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What is a gimbal & gimbal lock? Are they elated?
Table of Contents:
Gyroscopes are useful for measuring or maintaining orientation. Gyroscopic effect can be seen in many places, including vehicles, ships, airplanes, mobiles and earth too!
Let's look into all of those applications here! Before jumping into the applications, let's understand few basics.
Angular Momentum
Angular Momentum of a rigid body is defined as the product of a moment of inertia and angular velocity. It is a vector quantity, which means it has both magnitude and direction.
Torque
Torque is the product of the force applied and the perpendicular distance from the axis of rotation to the line of action of the force. Torque is an influence that tends to change the rotational motion of an object.
Right-hand rule
Consider L=Iω, where L is angular momentum, I is the moment of inertia and ω is angular velocity. The direction of angular velocity ω size and angular momentum L are defined to be the direction in which the thumb of your right-hand points when you curl your fingers in the direction of the disk’s rotation as shown in the figure.
Gyroscopic Effect
Let us consider the above example where the person is holding a bicycle wheel. When the wheel is rotated and held freely, after tilting it to the side, the person also experiences a pull towards that side. Wondering how that happens? This is the reason!
a = dv/dt: where a is acceleration, dv/dt is changing in velocity w.r.t. time. Acceleration and velocity both are vectors. It is not necessary that acceleration & velocity are in the same direction but the direction of dv and acceleration are always the same, in any case.
Similarly, τ = dL/dt:
where τ is Torque, dL/dt is the change in linear momentum wrt time. Similar to acceleration, torque τ and dL are always in the same direction.
The direction of ΔL is the same as the direction of the torque τ that creates it.
This is the reason why the person who tilted the rotating wheel, experienced a push to that side.
The Axis of spin is the axis about which the object rotates. The spin angular momentum is along the rotation axis as shown, but the torque about the support point is in a direction perpendicular to the angular momentum. The torque produces a change in L which is perpendicular to L. Such a change causes a change in direction of L as shown but not a change in its size. This circular motion is called precession. The torque required to produce angular acceleration is known as gyroscopic torque and is a couple that must be applied to the axis of the spin to cause it to rotate with angular velocity.
Gyroscopic effect is ability (tendency) of the rotating body to maintain a steady direction of its axis of rotation.
A reactive gyroscopic torque or reaction torque also acts on the axis of spin in opposite direction to the applied torque, which determines the motion of the object.
Gyroscopic Effect on Airplane
Let us consider an example below. Imagine you are viewing an aircraft taking left turn from your perspective and motor is rotation in anti-clockwise direction. Applying right hand rule to rotation in anti-clockwise direction for motor, the direction of axis of spin is towards you. Now image you are sitting in the plane and it is taking a left turn along the axis of precision. Again apply right hand rule along the rotation of axis of precision, to give direction of the vector upwards. Hence, as a result of direction of axis of spin & rotation of axis of precision, the direction of axis of active gyroscopic couple is away from the center as shown in figure. Opposite to this vector is reactive gyroscopic couple. Applying right had rule to reactive gyroscopic couple would make the tail of the airplane dip & rise the nose.
In this way, we can find out the effect of gyroscope on any device.
Gyroscopic effect on Ships:
Here, is one more example below. The Gyroscopic effect on ship when it is pitching downwards when seen from front and propeller rotates clockwise in the figure below.
Gyroscopic effect can also be seen on earth. Earth is a very large rotating body & is therefore both dynamically stable, with noticeable effects at a large scale, resulting from that rotation. It rotates at the speed of one rotation per day.
Gyroscopic devices (Gyroscope) & Application of Gyroscopic effect
Gyroscope, a device containing a rapidly spinning wheel or circulating beam of light that is used to detect the deviation of an object from its desired orientation.
Gyroscopic instruments in aircraft:
Heading indicator: No matter in whichever direction the aircraft rotates this instrument always resists the change in position, which helps us understand degree of rotation of the aircraft. The gyro is placed horizontal in this device.
Turn indicator: This device presses according to the turn taken by aircraft and measures the angle. The gyro is placed horizontal in this device.
Attitude indicator: It is also known as artificial horizon. It indicates the position of aircraft with respect to the earth's surface. The gyro is placed vertical in this device.
In rockets, the gyroscopes tell how fast the rocket is rolling.
Gyro sensors
Gyro sensors can measure the tilt and lateral orientation of the object whereas accelerometer can only measure the linear motion. Gyroscope sensors are also called as Angular Rate Sensor or Angular Velocity Sensors.
Gimbal & Gimbal Lock
A gimbal is a ring that is suspended so it can rotate about an axis.
Gimbals are typically nested one within another to accommodate rotation about multiple axes. 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. This problem may be overcome by use of a fourth gimbal, but it makes the machine bulky. 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. Modern practice is to avoid the use of gimbals entirely with the help of sensors.
Tops were invented in many different civilizations, including classical Greece, Rome, and China. Most of these were not utilized as instruments. The first instrument used more like an actual gyroscope was made by Johann Bohnenberger of Germany, who first wrote about it in 1817. The gyroscope was invented, and the effect named after it, in 1852 by Léon Foucault for an experiment involving the rotation of the Earth. Foucault's experiment to see the Earth's rotation (gyros, circle or rotation) was unsuccessful due to friction, which effectively limited each trial to 8 to 10 minutes, too short a time to observe significant movement. In the 1860s, the advent of electric motors made it possible for a gyroscope to spin indefinitely. The first functional gyrocompass was patented in 1904 by German inventor Hermann Anschütz-Kaempfe. In the first several decades of the 20th century, other inventors attempted (unsuccessfully) to use gyroscopes as the basis for early black box navigational systems. During World War II, the gyroscope became the prime component for aircraft and anti-aircraft gun sights. After the war, the race to miniaturize gyroscopes for guided missiles and weapons navigation systems. Gyroscopes continue to be an engineering challenge.
Summary
The direction of ΔL is the same as the direction of the torque τ that creates it.
The torque required to produce angular acceleration is known as gyroscopic torque and is a couple that must be applied to the axis of the spin to cause it to rotate with angular velocity.
Gyroscopic effect is ability (tendency) of the rotating body to maintain a steady direction of its axis of rotation.
A reactive gyroscopic torque or reaction torque also acts on the axis of spin in opposite direction to the applied torque, which determines the motion of the object.
Gyroscope, a device containing a rapidly spinning wheel or circulating beam of light that is used to detect the deviation of an object from its desired orientation.
A gimbal is a ring that is suspended so it can rotate about an axis.
Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism
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