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Theory of Gyrocompass

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A gyroscope, not to be confused with gyrocompass, is a spinning wheel mounted on gimbal so that the wheel's axis is free to orient itself in any way. When it is spun up to speed with its axis pointing in some direction, due to the law of conservation of angular momentum, such a wheel will normally maintain its original orientation to a fixed point in outer space (not to a fixed point on Earth).

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Theory of Gyrocompass

  1. 1. Gokul Lakshmanan lakshmanangokul7@gmail.com 1 CHAPTER 1 INTRODUCTION Everything is spinning. Right now, you are spinning around on the Earth at over 600 miles an hour. The Earth is spinning around the Sun at about67, 000 miles per hour. The entire Solar System is spinning around the center of the Milky Way Galaxy at 558,000 miles per hour. And this is nothing compared to the unbelievable speed that the electrons of every atom in the universe are spinning around their nuclei. From the galactic to the atomic scale, scientists have discovered everything is spinning. The gyroscope is one of the most remarkable and widely recognized toys in the world, yet few people realize it was originally developed by scientists to study spin and demonstrate that the Earth is rotating. Close observation of the astonishing behavior of gyroscopes led scientists to a much better understanding of spin and the development of a vast number of practical applications including the gyrocompass, flight instruments, the autopilot, gyroscopic stabilization and navigation for ships, airplanes, space stations and satellites. A gyroscope is a device used primarily for navigation and measurement of angular velocity. Gyroscopes are available that can measure rotational velocity in 1, 2, or 3 directions. 3-axis gyroscopes are often implemented with a 3-axis accelerometer to provide a full 6 degree-of- freedom (DOF) motion tracking system. Gyroscopes have evolved from mechanical-inertial spinning devices consisting of rotors, axles, and gimbals to various incarnations of electronic and optical devices. Each exploits some physical property of the system allowing it to detect rotational velocity about some axis. Simply put, a gyrocompass consists of a rotor that is journaled to spin about an axis. Often the spinning rotor is gimbaled and allowed to move freely. This spinning rotor has some very useful physical properties. The gimbals are a set of three rings, each with a pair of bearings initially at right angles. They let the platform twist about any rotational axis (or, rather, they let the platform keep the same orientation while the vehicle rotates around it). The gimbal was first described by the Greek inventor Philo of Byzantium. Philo described an eight-sided ink pot with an opening on each side, which can be turned so that while any face is on top, a pen can be dipped and inked - yet the ink never runs out through the holes of the other sides. This was done by the suspension of the inkwell at the center, which was mounted on a series of concentric metal rings so that it remained stationary no matter which way the pot is turned.
  2. 2. Gokul Lakshmanan lakshmanangokul7@gmail.com 2 CHAPTER 2 LITERATURE SURVEY In early times, people discovered the spinning top, a toy with a unique ability to balance upright while rotating rapidly. Ancient Greek, Chinese and Roman societies built tops for games and entertainment .The Maori in New Zealand have used humming tops, with specially-crafted holes, in mourning ceremonies. In 14th century England, some villages had a large top constructed for a warming-up exercise in cold weather. Tops were even used in place of dice, like the die in the contemporary fantasy game Dungeons & Dragons. It was not until the late 18th and early 19th centuries that scientists and sailors began attempting to use spinning tops as a scientific tool. At that time, sailors relied on sextants for navigation, measuring the angle between specific stars and the horizon. This method was limited, however, if choppy seas or fog obscured the true horizon, or clouds obscured the stars. Serson, an English scientist, noted in the 1740's that the spinning top had a tendency to remain level, even when the surface on which it rested was tilting. He suggested that sailors could use it as an artificial horizon on ships. Unfortunately, when Serson went to sea to test this idea the ship sank and everyone was lost. The first modern gyroscope was designed in 1810 by G.C. Bohnenberger. It was made with a heavy ball instead of a