# Elmer Sperry: Gyroscopic Compass, 1914

## Degrees of Freedom

A gyro has two basic mountings: one with three degrees of freedom, and one with only two degrees of freedom. A gyro having three degrees of freedom is able to rotate about three axes including its own axis of rotation. Foucault used such a model to illustrate the rotation of the earth, crafting a model with a gyro mounted in two rings. One ring rotated on a horizontal axis within the other, which in turn rotated on a vertical axis.

Remember that the gyro itself is a spinning mass mounted on a base, and therefore has its own axis. Its center of gravity is located at the intersection of all three axes of rotation. Foucault rotated the wheel of the gyro using a string, and aligned as optical sighting device on the gyro wheel. Observers noted that, as time passed, the wheel seemed to move out of alignment with the optical sighting device. The case here is the same of that of the pendulum outlined above: the sighting device rotated with the earth while the gyro maintained its orientation in space during the few minutes the wheel rotated at high speed. Foucault was unable to sustain the spinning of his gyro wheel, but later inventors would add a motor that would surmount this problem.

Foucault went on to experiment with a gyro having two degrees of freedom, hypothesizing that such a gyro could be used as a compass. He limited the gyro's degrees of freedom to two by weighting the interior ring of the gyroscope, thereby restraining its freedom of rotation about the horizontal axis. Due to the weight, the gyro became pendulous, and felt the force of gravity. Foucault predicted this result, going on to say that the force of gravity would cause the gyroscope to precess until the axis of rotation of the spinning wheel was parallel to the axis of rotation of the earth. With an axis thus oriented, the gyroscope would be pointing to true north.

Again Foucault was hampered by his inability to keep the wheel spinning at a high speed, but the later addition of a motor would once more solve this problem. Now that we have discussed the meaning of a "degree of freedom," it will be necessary to tackle the tricky topic of precession. This phenomenon facilitates the function of the gyroscope.