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hello sir amazing video, i am having trouble understanding as to how do you get the values for the displacement. can you just explain me the method for calculating the displacement value for the matrix?
Hi, why call the linear transformation such as homogeneous transform? Homogeneous can be a linear system AX=B B = [0 0 ... 0], but the transformation is only a function. However, thanks for this playlist is so useful.
What I did was I simply multiplied the three homogeneous transforms (H1, H2, H3) together using MATLAB and wrote out the final answer. You can use any software or even do the multiplication by hand. Does that clear out the confusion?
That's a great question! If you have rotations around the same axis, then yes! However, generally in the real world case, you would have rotations about different axes. So, it's always good to just multiply the H1*H2*... And then figure out the angles. I hope that answers your question.
Ok got it, since your transformations are relative to the moving frame and not relative to the fixed frame that's why you have done post multiplication
Actually we are transforming the fixed frame 'F' to M3 frame. In other words finding a homogeneous transform that represents the M3 frame in the fixed frame. Hope it makes sense. If there is still confusion, let me know
A homogenous transform is just a matrix that has a Rotation Matrix (A) and a displacement matrix (d) in it with the last row being all zeros except the last element, which is a '1'. Have a look here: i.ytimg.com/vi/3zeMsf0vcs4/maxresdefault.jpg ^ This picture is for a 3D homogeneous transformation matrix but the same principle applies for 2D as well. The only difference is that in 2D, the Rotation Matrix is 2x2 instead of 3x3 and the displacement vector is 2x1 instead of 3x1. I hope this makes sense and now you understand what a homogenous transformation is. If there is still any confusion, let me know and I will try to explain it again.
Hello sir. What does it the matrix H ? It is the rotation matrix ? If it is, then why we have say above that the matrix of rotation A is a 2x2 matrix only so how we added the zeros and the d vector coposants in the matrix H ?
Hi Akram, the H matrix is the homogeneous transform which is a matrix that combines the 2x2 rotation matrix and the displacement vector d into one. It makes life easy so that now you have one single matrix giving all the information you need. As far as why we have the two zeroes and a '1' in the last row- it is due to the way the homogenous matrix is derived. Give this video a watch in which I discuss how we get the homogeneous matrix: ruclips.net/video/QFTLH1C-9Qg/видео.html Although, this video is for the 3D spatial case but the same methodology (and reasoning) applies for the 2D case as well. Let me know if there is still any confusion and I will love to help.
✍Any Questions, doubts, or thoughts? Comment below (I read & respond to every comment).
👉Don't forget to SUBSCRIBE to the channel for more such videos & courses: bit.ly/Engineering-Simplified
hello sir amazing video, i am having trouble understanding as to how do you get the values for the displacement. can you just explain me the method for calculating the displacement value for the matrix?
Excellent color combination
Oh thanks! I took inspiration from Khan Academy.
Hi, why call the linear transformation such as homogeneous transform? Homogeneous can be a linear system AX=B B = [0 0 ... 0], but the transformation is only a function. However, thanks for this playlist is so useful.
Pretty helpful!
Glad you found it helpful!
Hey, thanks for the video and I did not understand the third column of the final H matrix. How did you find the values of 0.68, 4.79 and 1 ?
What I did was I simply multiplied the three homogeneous transforms (H1, H2, H3) together using MATLAB and wrote out the final answer.
You can use any software or even do the multiplication by hand.
Does that clear out the confusion?
3 cos (100 + 330) + 2 cos (100) | 3 sin (100 + 330) + 2 sin (100)
@@Gooliabunnyso the 280 won't even make a difference in the third column?
Hey, do you have any videos on inverse kinematics yet?
Hey! I am making a few videos on inverse kinematics now as we speak. Hopefully the IK will be after a couple of videos.
@@EngineeringSimplified Thanks!
@@zikondenyirenda please can you share the links to these videos on inverse kinematics?
how did you get 0.68 and 4.79
We just multiplied the three matrices H1*H2*H3 and got to this matrix.
can we simply add up the angles ?
during H1H2H3 multiplication?
That's a great question! If you have rotations around the same axis, then yes!
However, generally in the real world case, you would have rotations about different axes. So, it's always good to just multiply the H1*H2*... And then figure out the angles.
I hope that answers your question.
@@EngineeringSimplified thank you for the reply. that was helpful
Is there any way to find the displacement terms 0.68 and 4.79. Formula of some sort?
nvm boss, i just found it. EUREKA!!
Perfect!
Can you post the formula of how you got 0.68 and 4.79 please? thanks
Why haven't you written H = H3H2H1? As we are transforming from M3 to F
Ok got it, since your transformations are relative to the moving frame and not relative to the fixed frame that's why you have done post multiplication
Actually we are transforming the fixed frame 'F' to M3 frame. In other words finding a homogeneous transform that represents the M3 frame in the fixed frame.
Hope it makes sense. If there is still confusion, let me know
Yes it's clear now. Thanks
@@zaidakhtar3093 perfect!
There's no explanation of Homogeneous transformation in this playlist robotics 101
A homogenous transform is just a matrix that has a Rotation Matrix (A) and a displacement matrix (d) in it with the last row being all zeros except the last element, which is a '1'.
Have a look here: i.ytimg.com/vi/3zeMsf0vcs4/maxresdefault.jpg
^ This picture is for a 3D homogeneous transformation matrix but the same principle applies for 2D as well. The only difference is that in 2D, the Rotation Matrix is 2x2 instead of 3x3 and the displacement vector is 2x1 instead of 3x1.
I hope this makes sense and now you understand what a homogenous transformation is. If there is still any confusion, let me know and I will try to explain it again.
In fact, I have posted a video for this just now: ruclips.net/video/IR00J55F76M/видео.html
Hope it helps!
Can you explain in detail homogenous transfer that Matrix
How it will transform
Did you manage to see the previous video? That covers exactly what I think you are asking.
Why is the displacement for H2 2 for x axis but 0 for y axis? If the x value was increased, wouldn’t y value also increase correspondingly?
X value is only increasing since the n-1 frame moves along n frame in x direction
Hello sir. What does it the matrix H ? It is the rotation matrix ? If it is, then why we have say above that the matrix of rotation A is a 2x2 matrix only so how we added the zeros and the d vector coposants in the matrix H ?
Hi Akram, the H matrix is the homogeneous transform which is a matrix that combines the 2x2 rotation matrix and the displacement vector d into one. It makes life easy so that now you have one single matrix giving all the information you need.
As far as why we have the two zeroes and a '1' in the last row- it is due to the way the homogenous matrix is derived. Give this video a watch in which I discuss how we get the homogeneous matrix: ruclips.net/video/QFTLH1C-9Qg/видео.html
Although, this video is for the 3D spatial case but the same methodology (and reasoning) applies for the 2D case as well.
Let me know if there is still any confusion and I will love to help.