wheel, but since it had no scientific application, it faded into history A French scientist in the 19th Century, Fleuriais, created a top that was continuously powered by air jets blowing into mini-buckets on the rim of the wheel - a process that has been used for thousands of gyros since.. The invention of the gyroscope is often attributed to Leon Foucault, a French scientist who gave it the name and conducted many experiments using gyroscopes. In 1852, he used a gyroscope to demonstrate the Earth is rotating. The first, not yet practical, form of gyrocompass was patented in 1885 by Marinus Gerardus van den Bos. Usable gyrocompass was invented in 1906 in Germany by Hermann Anschütz- Kaempfe, and after successful tests in 1908 became widely used in German Imperial Navy. The gyrocompass was an important invention for nautical navigation because it allowed accurate determination of a vessel’s location at all times regardless of the vessel’s motion, the weather and the amount of steel used in the construction of the ship. In the United States, Elmer Ambrose Sperry produced a workable gyrocompass system (1908: patent #1,242,065), and founded the Sperry Gyroscope Company. The unit was adopted by the U.S. Navy (1911), and
  3. 3. Gokul Lakshmanan lakshmanangokul7@gmail.com 3 played a major role in World War I. The Navy also began using Sperry's "Metal Mike": the first gyroscope-guided autopilot steering system. In the following decades, these and other Sperry devices were adopted by steamships such as the RMS Queen Mary, airplanes, and the warships of World War II. After his death in 1930, the Navy named the USS Sperry after him. Fig 2.1 The 1889 Dumoulin-Krebs gyroscope Meanwhile, in 1913, C. Plath (a Hamburg, Germany-based manufacturer of navigational equipment including sextants and magnetic compasses) developed the first gyrocompass to be installed on a commercial vessel. C. Plath sold many gyrocompasses to the Weems’ School for Navigation in Annapolis, MD, and soon the founders of each organization formed an alliance and became Weems & Plath. Fig 2.2: Gyroscope invented by Léon Foucault in 1852
  4. 4. Gokul Lakshmanan lakshmanangokul7@gmail.com 4 CHAPTER 3 THEORY 3.1 Gyroscope A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. Mechanically, a gyroscope is a spinning wheel or disc in which the axle is free to assume any orientation. Although this orientation does not remain fixed, it changes in response to an external torque much less and in a different direction than it would with the large angular momentum associated with the disc's high rate of spin and moment of inertia. The device's orientation remains nearly fixed, regardless of the mounting platform's motion, because mounting the device in a gimbal minimizes external torque. 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, fiber optic gyroscopes, and the extremely sensitive quantum gyroscope. Applications of gyroscopes include inertial navigation systems where magnetic compasses would not work (as in the Hubble telescope) or would not be precise enough (as in ICBMs), or for the stabilization of flying vehicles like radio-controlled helicopters or unmanned aerial vehicles. Within mechanical systems or devices, a conventional gyroscope is a mechanism comprising a rotor journaled to spin about one axis, the journals of the rotor being mounted in an inner gimbal or ring; the inner gimbal is journaled for oscillation in an outer gimbal for a total of two gimbals. The outer gimbal or ring, which is the gyroscope frame, is mounted so as to pivot about an axis in its own plane determined by the support. This outer gimbal possesses one degree of rotational freedom and its axis possesses none. The next inner gimbal is mounted in the gyroscope frame (outer gimbal) so as to pivot about an axis in its own plane that is always perpendicular to the pivotal axis of the gyroscope frame (outer gimbal). This inner gimbal has two degrees of rotational freedom. The axle of the spinning wheel defines the spin axis. The rotor is designed to spin about an axis, which is always perpendicular to the axis of the inner gimbal. So the rotor possesses three degrees of rotational freedom and its axis possesses two. The wheel responds to a force applied about the input axis by a reaction force about the output axis. The behavior of a gyroscope can be most easily appreciated by consideration of the front wheel of a bicycle. If the wheel is leaned away from the vertical so that the top of the wheel moves to the left, the forward rim of the wheel also turns to the left. In other words, rotation on one axis of the turning wheel produces rotation of the third axis.
