular position versus time, determine the instantaneous angular velocity at a particular time
and the average angular velocity between any two particular times.
10.09 Identify instantaneous angular speed as the magnitude
of the instantaneous angular velocity.
10.10 Given angular velocity as a function of time, calculate
the instantaneous angular acceleration at any particular
time and the average angular acceleration between any
two particular times.
10.11 Given a graph of angular velocity versus time, determine the instantaneous angular acceleration at any particular time and the average angular acceleration between
any two particular times.
10.12 Calculate a body’s change in angular velocity by
integrating its angular acceleration function with respect
to time.
10.13 Calculate a body’s change in angular position by integrating its angular velocity function with respect to time.
This document discusses governors and gyroscopes. It defines governors as automatic speed control mechanisms that use centrifugal or inertia forces to regulate fuel supply and maintain engine speed. Gyroscopes use conservation of angular momentum to maintain orientation. Their applications include navigation, stabilization of vehicles like helicopters, and maintaining direction in tunnel mining. The document also describes how gyroscopes produce gyroscopic couples that affect a ship's motion during turns, pitching, and rolling.
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1. Magnetic compasses indicate magnetic north using the Earth's magnetic field, while gyro compasses indicate true north by measuring the Earth's rotation and are unaffected by magnetic fields.
2. A gyroscope maintains its orientation in space regardless of movement by relying on the principle of gyroscopic inertia. It has three degrees of freedom and its orientation remains fixed due to precession caused by external torques.
3. Errors in gyrocompasses like speed error and ballistic deflection error occur due to the Earth's rotation and changes in a ship's speed or course, but can be compensated for through electrical adjustments and a dual rotor design.
Angular momentum in terms of rigid bodyZeeshan Afzal
Large helicopters have two overlapping rotors that rotate in opposite directions, cancelling each other's angular momenta and preventing the helicopter body from rotating. Small helicopters use a tail rotor to counteract the overhead rotor's torque and allow steering. Helicopters apply angular momentum principles to achieve stable vertical flight.
The document discusses a presentation on case studies of pressure sensors. It begins with defining a pressure sensor as an instrument that determines the actual pressure applied to it using a pressure sensitive element. It then discusses the typical working principles of pressure sensors, including a case study on a piezoresistive pressure sensor. Various applications of pressure sensors are also mentioned such as in engineering, aviation, and other industries.
This document provides an overview of mechanical science concepts related to linear motion. It defines key terms like displacement, velocity, acceleration, and discusses displacement-time and velocity-time graphs. Uniform acceleration equations of motion are derived. Gravity is described as causing uniform acceleration. Projectile motion is analyzed by resolving velocities into horizontal and vertical components. Examples demonstrate calculating projectile range and maximum height.
This document discusses the concepts of static equilibrium, stability, and center of buoyancy as they relate to floating bodies. It states that a body is in stable equilibrium if, when displaced and released, it returns to its original position. Neutral equilibrium means a body retains its displaced position, while unstable equilibrium means displacement increases after release. The center of buoyancy is the centroid of the submerged volume, and its interaction with the center of gravity determines a body's attitude in the water.
1. The document discusses gyroscopic couple, which acts on a spinning object that is rotating about another axis.
2. It provides examples of gyroscopic couple in naval ships, where the spinning of propeller shafts affects steering, pitching, and rolling.
3. The document also examines the gyroscopic couple and centrifugal couple in vehicles like cars and motorcycles taking turns, and how this affects their stability.
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- Personnel must be trained to react correctly in emergencies, use survival equipment properly, and take measures to ensure their own survival and others.
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Personal Survival and Social Responsibilities(PSSR)nmahi96
This document provides an introduction and index for a course booklet on personal safety and social responsibilities for seafarers. It includes sections on complying with emergency procedures, preventing pollution, observing safe working practices, effective communication and human relationships on board ships, understanding and mitigating fatigue, and the Maritime Labour Convention. The index lists these topics and their page numbers. Various types of ships are also defined, such as container ships, bulk carriers, tankers, and passenger, offshore, fishing and special purpose vessels. Key parts of a ship like the hull, engine room, bridge, funnel, accommodation, and mast are briefly described.
Indus Seafarers Training Academy (ISTA) is an ISO 9001:2015 certified training academy located in Chennai, India that has been approved by the Directorate General of Shipping, Ministry of Shipping, Government of India since 1998. ISTA's office address is in Indus Campus on Manali Saravan Street in Kumanamchavadi near Mangadu Main Road in Chennai, and can be contacted via their website, email, or several phone numbers listed.
