[Q] How to calculate the difference between two coordinate frames refereed to one of them, not the world frame?

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.

Thank you

submitted by /u/Biomacs
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