  5. 5. Gokul Lakshmanan lakshmanangokul7@gmail.com 5 A gyroscope flywheel will roll or resist about the output axis depending upon whether the 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. The center of gravity of the rotor can be in a fixed position. The rotor simultaneously spins 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 about the fixed point. Some gyroscopes have mechanical equivalents substituted for one or more of the elements. For example, the spinning rotor may be suspended in a fluid, instead of being pivotally mounted in gimbals. A control moment gyroscope (CMG) is an example of a fixed-output-gimbal device that is used on spacecraft to hold or maintain a desired attitude angle or pointing direction using the gyroscopic resistance force. In some special cases, the outer gimbal (or its equivalent) may be omitted so that the rotor has only two degrees of freedom. In other cases, the center of gravity of the rotor may be offset from the axis of oscillation, and, thus, the center of gravity of the rotor and the center of suspension of the rotor may not coincide. In addition to being used in compasses, aircraft, computer pointing devices, etc., gyroscopes have been introduced into consumer electronics. Since the gyroscope allows the calculation of orientation and rotation, designers have incorporated them into modern technology. The integration of the gyroscope has allowed for more accurate recognition of movement within a 3D space than the previous lone accelerometer within a number of smartphones. Gyroscopes in consumer electronics are frequently combined with accelerometers (acceleration sensors) for more robust direction- and motion-sensing. 3.2 Properties A free gyroscope maintains its axis. Gyroscopes can be used to construct gyrocompasses, which complement or replace magnetic compasses (in ships, aircraft and spacecraft, vehicles in general), to assist in stability (Hubble Space Telescope, bicycles, motorcycles, and ships) or be used as part of an inertial guidance system. Gyroscopic effects are used in tops, boomerangs, yo- yos, and Power balls. Many other rotating devices, such as flywheels, behave in the manner of a gyroscope, although the gyroscopic effect is not being used. When the gyroscope is not free (under the influence of torques), it exhibits a number of behaviors including precession and stability. The fundamental equation describing the behavior of the gyroscope is:
  6. 6. Gokul Lakshmanan lakshmanangokul7@gmail.com 6 where the pseudo vectors τ and L are, respectively, the torque on the gyroscope and its angular momentum, the scalar I is its moment of inertia, the vector ω is its angular velocity, and the vector α is its angular acceleration. It follows from this that a torque τ applied perpendicular to the axis of rotation, and therefore perpendicular to L, results in a rotation about an axis perpendicular to both τ and L. This motion is called precession. The angular velocity of precession ωP is given by the cross product: τ = ωP ∗L Precession can be demonstrated by placing a spinning gyroscope with its axis horizontal and supported loosely at one end. Instead of falling, as might be expected, the gyroscope appears to defy gravity by remaining with its axis horizontal, when the other end of the axis is left unsupported and the free end of the axis slowly describes a circle in a horizontal plane, the resulting precession turning. This effect is explained by the above equations. The torque on the gyroscope is supplied by a couple of forces: gravity acting downward on the device's center of mass, and an equal force acting upward to support one end of the device. The rotation resulting from this torque is not downward, as might be intuitively expected, causing the device to fall, but perpendicular to both the gravitational torque (horizontal and perpendicular to the axis of rotation) 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. Precession is an interesting property of gyroscopes. But how can it be used to create useful sensors? Gyroscopes can be used to measure orientation, tilt (gravity), and external force. Gyroscopes are also used to determine the position of a body in space, but this often requires the integration of additional sensors like accelerometers. Some of the more common applications of gyroscopes will be discussed here in greater detail. Precession is the phenomenon observed in the bicycle wheel experiment. If an input force is applied against the spin axis the wheel will resist it by generating an output force perpendicular and proportional to the input. One typical type of gyroscope is made by suspending a relatively massive rotor inside three rings called gimbals. Mounting each of these rotors on high quality bearing surfaces insures that very little torque can be exerted on the inside rotor.
