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.

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).