Hello robotics community,
The topic of homogeneous transformations is very interesting. However its appearance in the first chapters of robotics books/lectures, in practice it may be confusing.
I am thinking about a question, and not very sure if it makes sense or not. If we have a world frame W and two arbitrary frames T_1 and T_2 refereed to the world frame. It is not hard to calculate the difference between them T_1_2 (transformation from 1 to 2) or T_2_1 (transformation from 2 to 1) and this difference is refereed to the world frame. My question is, How can we refer this difference in transformation to any of the arbitrary transformations T_1 or T_2? Does this make sense?
I got this question when trying to rotate an arbitrary frame about another arbitrary frame. I will share with you an image of the result it is also interesting.