  7. 7. Gokul Lakshmanan lakshmanangokul7@gmail.com 7 Fig 3.1: Gyroscope 3.3 Angular momentum In physics, angular momentum, moment of momentum, or rotational momentum is a measure of the amount of rotation an object has, taking into account its mass, shape and speed. It is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis. The angular momentum of a system of particles (e.g. a rigid body) is the sum of angular moment of the individual particles. For a rigid body rotating around an axis of symmetry (e.g. the blades of a ceiling fan), the angular momentum can be expressed as the product of the body's moment of inertia, I, (i.e., a measure of an object's resistance to changes in its rotation velocity) and its angular velocity, ω. In this way, angular momentum is sometimes described as the rotational analog of linear momentum. For the case of an object that is small compared with the radial distance to its axis of rotation, such as a rubber ball swinging from a long string or a planet orbiting in an ellipse around the Sun, the angular momentum can be approximated as the cross product of its linear momentum,
  8. 8. Gokul Lakshmanan lakshmanangokul7@gmail.com 8 mv, and its position relative to the point about which it is rotating, r. Thus, the angular momentum, L, of a particle with respect to some point of origin is as follows. Fig 3.2: Precession Angular momentum is conserved in a system where there is no net external torque, and its conservation helps explain many diverse phenomena. For example, the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum. The very high rotational rates of neutron stars can also be explained in terms of angular momentum conservation. Moreover, angular momentum conservation has numerous applications in physics and engineering (e.g., the gyrocompass). The angular momentum, L, of a particle about a given origin is defined as: Where r is the position vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product. As seen from the definition, the derived SI units of angular momentum are Newton meter seconds (N·m·s or kg·m2 /s) or joule seconds (J·s). Because of the cross product, L is a pseudo vector perpendicular to both the radial vector r and the momentum vector p and it is assigned a sign by the right-hand rule. For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:
  9. 9. Gokul Lakshmanan lakshmanangokul7@gmail.com 9 Fig 3.3: Angular momentum Where I is the moment of inertia of the object (in general, a tensor quantity), and ω is the angular velocity. The angular momentum of a particle or rigid body in rectilinear motion (pure translation) is a vector with constant magnitude and direction. If the path of the particle or center of mass of the rigid body passes through the given origin, its angular momentum is zero. Angular momentum is also known as moment of momentum. The angular momentum of a rigid object is also defined as the product of the moment of inertia and the angular velocity. It is analogous to linear momentum and is subject to the fundamental constraints of the conservation of angular momentum principle if there is no external torque on the object. Angular momentum is a vector quantity. It is derivable from the expression for the angular momentum of a particle 3.4 Gyrocompass A gyrocompass is a type of non-magnetic compass which is based on a fast-spinning disc and rotation of the Earth (or another planetary body if used elsewhere in the universe) to automatically find geographical direction. Although one important component of a gyrocompass
  10. 10. Gokul Lakshmanan lakshmanangokul7@gmail.com 10 is a gyroscope, these are not the same devices; a gyrocompass is built to use the effect of gyroscopic precession, which is a distinctive aspect of the general gyroscopic effect. Gyrocompasses are widely used for navigation on ships, because they have two significant advantages over magnetic compasses 1) They find true north as determined by Earth's rotation, which is different from, and navigationally more useful than, magnetic north. 2) They are unaffected by ferromagnetic materials, such as ship's steel hull, which change the magnetic field. Gyrocompasses use a spinning rotor to locate true north, however, an additional torque is needed to offset forces exerted by the Earth’s rotation. Using weights is the most practical method for providing the offset torque. Weights force the axis of rotation to remain horizontal with respect to the earth’s surface. Being thus constrained the gyroscope continually realigns itself, pointing towards true north. Most sophisticated aircraft and missile systems use Inertial Navigation System (INS) to determine their location and orientation. The gyrocompass sensor is only one component of the INS but it is very important. It provides information about the plant’s orientation. Combining orientation information with data collected from accelerometers an onboard computer can determine the objects location.
