Intro2Robotics Lecture 3b: Composition of Rotations, Homogeneous transformations,

Lecture 3 is divided into 2 parts:

[reik]

2:40 I didn't find this pre-mul/post-mul rule obvious, here the proof: If R = X'' Y' Z is a rotation expressed in terms of rotations with respect to current frame, which means rotate by respective angles around current Z-axis, then current Y'-axis followed by current X''-axis, you can express the same final rotation R in terms of rotations with respect to world frame by first expressing rotations with respect to current frame in terms of world frame Y'=Z Y Z^-1 and X''=(Y' Z) X (Y' Z)^-1 = (Z Y) X (Z Y)^-1 and then simplify step by step R = X'' Y' Z = X'' (Z Y Z^-1) Z = X'' Z Y = (Z Y) X (Z Y)^-1 Z Y = Z Y X.