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# Mathematical definition of Tx,Ty,Tz,Rz,Ry',Rx"

the more I work, the more I got confused,
although I am trying to find the pattern in Z, y', x" I want to know from the developer.
what is the mathematical definition of the rotation part?
suppose in the rhino I have x, y, z and angle with xy plane, angle with xz plane and angle with yz plane then is there a relation or formula that I can use to determine the Z, y', x"?
Hi Dibash,

Do you know about Euler angles? Z, Y', X'' is one "flavor" of Euler angles.

If you are not familiar with the subject, I can recommend this link: https://www.mecademic.com/resources/Eule...ler-angles
It was most likely written by Pr. Ilian Bonev. He supervised the work of RoboDK's main developer and mine during our studies (different times and different projects).

This is a short explanation, more research may be needed. But that should be a good starting point.
Hope it helps.

Jeremy
Find useful information about RoboDK and its features by visiting our Online Documentation and by watching tutorials on our Youtube Channel

i read it, it's confusing probably because its new, although I make my own formula, and luckily it worked, (maybe only for 1 project)
can you help me in simplify the above instruction,
in csv i have x, y, z, the angle between given line and z-axis, y-axis, x-axis
how can I call it in python to get the value of x,y,z,z,y',x"
You need to do more researches on the topic or Euler angles.
It's one of the hard parts of robotics, but a needed one. I don't really have any other read to point you towards as I did not study this topic in English, sending you manuals in French wouldn't be super helpful.

I took a quick look at the Wiki page and it seems interesting and informative. I also saw a few videos on YouTube.

"in csv i have x, y, z, the angle between given line and z-axis, y-axis, x-axis", this means that you have X,Y,Z,rz,ry,rx this is another valid representation of the Euler angles.
You can play a bit with that. In your robot panel, where you see the position of the TCP with respect to the Reference Frame, you can use the drop-down menu to switch from XYZ rz,ry',rx'' and X,Y,Z,rz,ry,rx.

Jeremy
Find useful information about RoboDK and its features by visiting our Online Documentation and by watching tutorials on our Youtube Channel

I solve the problem for now, but when I saw the postprocessor code of irc5,  the code already has a matrix that calculates the Euler angle.
I hope you will make a video on this topic,
thank you,

The code is in  ABB Rapid irc5 post-processor, from line 908,

Code:
```def Pose(xyzrpw):    [x,y,z,r,p,w] = xyzrpw    a = r*math.pi/180    b = p*math.pi/180    c = w*math.pi/180    ca = math.cos(a)    sa = math.sin(a)    cb = math.cos(b)    sb = math.sin(b)    cc = math.cos(c)    sc = math.sin(c)    return Mat([[cb*ca, ca*sc*sb - cc*sa, sc*sa + cc*ca*sb, x],[cb*sa, cc*ca + sc*sb*sa, cc*sb*sa - ca*sc, y],[-sb, cb*sc, cc*cb, z],[0,0,0,1]])```
I SOLVE THE PROBLEM I THINK A EASY WAY,

https://youtu.be/ROJbOXm4XIo
Nice!
Find useful information about RoboDK and its features by visiting our Online Documentation and by watching tutorials on our Youtube Channel

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