# Accelerometer and angles calculation

I was reading on https://www.analog.com/en/app-notes/an-1057.html about the accelerometer and how it is used to calculate the pitch, roll, and yaw. However, I have several issues to understand the formulas. For example, in the picture attached I am not understanding how can the angles in b) be different then each other? isn't it a rotation around the y axis? and the same apply for the other pictures? So the first issue with me is understanding why the angles are not equal thus is affecting my understanding on the equations 11 to 13.

Thank you for your help

Image

• Maybe add the equations to your query using mathjax? For ease of the reader. Commented Nov 17, 2022 at 20:55

The reference position is taken as the typical orientation of a device with the $$x$$- and $$y$$-axes in the plane of the horizon (0 g field) and the $$z$$-axis orthogonal to the horizon (1 g field). This is shown in Figure 12 with $$\theta$$ as the angle between the horizon and the $$x$$-axis of the accelerometer, $$\psi$$ as the angle between the horizon and the $$y$$-axis of the accelerometer, and $$\phi$$ as the angle between the gravity vector and the $$z$$-axis. When in the initial position of 0 g on the $$x$$- and $$y$$-axes and 1 g on the $$z$$-axis, all calculated angles would be $$0°$$.
• @tonyjk: You're stuck on Euler/Tait-Bryan angles. The ones shown above, $\theta$, $\psi$, $\phi$ are not; they are not "pitch", "roll", and "yaw". They are defined differently. How they are defined, is clearly explained in the text. The problem is you're trying to think about them in terms of Euler/Tait-Bryan angles, which is wrong. Besides, Euler/Tait-Bryan angles are a horribly bad way to describe orientation anyways, because of gimbal lock. Versors (unit quaternions) or bivectors are a much better option. Commented Nov 20, 2022 at 9:36