Rigid Body Kinematics Introduction | Rotation Matrix Relating Frames in 3D | Direction Cosine Matrix

[@jiyanbaranbukun]

Thanks a lot Professor, very clear and intuitive explanation!

[@sahhaf1234]

Thank you very much, Dr. Ross. This was an excellent presentation.

[@danieltal7277]

awsome video thianks!!!

[@ProfessorRoss]

You're awesome for watching!

[@tabhashim3887]

At 12:56 Shouldn’t the parameterized C matrix switch the negative on the sin. Because looking at it from a transformation point of view, the n1 vector will have to shrink in the x direction, and go up in the y direction. But based off of this matrix, it would go down. I guess what I am trying to say is that this is for a CW not CCW rotation which is what is shown

[@윤현만-n3v]

설명이 좋네요

[@ProfessorRoss]

고맙습니다

[@julianer1818]

Hey Dr.Shane, Thanks a lot for the video! But I have one problem, I feel like my basic knowledge of vectors is hindering me to understand kinematics. How far do I have to relearn vectors so I can understand kinematics? Can you give me any advice or help? Thanks in advance 👍 I’m in my first year at uni studying mechanical engineering and I‘m lost atm.

[@brendawilliams8062]

Thankyou

[@_tasneem7378]

Can I get the PDF copy of the book!

[@ashwin372]

which book? can you please give me the name and author? i have Electronics engineering degree but need to learn kinematics for robotics

[@FLMKane]

So um...my prof back in the day was very adamant that frames ate attached to a body, points are NOT. What's your opinion about that?

[@ProfessorRoss]

I don't understand what is meant by "points are not attached to a body".

[@FLMKane]

@@ProfessorRoss the assumption was that we can put infinite points on a body and also move them around arbitrarily. So the only fixed point was assumed to be the cg. Every other point was just there for convenience (Assuming we are talking about a single rigid body for convenience)

[@markengel7545]

Pray tell: Which ‘book” do you refer to?

[@ProfessorRoss]

The one listed in the description

[@TriThom50]

Why is that not a vector? A vector could consist of multiple other vectors?

[@bidhayakgoswami2564]

9.38 min: You could have written [b1 b2]=[ n1 n2] [ C ] where n1, n2, b1, b2 are column vectors (basis vectors) and C is the matrix of cosines,. 'Vectrix' is neither a good nor a correct way to write or teach. Any vector (say v) with representation u=[ u1 u2] in frame 2 will become C.u in frame 1. As u and Cu are of same length , C'C=I. Therefore, C is in SO(3). It has an eigenvalue equal to 1 (an invariant direction, axis of rotation in this case) and a pair of complex conjugate eigenvalues (invariant subspace, plane perpendicular to axis of rotation).