Angle-Set Conventions

Ways to rotate around an axis with rotational matrices.


Summary

[#Fixed Angles](/notes/vault/#Fixed Angles) $$ R_Z(45\deg) \cdot \ ^\text{Base}_\text{TCP}R \Rightarrow \text{Rotate toolhead } 45 \deg \text{round the \textit{base} z-axis} $$

[#Euler Angles](/notes/vault/#Euler Angles) $$ ^\text{Base}_\text{TCP}R \cdot R_Z(45\deg) \Rightarrow \text{Rotate toolhead } 45 \deg \text{round the \textit{toolhead} z-axis} $$


Fixed Angles

The coordinate system stays fixed.

fixed-angles.png

Rotational Matrices

Here we left-multiply (from right to left) the rotational matrices.


Euler Angles

“Each rotation is performed about an axis of the coordinate system from the last step” - IƱigo Iturrate

The coordinate system changes whenever you do a rotation.

auler-angles.png

Rotational Matrices

euler-angles-with-matrices.png