  11. 11. Gokul Lakshmanan lakshmanangokul7@gmail.com 11 Fig 3.4 A Marine gyrocompass A gyroscope, not to be confused with gyrocompass, is a spinning wheel mounted on gimbal so that the wheel's axis is free to orient itself in any way. When it is spun up to speed with its axis pointing in some direction, due to the law of conservation of angular momentum, such a wheel will normally maintain its original orientation to a fixed point in outer space (not to a fixed point on Earth). Since our planet rotates, it appears to a stationary observer on Earth that a gyroscope's axis is completing a full rotation once every 24 hours. Such a rotating gyroscope is used for navigation in some cases, for example on aircraft, where it is known as heading indicator, but cannot ordinarily be used for long-term marine navigation. The crucial additional ingredient needed to turn such gyroscope into a gyrocompass, so it would automatically position to true north is some mechanism that results in an application of torque whenever the compass's axis is not pointing north. One method uses friction to apply the needed torque, the gyroscope in a gyrocompass is not completely free to reorient itself; if for instance a device connected to the axis is immersed in a viscous fluid, then that fluid will resist reorientation of the axis. This friction force caused by the
  12. 12. Gokul Lakshmanan lakshmanangokul7@gmail.com 12 fluid results in a torque acting on the axis, causing the axis to turn in a direction orthogonal to the torque (that is, to precess) along a line of longitude. Once the axis points toward the celestial pole, it will appear to be stationary and won't experience any more frictional forces. This is because true north is the only direction for which the gyroscope can remain on the surface of the earth and not be required to change. This axis orientation is considered to be a point of minimum potential energy. Fig 3.5: Gyrocompass Another, more practical, method is to use weights to force the axis of the compass to remain horizontal (perpendicular to the direction of the center of the Earth), but otherwise allow it to rotate freely within the horizontal plane. In this case, gravity will apply a torque forcing the compass's axis toward true north. Because the weights will confine the compass's axis to be horizontal with respect to the Earth's surface, the axis can never align with the Earth's axis (except on the Equator) and must realign itself as
  13. 13. Gokul Lakshmanan lakshmanangokul7@gmail.com 13 the Earth rotates. But with respect to the Earth's surface, the compass will appear to be stationary and pointing along the Earth's surface toward the true North Pole. Since the gyrocompass's north-seeking function depends on the rotation around the axis of the Earth that causes torque-induced gyroscopic precession, it will not orient itself correctly to true north if it is moved very fast in an east to west direction, thus negating the Earth's rotation. However, aircraft commonly use heading indicators or directional gyros, which are not gyrocompasses and do not position themselves to north via precession, but are periodically aligned manually to true north. If a gyroscope is placed at the equator with its spin axis pointing east-west, as the earth turns on its axis, gyroscopic inertia will tend to keep the plane of rotation constant. To the observer, it is the gyroscope which is seen to rotate, not the earth. This effect is called the horizontal earth rate, and is maximum at the equator and zero at the poles. At points between, it is equal to the cosine of the latitude. If the gyro is placed at a geographic pole with its spin axis horizontal, it will appear to rotate about its vertical axis. This is the vertical earth rate. At all points between the equator and the poles, the gyro appears to turn partly about its horizontal and partly about its vertical axis, being affected by both horizontal and vertical earth rates. In order to visualize these effects, remember that the gyro, at whatever latitude it is placed, is remaining aligned in space while the earth moves beneath it. 3.5 Gimbal A gimbal is a pivoted support that allows the rotation of an object about a single axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of the rotation of its support (e.g. vertical in the first animation). For example, on a ship, the gyroscopes, shipboard compasses, stoves, and even drink holders typically use gimbals to keep them upright with respect to the horizon despite the ship's pitching and rolling. The gimbal suspension used for mounting compasses and the like is sometimes called a Cardan suspension after Italian mathematician and physicist Gerolamo Cardano (1501–1576) who described it in detail. However, Cardano did not invent the gimbal, nor did he claim to. The device has been known since antiquity and may not have a single identifiable inventor.
  14. 14. Gokul Lakshmanan lakshmanangokul7@gmail.com 14 Fig 3.6: How a gimbal works In inertial navigation, as applied to ships and submarines, a minimum of three gimbals are needed to allow an inertial navigation system (stable table) to remain fixed in inertial space, compensating for changes in the ship's yaw, pitch, and roll. In this application, the Inertial Measurement Unit (IMU) is equipped with three orthogonally mounted gyros to sense rotation about all axes in three-dimensional space. The gyro outputs drive motors controlling the orientation of the three gimbals as required to maintain the orientation of the IMU. In turn, angular measurement devices called "resolvers" mounted on the three gimbals provide the nine cosine values for the direction cosine matrix needed to orient the ship.