Indus Seafarers Training Academy (ISTA) is an ISO 9001:2015 certified training academy located in Chennai, India that has been approved by the Directorate General of Shipping, Ministry of Shipping, Government of India since 1998. ISTA's office address is in Indus Campus on Manali Saravan Street in Kumanamchavadi near Mangadu Main Road in Chennai, and can be contacted via their website, email, or several phone numbers listed.
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1. UNIT-I
PRECESSION
Introduction:
We have already discussed that,
1. When a body moves along a curved path with a uniform linear velocity, a force in the
direction of centripetal acceleration (known as centripetal force) has to be applied
externally over the body, so that it moves along the required curved path. This external
force applied is known as active force.
2. When a body, itself, is moving with uniform linear velocity along a circular path, it is
subjected to the centrifugal force radially outwards. This centrifugal force is called
reactive force. The action of the reactive or centrifugal force is to tilt or move the body
along radially outward direction
Precessional Angular Motion:
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 ω in a
plane at right angles to the paper.
2. After a short interval of time δt, let the disc be spinning about the new axis of spin OX ′
(at an angle δθ) with an angular velocity (ω + δω). Using the right hand screw rule, initial
angular velocity of the disc (ω) is represented by vector ox; and the final angular velocity
of the disc (ω + δω) is represented by vector ox′ as shown in Fig. 14.1 (b). The vector xx′
represents the change of angular velocity in time δt 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.
Where dθ/dt is the angular velocity of the axis of spin about a certain axis, which is
perpendicular to the plane in which the axis of spin is going to rotate. This angular
velocity of the axis of spin (i.e. dθ/dt) is known as angular velocity of precession and is
denoted by ωP. The axis, about which the axis of spin is to turn, is known as axis of
precession. The angular motion of the axis of spin about the axis of precession is known
as precessional angular motion.
3. 1. The axis of precession is perpendicular to the plane in which the axis of spin is going
to rotate.
2. If the angular velocity of the disc remains constant at all positions of the axis of spin,
then dθ/dt is zero; and thus αc is zero.
3. If the angular velocity of the disc changes the direction, but remains constant in
magnitude,
Then angular acceleration of the disc is given by
αc = ω.dθ/dt = ω.ωP
The angular acceleration αc is known as gyroscopic acceleration.
Gyroscopic Couple:
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. (a). Since the
plane in which the disc is rotating is parallel to the plane YOZ, therefore it is called plane
of spinning. The plane XOZ is a horizontal plane and the axis of spin rotates in a plane
parallel to the horizontal plane about an axis OY. In other words, the axis of spin is said to
be rotating or processing about an axis OY. Inother words, the axis of spin is said to be
rotating or processing about an axis OY (which is perpendicular to both the axes OX and
OZ) at an angular velocity ωP rap/s. This horizontal plane XOZ is called plane of
precession and OY is the axis of precession.
Let
I = Mass moment of inertia of the disc about OX, and
ω = Angular velocity of the disc.
Angular momentum of the disc = I.ω
Since the angular momentum is a vector quantity, therefore it may be represented by the
vector ox, as shown in Fig (b). The axis of spin OX is also rotating anticlockwise when
seen from the top about the axis OY. Let the axis OX is turned in the plane XOZ through a
small angle δθ radians to the position OX ′ , in time δt seconds. Assuming the angular
velocity ω to be constant, the angular momentum will now be represented by vector ox′.
4. Effect of the Gyroscopic Couple on an Aeroplane
The top and front view of an aeroplane are shown in Fig (a).
Let engine or propeller rotates in the clockwise direction when seen from the rear or tail
end and the aeroplane takes a turn to the left.
5.
6. 1. When the aeroplane takes a right turn under similar conditions as discussed above, the
effect of the reactive gyroscopic couple will be to dip the nose and raise the tail of the
aeroplane.
2. When the engine or propeller rotates in anticlockwise direction when viewed from the
rear or tail end and the aeroplane takes a left turn, then the effect of reactive gyroscopic
couple will be to dip the nose and raise the tail of the aeroplane.
3. When the aeroplane takes a right turn under similar conditions as mentioned in note 2
above, the effect of reactive gyroscopic couple will be to raise the nose and dip the tail
of the aeroplane.
4. When the engine or propeller rotates in clockwise direction when viewed from the
front and the aeroplane takes a left turn, then the effect of reactive gyroscopic couple will
be to raise the tail and dip the nose of the aeroplane.
5. When the aeroplane takes a right turn under similar conditions as mentioned in note
4-above, the effect of reactive gyroscopic couple will be to raise the nose and dip the
tail of the aeroplane.
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.
