How gyroscopes work

The final component of the inertia measurement unit are the sensors that measure angular velocity, and these are commonly referred to as gyroscopes. You might have had a gyroscope as a toy when you were a child, and it is difficult to understand the relationship between this toy gyroscope, which can balance on the end of a pencil with a device that can measure angular velocity. To understand how we can use a gyroscope as an angular velocity sensor, we need to get right back to fundamentals of spinning bodies. Here, we have a disc which is spinning about the axis shown by the dotted line, and it is spinning with an angular velocity, omega g and the disc has got a rotational inertia, j. We refer to the angular momentum of this disc and give that the symbol h. h is j times omega g. Now, let's imagine that I apply a torque to this rotating disc. If I do that, the disc wants to rotate about the axis shown by the blue arrow. It's the cross product of the vector h and the vector Tau.

What we have here is a gyroscope and at the moment, the device is not spinning we can see that it moves very freely and nicely inside its gimbal mechanism. If I turn the motor on, it takes a little moment to come up to speed, it now behaves very very differently.

Now, I'm going to rotate the spinning disc assembly about the blue arrow and now; the spinning disc is going to exert a torque about the red arrow, and that torque is the cross product of the vectors omega and h. So, how do I measure the torque? If the disc axis is supported by two bearings then, this torque will exert a force up on one bearing and down on the other bearing, and those forces can be measured. The spinning disc then has converted the angular velocity omega into a torque which is then, measured using force sensors.

Importantly, if I pull on this axis of the gyroscope with a rubber band, I am basically going to exert a force on it. And so, I pull in this direction. You will see that the gyroscope is trying to rotate about an axis like this.

Angular velocity sensors based on spinning discs are not very common anymore. They tend to be rather bulky and require a lot of power to keep that disc spinning. Sensors today are based on vibrating rather than rotating element, but we still tend to call them gyroscopes or gyroscopic sensors. The vibrating elements are fabricated using ‘MEMS’ technology. So, the sensing elements themselves are microscopic in size but the underlying principle is the same. Angular velocity in the sensor causes forces or torques to be exerted on the micro scale elements and that leads to displacements, which can be measured and amplified to produce an angular velocity signal. As with accelerometers and magnetometers it is very common to package three gyroscope sensors into a single chip, and they are arranged orthogonally again so they measure the three components of the angular velocity vector. Just as you have accelerometers in your head, you also have gyroscopes in your head and once again, these are in the inner ear assembly. In particular, the three very distinctive elements known as the semi-circular canals. These are very thin tubes filled with fluid and rotational motion of your head causes the liquid in those tubes to move. The motion of a fluid is detected by tiny hair cells within the canals, and this leads to an angular velocity signal to your brain. The angular velocity signal is combined with motion information that comes from your eyes. If these two signals are not consistent, it leads to a problem which we experience as motion sickness, that's when our inner ear is telling us that our body is moving in one way, but our eyes tell us that our body is moving in a different way. So, this is motion sickness or sea sickness, and our body responds rather illogically by wanting us to throw up.