  15. 15. Gokul Lakshmanan lakshmanangokul7@gmail.com 15 Fig 3.7 A 3 axis gimbal gyroscope In inertial navigation systems, gimbal lock may occur when vehicle rotation causes two of the three gimbal rings to align with their pivot axes in a single plane. When this occurs, it is no longer possible to maintain the sensing platform's orientation. 3.6 Gimbal lock Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space. The word lock is misleading: no gimbal is restrained. All three gimbals can still rotate freely about their respective axes of suspension. Nevertheless, because of the parallel orientation of two of the gimbals axes there is no gimbal available to accommodate rotation along one axis. This problem may be overcome by use of a fourth gimbal, intelligently driven by a motor so as to maintain a large angle between roll and yaw gimbal axes. Another solution is to rotate one or more of the gimbals to an arbitrary position when gimbal lock is detected and thus reset the device.
  16. 16. Gokul Lakshmanan lakshmanangokul7@gmail.com 16 Fig 3.8: Gimbal Lock Modern practice is to avoid the use of gimbals entirely. In the context of inertial navigation systems, that can be done by mounting the inertial sensors directly to the body of the vehicle (this is called a strapdown system)[3] and integrating sensed rotation and acceleration digitally using quaternion methods to derive vehicle orientation and velocity. Another way to replace gimbals is to use fluid bearings or a flotation chamber 3.7 Purpose of Gyrocompass a) For Navigation. b) To Stabilize Airplane and Ship. a) Gyrocompass for navigation Gyrocompass is used for navigation purpose in ships, airplanes and even in space crafts. Apollo missions to moon are also guided by gyrocompass.
  17. 17. Gokul Lakshmanan lakshmanangokul7@gmail.com 17 For assisting navigation the axis of rotation of gyro is aligned to point towards the geographical north. Since no external torque acts on the axis of rotation the gyro will always point towards geographical north irrespective of the motion of ship. b) Gyrocompass for stabilization Stabilization of ships and airplanes are attained with the help of gyrocompass. A gyrocompass serves as an instrument to measure the instability and send necessary signals. A Gyrocompass is mounted on Airplane or Ship. Variation in alignment of gimbal frame with respect to axis of rotation of gyro is used judge the amount of pitch, roll and yaw experienced by Airplane or ship. The degree of pitch, yaw or roll experienced by the ship is measured and converted into electrical signal by a transducer which is then send to the pilot or captain of the ship.
  18. 18. Gokul Lakshmanan lakshmanangokul7@gmail.com 18 CHAPTER 4 DESIGN CALCULATIONS 4.1 Components and Specifications The gyrocompass was constructed from various type of materials selected by considering their properties such as strength, rigidity, weight etc. We have used a metallic disc of diameter 178.8mm as a rotating gyro to demonstrate the gyroscopic properties. The gimbal frame is constructed using GI Hollow pipes of diameter 19.5mm and length 6m.ballbearings of diameter 19.5mm are used to connect the three gimbal frames. Table 4.1 Components and Specifications COMPONENT SPECIFICATIONS 1) DISC a. DIAMETER = 178.8 mm. b. MASS = 1.5 kg. 2) BALL BEARING a. DIAMETER = 19.5 mm. b. Nos. = 6 3) PIPE (G I) a. DIAMETER = 19.5 mm. b. LENGTH = 6 m.
