---
title: Gyroscope
created_date: 2025-06-30
updated_date: 2025-06-30
aliases:
tags:
---
# Gyroscope
A gyroscope is a device to measure angular orientation and angular velocity. Traditionally it was a spinning wheel mounted on three gimbals.

Modern simpler devices make use of the coriolis effect and use vibrating structures instead of a rotating one.

## MEMS Gyroscope
A mems gyroscope makes use of a vibrating structure instead of a rotating structure, which makes it much simpler to manufacture. 

A drive frame (yellow) is oscillated (usually at 10-40kHz). 
When the sensor is rotated, the red mass is moved to either side and thus reducing/increasing the contacts to the blue sensing structure. See [How MEMS Accelerometer Gyroscope Magnetometer Work & Arduino Tutorial - YouTube](https://youtu.be/eqZgxR6eRjo?t=59) for more details.
![[Pasted image 20250630155216.png]]

### Math
- The base frequency of vibration: $\omega_r$
- acceleration due to coriolis effect: $a_c = 2(\Omega \times v)$, where $v$ is a velocity and $\Omega$ is an angular rate of rotation.
- The vibration has an expected in-plane velocity and position, which is not interesting. However, a rotation induces an out-of-plane motion $y_{op}$ which we can measure and thus determine the rate of rotation:
$$ y_op = \frac{F_c}{k_{op}} = \frac{1}{k_{op}} 2m\Omega X_{ip}\omega_r cos(\omega_r t)$$

### Coriolis Force

$$ F_c = -2m(\Omega \times v)$$