Hello
i make a worksheet for calculate transformation matrix:
first i write Rx Ry Rz rotation matrix
in second time (it's not mandatory), i define passage order of passage. by habit i use Cardan (or reverse RTL)
after i have the matrix position : X Y Z RX RY RZ
(in this matrix i have 1 line or over 1000 lines)
I define a transformation function, in this i use an homogeneous matrix
in this matrix, the first 3x3 are the rotation matrix (matrix of cosine) and the last matrix 3x1 are the position matrix
Now , my problem:
I want to calculate all transformation matrix (with T function) for all Position matrix
exemple:
T(0,-2,0,-1,-5,0.5)
T(1,0,5,0,-1,1)
and other ...
and finally i want 1 matrix with all submatrix
1) By default vectors and matrices start numbering their elements with 0, not with 1 as you thought. So your function T() won't work for a single set of six values (you should always test your function!).
Fortunately there is a system variable ORIGIN and if you set it to 1 by typing ORIGIN:=1 at the top of the sheet, or use a global assignment anywhere on the sheet or set the variable via the menu ("Calculation" ribbon) then your sheet works OK.
2) Here is one possible way to achieve what you demanded:
P6 worksheet attached
it is complicated because there is no real standard about this.
Eleur don't use Ry because use 2 . Rz with another angle parameter
some people calling all order passage 'Euler angle' even for Cardan, RTL (roll,pitch,yaw)
another solution! use quaternion 😅 but i don't know this 😉
it's good for me with Werner's solution (your solution is more compact, but I understand Werner's writing better)
first of all a big thank you for your precious advice which helps me to learn Mathcad. It's not easy forme, but i try and i hold on. And excuse me for my approximate language.
Now i update my worksheet, but I'm breaking my head over how to write. I know that i want ... but i can't write it.
Please see the attached file, i can to explain it .
i try it
But it's wrong, because the i parameter for Bi point is not the same for traj
is it possible to introduce another parameter in for loop ?
I think I am getting closer, but I cannot write the calculation for each iteration of the transformation matrix
Ok, I'm getting closer, but I can't seem to display all the sub matrices. Only the last result appears
You have to nest the loops. The i-loop has to do its work inside of the j-loop, because you want its calculaton done for every element in traj and not just for the last one.
Furthermore its not necessary to keep all matrices "Result" (called them "Res" now) , so I overwrite "Res" in every run of the outer j-loop.
obviously is necessary to kill the last line in all submatrix in Bi_dep because this comes from homogeneous transformation
I try it , but the value are wrong
if i control the result for the yellow line with the green parameter
the correct values are in blue
I did a new check, my program is wrong, it's clear
if i calculate manualy, the green value are right, if i calculate with my program, the value are wrong
and finally (until the next time😅)
now i have my final matrix, where "course V1" and next are the stroke cylinder, and L1 and next are the 3D lenght betwen 2 points in 3D
now i want to extract the extremum
for example :
i search the max and min length for all length between 2 points
i search the max and min stroke for all cylinder
and when i find it, i want the extract position where i find it.
and is it possible to display the angle value Rx Ry Rx in degree ?
and for the fun, it is possible to make a draw
on the Y-axis the cylinder lenght
on the X- axis the number of 3D point
i have 6 cylinder, so i have 1 curve for each cylinder
