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PRECESSION

To provide useful information, a gyro's spin axis must be related to some reference, usually the Earth's surface. This is done by using the second fundamental property of a gyro - PRECESSION. The gyro is precessed until its spin axis is pointed in the desired direction. So far we have covered precession in very general terms. The following paragraphs will cover this "gyro action" in more detail.

We can show precession by using the models in figure 3-7, view (A) and view (B). The gyro wheel is mounted so it is free to have its spin axis pointed in any direction. Here the wheel rotates in a flat loop called the gyro case (inner gimbal). The gyro case is pivoted in the gimbal ring (outer gimbal) and the gyro can swing about the Z axis. The gimbal ring itself turns on pivots that connect it to the fork (support). The fork permits the gyro to tilt from side to side about the Y axis.

Figure 3-7A. - Gyro action.

Figure 3-7B. - Gyro action.

Regardless of how the fork is placed, the spinning gyro wheel is free to lie in any given plane. That's why it is called a free gyroscope in this type of mounting.

To show the effect of precession, we can push down on the gimbal ring at point A at the nearer end of the Z-Z axis. (See view A of figure 3-7.) You might expect the ring to tilt around the Y-Y axis. Instead, the gyro case will tilt about the Z-Z axis. You can see the effect of this precession in view B.

Here's a rule that applies to all spinning gyros: THE GYRO WILL ALWAYS PRECESS AT RIGHT ANGLES TO THE DIRECTION OF THE APPLIED FORCE. Look at view A again. If we keep pushing down on the gimbal ring at point (A), the gyro case will keep turning until the spin axis of the gyro wheel is horizontal. Then there will be no further precession. At this point the gyro wheel will be spinning in the same direction in which the applied force is pushing.

Here's another rule: A GYRO ALWAYS PRECESSES IN A DIRECTION TENDING TO LINE ITSELF UP SO THAT ITS ROTOR SPINS IN THE SAME DIRECTION THAT THE APPLIED FORCE IS TRYING TO TURN IT. In other words, the direction of spin chases the applied force. When the direction of spin and the applied force are in the same direction, precession stops.

Now, compare the spin (X) axis in the two parts of figure 3-7. In view A, the spin axis is vertical. In view B, the spin axis has moved from the vertical until it is much closer to being horizontal. By applying the right amount of force in the right place, we have a method of "aiming" the spin axis so that it points to the specific fixed direction in space where we want it. The property of PRECESSION makes the property of RIGIDITY useable.

You should understand that most forces, when applied to the gyro mounting, do not cause precession. For instance, you can swing the fork around in any direction, and the motion will merely be taken up in the Y-Y and Z-Z axes. Similarly, a force applied lengthwise along one of the axes will have no effect.

Any force acting through the center of gravity of the gyroscope does not change the angle of the plane of rotation but moves the gyroscope as a unit. The position of its spin axis in space is not changed. Such forces as those stated above, operating through the center of gravity, are forces of TRANSLATION. In other words, the spinning gyroscope may be moved freely in space by means of its supporting frame, without disturbing the plane of rotation of the rotor. This condition exists because the force that is applied through the supporting frame, acting through the center of gravity produces no torque on the gyro rotor. ONLY THOSE FORCES TENDING TO TILT THE GYRO WHEEL ITSELF WILL CAUSE PRECESSION.

Let's consider further the important characteristic of gyroscopic precession. For a given amount of force, the rate of precession of a gyro is governed by the weight, shape, and speed of the rotor. These factors are the same as those that determine the rigidity of a gyro. Therefore, there is a definite relationship between the rigidity of a gyro and the rate at which a given force will cause it to precess. The greater the rigidity of a gyro, the more difficult it is to cause precession, and the less precession there will be for a given force.

A gyro will resist any force that attempts to change the direction of its spin axis. However, it will move (precess) in response to such force; NOT in the direction of the applied force, but at right angles to it.

The direction a gyro will precess also depends on the direction the gyro is spinning. Precession is actually the result of two forces: angular momentum (spinning force) and the applied force (torque). The direction of precession is always offset from the direction of the applied force. The offset is always in the direction of rotor spin.

For example, when a force is applied upward on the inner gimbal, as shown in figure 3-8, the force may be visualized as applied in an arc about axis Y-Y. This applied force is opposed by the resistance of gyroscopic inertia, preventing the gyro from rotating about axis Y-Y. With the rotor spinning clockwise, the precession will take place 90 clockwise from the point of applied force. The gyro precesses about axis Z-Z in the direction of the arrow "P".

Figure 3-8. - Force applied to a gyro.

The motions of a gyroscope can be analyzed according to three basic quantities:

  • SPIN (the angular velocity of the gyro rotor).
  • TORQUE (the rotary motion applied to change the direction of the rotor axis).
  • PRECESSION (the resulting angular change of the spin axis when torque is applied).

The above quantities are related to vectors so that the relative directions may be easily compared. The SPIN VECTOR lies along the spin axis of the rotor with an arrow indicating the direction of rotation. The TORQUE VECTOR represents the axis about which the applied force is felt. The PRECESSION VECTOR represents the axis about which precession occurs. In all the above cases the direction of the vector is such that the quantity (spin, torque, or precession) is in a clockwise direction if viewed from the tail of the vector.

A simple hand rule will help you determine the direction of the SPIN VECTOR. (See fig. 3-9.) Curve the fingers of your fight hand in the direction in which the rotor is turning as if you intended to grasp the rotor. Your thumb will point in the direction of the spin vector. Similar rules will give you the direction of the TORQUE VECTOR and the PRECESSION VECTOR. With the fingers of your right hand wrapped in the direction of the applied torque (die direction the gyro would rotate if the rotor were not spinning), your thumb points in the direction of the torque vector. Placing your curved fingers in the direction of precession will place your thumb pointing in the direction of the precession vector.

Figure 3-9. - Determining spin vector direction.

All three motions are rotary (angular) and can be represented by vectors that point in such a direction that when you look in the direction of the vector the rotary motion around the vector is clockwise.

Another hand rule convenient for determining the DIRECTION OF PRECESSION uses the fingers of the right hand. This method may not be new to you. A similar method is applied to electric motors (see NEETS, module 5).

You may represent the three vectors listed above by arranging the thumb, forefinger, and middle finger of your right hand mutually perpendicular as shown in figure 3-10. Your thumb points in the direction of the precession vector, your middle finger points in the direction of the torque vector, and your forefinger points in the direction of the spin vector. You can consider these vectors as the axes about which angular motion takes place. If you look in the directions your fingers and thumb point, you can visualize that all the rotary motions are clockwise as indicated in figure 3-10.

Figure 3-10. - Right-hand rule for determining direction of precession.

This three-finger rule is useful for analyzing any gyroscope motion problem because if the directions of any two of the three vectors are known, the direction of the third vector can be found and the motion around this vector may be determined.

Q.9 What type of force acts ONLY through the center of gravity of a gyro, and does NOT cause precession? answer.gif (214 bytes)
Q.10 The amount of precession that results from a given force is determined by what quantity? answer.gif (214 bytes)
Q.11 What factor determines the direction a gyro will precess in response to a particular force? answer.gif (214 bytes)
Q.12 When using the tight-hand rule to determine precession, which finger indicates the direction of the applied force?answer.gif (214 bytes)




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