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The free Gyroscope and its properties




The term "gyroscope" applies to a physical body that spins rapidly around its axis of symmetry and is suspended in such a way that the axis of rotation can occupy any position in space.

In the field of engineering, the gyroscope is usually a heavy disc; practically in all modern instruments the disc is the rotor of an electric motor. One of the ways of suspending the gyroscope is to mount it in gimbals. Being suspended in such a manner, the gyroscope is rendered the possibility to turn round any of the fol­lowing three axes which are mutually perpendicular and intersect in one point:

(a) Axis AB — the axis of rotation of the gyroscope rotor cal­led the main axis or spinning axis;

(to) Axis CD — the slewing axis of gimbal inner ring;

(c) Axis EF — the slewing axis of gimbal outer ring.

The three possible axes of rotation of the gyroscope are re­garded its degrees of freedom; such a gyroscope possesses, the­refore, three degrees of freedom.

The point 0 where the three axes intersect is known as the point of gyroscope suspension. It is the only immobile point when the gyroscope swings ro­und any of its three axes.

A gyroscope possess­ing three degrees of free­dom can be regarded a free or neutral gyroscope on condition 'that the cen­tre of gravity of the whole system consisting of rotor and gimbal rings coinci­des with the point of sus­pension 0 and no external moments are applied to the gyroscope.

Due to fast spinning, the free gyroscope acqui­res a number of interest­ing features which are widely utilized in all kinds of gyroscopic instru­ments.

Here are the basic pro­perties of a free gyros­cope:

The main axis of the free gyroscope possesses stability, that is, it tends to maintain the direction it was given initially in relation to space.

The stability inherent to the main axis is the more pronoun­ced, the more accurately the centre of gravity of the system coin­cides with the point of gyroscope suspension (that is, the better has the gyroscope been balanced out), the lesser is friction in the gimbal axes, and the greater is the weight of the gyroscope, its diameter and rate of spinning.

The stability of the main axis makes it possible to utilize the tree gyroscope as an instrument for detecting the rotation of the Earth, because the gyroscope axis performs an apparent (visible) motion in relation to earthly objects.

Under the action of an external force applied to the gimbals rings of the gyroscope its axis moves in a direction perpendicular to that of the force acting.

This peculiar feature of a free gyroscope is called processive movement or precession. Precession of the gyroscope takes place all the while the external force is present and ceases when the force stops acting.

There is a special rule of poles which is used for determining the direction of precession.

The gyroscope pole is that end of its main axis from the side of which the rotation is seen taking place counter-clockwise.

The pole of force is that end of a gyroscope axis from the side of which the force is seen acting counter-clockwise.

The rule of poles reads as follows: when a moment of external force is acting on a gyroscope, its pole moves towards the pole of force along the shortest way.

The product I Ω. of gyroscope inertia moment and its spinning rate is known as the kinetic moment of the gyroscope. It is usually depicted as a vector directed along the main axis pointing to­wards the pole of the gyroscope.

The rate of precession of the gyroscope axis can be estimated according to the following formula:

where is the rate of precession;

M is the moment of external force.

Words to be learnt:

gimbal — универсальный шарнир

to intersect — пересекаться

slewing axis — вращающаяся ось

suspension — подвешивание, нить подвеса

to coincide — совпадать

inherent (in) — присущий

kinetic moment — кинетический момент

to depict — изображать, описывать

to estimate — оценить

 

EXERCISES

1. What's the Russian for:

to spin, symmetry, to mount, gimbal, mutually, rotation, spinning axis, suspension, immobile, swing, neutral, inherent, friction, earthly, precession, counter-clockwise.

2. Answer the following questions: 1) What does gyroscope mean?

2) What is the way of suspending the gyroscope? 3) What are the basic properties of a free gyroscope? 4) Is there a special rule of poles which is used for determining the direction of

poles?

5) Explain the rule of poles.

6) How can the rate of precession of the gyroscope axis be estimated?

 

3. Match words with their meanings: 1) diagram a) general law of cause and effect 2) principle b) not exactly divisible by two

3) phenomenon c) reasoned account offered to explain facts

4) odd d) design or plan to explain something

5) theory e) treatment shown towards other things

6) behavior f) thing that is known to exist by the senses

 

4. Discuss the following topics; 1) The way of suspending the gyroscope. 2) The peculiar features of a free gyroscope.

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