DEGREES OF FREEDOM

A gyro can have different degrees of freedom, depending on the number of gimbals in which it is supported and the way the gimbals are arranged. Do not confuse the term "degrees of freedom" with an angular value such as degrees of a circle. The term, as it applies to gyros, is an indication of the number of axes about which the rotor is free to precess.

A gyro mounted in two gimbals has two degrees of freedom. When two gimbals are used, the gyro is said to be UNIVERSALLY MOUNTED. This arrangement provides two axes about which the gyro can precess. These two axes and the spin axis intersect at the center of gravity of the entire system (excluding the support). Because of this arrangement, the force of gravity does not exert a torque to cause precession. The rotor, inner gimbal, and outer gimbal are balanced about the three principal axes.

TWO DEGREES-OF-FREEDOM GYROS

The two-degrees-of-freedom (free) gyros can be divided into two groups. In the first group, the gyro's spin axis is perpendicular to the surface of the Earth. Thus the gyro's rotor will spin in a horizontal plane. These gyros are used to establish vertical and horizontal planes to be used where stabilized reference planes are needed.

In the second group, the gyro's spin axis is either parallel to the surface of the Earth or at some angle other than perpendicular. The spin axis of the gyro in the gyrocompass, for example, is maintained in a plane parallel to the surface of the Earth It is aligned in a plane of the north-south meridian. Once set, it will continue to point north as long as no disturbing force causes it to precess out of the plane of the meridian.

Effect of Rotation of the Earth

As you have learned, a free gyro maintains its spin axis fixed in space, and not fixed relative to the Earth's surface. To understand this, imagine yourself in a space ship somewhere out in space and looking at the South Pole of the Earth. You see a sphere rotating clockwise, with the South Pole in the center. Maneuver your ship until it is on a direct line with the South Pole and then cut in the automatic controls to keep it in this position. You will now see the Earth make a complete rotation every 24 hours.

You could keep track of that rotation by driving a big post into the Equator as shown in view A of figure 3-11. If this post were upright at 1200, the Earth's rotation would carry it around so it would be pointing to your right at 1800. Likewise, the Earth's rotation would carry the post around so that at 2400 it would be upside down. Then, at 0600 the next day, the post would be pointing to your left. Finally, at 1200 the next day the post would be back in its original position, having been carried, with the Earth, through its complete rotation. Notice that the post has many positions as you observe it - because it is attached to the Earth's surface and does not have rigidity in space.

Figure 3-11A. - Fixed direction in space. Post on the equator viewed from space.

If you put a gyroscope in place of the stake, you will see a different action. Imagine a gyroscope mounted at the Equator with its spin axis aligned with the E/W axis of the Earth. The gyro is spinning and has rigidity in space. Now look at view B. At 1200 the spinning axis is horizontal with respect to the Earth's surface. At 1800 the spinning axis is vertical with respect to the Earth's surface; but the gyro is still spinning in the same plane as before, and the black end is pointing away from the Earth's surface. At 2400, the spinning axis is again horizontal. At 0600 the spinning axis is again vertical, and the black end points toward the Earth. Finally, at 1200 the next day, the gyro is in the same position as when it started. The plane of spin of the gyro wheel did not change direction in space while the gyro rotated with the Earth. This is because the gyro is rigid in space.

Figure 3-11B. - Fixed direction in space. Gyro on equator viewed from space.

You have just imagined observing the gyro from space. Now, let's come back to Earth and stand right next to the gyro. Look at the gyro in view C. From your viewpoint on Earth, the spinning axis appears to make one complete rotation in one day. As you know, the gyro is rigid, and both you and the Earth are rotating. The effect of the Earth's rotation on a gyro is sometimes called APPARENT DRIFT, APPARENT

PRECESSION, or APPARENT ROTATION.

Figure 3-11C. - Fixed direction in space. Gyro on equator viewed from earth.

Effect of Mechanical Drift

A directional error in a gyro is produced by random inaccuracies caused by mechanical drift and the effect of the Earth's rotation (apparent drift).

We shall see later how it is corrected for in the equipment. First, let's consider the causes of mechanical drift.

There are three general sources of mechanical drift:

• Unbalance. A gyro often becomes dynamically unbalanced when operated at a speed or temperature other than that for which it was designed.
• The static balance of the gyro is upset when its center of gravity is not at the intersection of the three major axes. Some unbalance of both types will exist in any gyro since manufacturing processes cannot produce a perfectly balanced gyro.
• Bearing friction. Friction in the gimbal bearings results in loss of energy and incorrect gimbal positions. Friction in the rotor bearings causes mechanical drift only if the friction is not symmetrical. An even amount of friction all around in a rotor bearing results only in a change of the speed of rotation.
• Inertia of gimbals. Energy is lost whenever a gimbal rotates because of the inertia of the gimbal. The greater the mass of the gimbal, the greater the drift from this source.

The complete elimination of mechanical drift in gyros appears to be an impossibility. However, by proper design it has been kept to a minimum.

Any error that still exists can be corrected for.

Q.13 A universally mounted gyro has how many degrees of freedom?
Q.14 If a free gyro is placed at the equator at 1200 in a vertical position; in what position should it be at 1800?
Q.15 What are the three causes of mechanical drift in a gyro?