7. Effect of Gyroscopic Couple on a Naval Ship during Steering:
Steering is the turning of a complete ship in a curve towards left or right, while it
moves forward. Consider the ship taking a left turn, and rotor rotates in the clockwise
direction when viewed from the stern, as shown in Fig.. The effect of gyroscopic couple
on a naval ship during steering taking left or right turn may be obtained in the similar
way as for an aeroplane
.
When the rotor of the ship rotates in the clockwise direction when viewed from
the stern, it will have its angular momentum vector in the direction ox as shown in Fig.
(a). As the ship steers to the left, the active gyroscopic couple will change the angular
momentum vector from ox to ox′. The vector xx′ now represents the active gyroscopic
couple and is perpendicular to ox. Thus the plane of active gyroscopic couple is
perpendicular to xx′ and its direction in the axis OZ for left hand turn is clockwise as
shown in Fig.. The reactive gyroscopic couple of the same magnitude will act in the
opposite direction (i.e. in anticlockwise direction). The effect of this reactive gyroscopic
couple is to raise the bow and lower the stern.
8. 1. When the ship steers to the right under similar conditions as discussed above,
the effect of the reactive gyroscopic couple, as shown in Fig. will be to raise the stern
and lower the bow.
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.
4. When the rotor rotates in the clockwise direction when viewed from the bow or fore
end and the ship is steering to the left, then the effect of reactive gyroscopic couple will
be to raise the stern and lower the bow.
5. When the ship is steering to the right under similar conditions as discussed in note 4
above, then the effect of reactive gyroscopic couple will be to raise the bow and lower
the stern.
6. The effect of the reactive gyroscopic couple on a boat propelled by a turbine taking left
or right turn is similar as discussed above.
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. (a). In this case, the transverse axis is the axis of
precession. The pitching of the ship is assumed to take place with simple harmonic
motion i.e. the motion of the axis of spin about transverse axis is simple harmonic.
9.
10. Effect of Gyroscopic Couple on a Naval Ship during Rolling:
We know that, for the effect of gyroscopic couple to occur, the axis of precession
should always be perpendicular to the axis of spin. If, however, the axis of precession
becomes parallel to the axis of spin, there will be no effect of the gyroscopic couple
acting on the body of the ship. In case of rolling of a ship, the axis of precession (i.e.
longitudinal axis) is always parallel to the axis of spin for all positions. Hence, there is no
effect of the gyroscopic couple acting on the body of a ship.
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 turn
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 the road
surface.
Let
m = Mass of the vehicle in kg,
W = Weight of the vehicle in newtons = m.g,
rW = Radius of the wheels in metres,
R = Radius of curvature in metres (R > rW),
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
11. A little considereation will show, that the weight of the vehicle (W) will be equally
distributed over the four wheels which will act downwards. The reaction between each
wheel and the road surface of the same magnitude will act upwards.
Therefore
Road reaction over each wheel = W/4 = m.g /4 newtons
Let us now consider the effect of the gyroscopic couple and centrifugal couple on the
vehicle.
1. Effect of the gyroscopic couple
Since the vehicle takes a turn towards left due to the precession and other rotating parts,
therefore a gyroscopic couple will act.
We know that velocity of precession,
ωP = v/R
12. 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. Due to the gyroscopic couple, vertical reaction on the road
surface will be produced. The reaction will be vertically upwards on the outer wheels and
vertically downwards on the inner wheels. Let the magnitude of this reaction at the two
outer or inner wheels be P newtons. Then
2. Effect of the centrifugal couple:
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 the vehicle.
We know that centrifugal force,
This overturning couple is balanced by vertical reactions, which are vertically upwards
on the outer wheels and vertically downwards on the inner wheels.
Let the magnitude of this reaction atthe two outer or inner wheels be Q. Then
13. A little consideration will show that when the vehicle is running at high speeds, PI may
be zero or even negative. This will cause the inner wheels to leave the ground thus
tending to overturn the automobile.
In order to have the contact between the inner wheels and the ground, the sum of P/2 and
Q/2 must be less than W/4.
Stability of a Two Wheel Vehicle Taking a Turn:
Consider a two wheel vehicle (say a scooter or motor cycle) taking a right turn as shown
in
Let
m = 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,
rW = Radius of the wheels,
R = Radius of track or curvature,
IW = Mass moment of inertia of each wheel,
IE = Mass moment of inertia of the rotating parts of the engine,
ωW = Angular velocity of the wheels,
ωE = Angular velocity of the engine,
G = Gear ratio = ωE / ωW,
v = Linear velocity of the vehicle = ωW × rW,
14. θ = Angle of heel. It is inclination of the vehicle to the vertical for
quilibrium.