LESSON

# How gyroscopes work

#### Transcript

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.

#### Code

There is no code in this lesson.

We learn the principles behind ‘gyros’, sensors that measure angular velocity with respect to the universe. ### Professor Peter Corke

Professor of Robotic Vision at QUT and Director of the Australian Centre for Robotic Vision (ACRV). Peter is also a Fellow of the IEEE, a senior Fellow of the Higher Education Academy, and on the editorial board of several robotics research journals.

### Skill level

This content assumes an understanding of high school-level mathematics, e.g. trigonometry, algebra, calculus, physics (optics) and some knowledge/experience of programming (any language).