  19. 19. Gokul Lakshmanan lakshmanangokul7@gmail.com 19 4.2 Cost of Production The total cost of production was 1350 Indian rupees and it was spend on various parts and components as shown in table 4.2 below. Cost for transportation was also included in total cost along with accessories like bottles of paint. The total cost was kept as low as possible. Table 4.2: Cost of production Component Specification Cost (in Rupees) Bearing 6.nos 300 Disc 1 100 G I Pipe 6meters 440 Nuts and Bolts 8.nos 30 Transportation 200 Paint 3 Bottles 280 TOTAL 1350
  20. 20. Gokul Lakshmanan lakshmanangokul7@gmail.com 20 4.3 Calculation For a rotating gyro with mass ‘M’ and radius ‘r’. Angular momentum is given by: =∗∗ Where‘’is the tangential velocity of gyro. The value of angular momentum should be large enough to oppose any torque which the gyro experience due to self-weight. Here we have M=1.5 kg r=0.1788 m Also =ω∗r Where angular velocity ω= 2πrN/60 rad So, L=1.5∗0.1788∗(2π∗0.1788∗N/60) L=0.005N kg m2 /s Angular momentum experienced by gyro depends of its speed N (rpm) and it should be sufficient enough to resist any torque due to self-weight of gyro within the gimbal.
  21. 21. Gokul Lakshmanan lakshmanangokul7@gmail.com 21 4.4 Designed Gyrocompass Fig 4.1 Designed Gyrocompass
  22. 22. Gokul Lakshmanan lakshmanangokul7@gmail.com 22 CHAPTER 5 ADVANTAGES DISADVANTAGES Gyrocompass have both advantages and disadvantages.Various advantages and disadvantages of a typical gyrocompass are listed below. Table 5.1: Advantages and Disadvantages of Gyrocompass Advantages Disadvantages Seeks geographic (true) north instead of magnetic. Loses orientation as Earth rotates unless torque is applied in opposite rotation cheap, self-contained, simple, not easily damaged Gimbal lock occur when two axis align parallel to each other Can be used near the earth’s magnetic poles, where magnetic compass is useless. Requires a constant source of electrical power and is sensitive to power fluctuations. Unaffected by surrounding metals. Requires periodic maintenance by qualified technicians. Gyrocompasses need no magnetic corrections Excessive weight and space requirements
  23. 23. Gokul Lakshmanan lakshmanangokul7@gmail.com 23 CONCLUSION Gyrocompass is a type of non-magnetic compass which is based on a fast-spinning disc. Within mechanical systems or devices, a conventional gyroscope is a mechanism comprising a rotor journaled to spin about one axis, the journals of the rotor being mounted in an inner gimbal or ring; the inner gimbal is journaled for oscillation in an outer gimbal for a total of two gimbals. This project work helped us to gain practical knowledge about GYROCOMPASS and also helped us to physically test various gyroscopic properties. The gyrocompass was constructed in time and is tested for accuracy. Care was taken to avoid gimbal lock during testing by holding 3 frames perpendicular to each other and avoiding them from aligning in a single plain. The gyrocompass was working as expected and we are able to demonstrate its precession and stability. The project helped us to understand and solve the difficulties which one encounter while performing a project work. This project also helped to understand the effect of gimbal lock on a practical gyrocompass and need to avoid it. By performing a well-planned design and construction process we are able to construct a 3 axis gimbal gyrocompass and test its properties.
  24. 24. Gokul Lakshmanan lakshmanangokul7@gmail.com 24 REFERENCE [1]H.Hamilton,Mabie Charles F.Reinholtz , Mechanism and dynamics of Machinery, John Wiley sons. [2]J.E.Shigley J.J.Uicker Jr.,Theory of Machines and Mechanisms, Mc Graw Hill. [3]Dynamics of Machinery - Theory and Applications – Springer [4]S.S Rattan, Theory of Machines, Tata Mc Graw Hill. [5]V.P. Singh, Theory of Machines, Dhanpat Rai and Co. [6]Erdman A.G Sandor G.N., Mechanism Design: Analysis and Synthesis [7]Nasiri, S. (2006, July). A Critical Review of Gyroscopes Technology and Commercialization Status. Retrieved Feb 15, 2009, from InvenSense [8]Gyroscope Application Examples. Retrieved February 15, 2009, from Conventor [9]Kaumualii High School. (2004). Bicycle Wheel Gyro. Retrieved February 14, 2009 [10] The gyroscope pilots ships planes. Life: 80–83. Mar 15, 1943

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