3D vectors to variables A, B and C

Hm... I suspect that the answer involves converting from the Normal Vector to a matrix, then converting from the matrix to KUKA ABC angles.

Generally, when converting from any robot brand Euler orientation to any other brand, the matrix is always the intermediate step. The matrix notation for a given orientation is always the same. I imagine the Normal Vector converts similarly.

This thread goes into detail about converting from ABC to matrix:

Thread

Going from KUKA Euler angles to transformation matrix.

Hi.

I've recently run a series of tests on a KR-60 Robot using a KRC2 controller.

I have position data at the tool center point, in the tool frame and I'm interested in getting position data from a DIFFERENT point on the tool for which I have the coordinates in the tool frame.

I've created a 4x4 transformation matrix that represents the motion of the tool during the test, and I will multiply the vector of the point I'm interested in by that matrix to get its final position.

The only thing I'm a bit…

abrady

Dec 15th 2015

You'll need to find an appropriate algorithm for converting from the NV you're using to matrix notation.

One item of note: your Normal Vector does not appear to control the rotation around said vector, the so-called "clocking". IIRC, you need two orthogonal NVs to fully define an Euler rotation.

create 3x3 rotation matrix then compute angles A,B,C using MAT_TO_RPY()

GLOBAL DEF MAT_TO_RPY (T[,]:out, A:out, B:out, C:out)
  REAL T[,], A, B, C
  REAL SIN_A, COS_A, SIN_B, ABS_COS_B, SIN_C, COS_C
  A = ARCTAN2 (T[2,1], T[1,1])
  SIN_A = SIN(A)    
  COS_A = COS(A) 
  SIN_B = -T[3,1]
  ABS_COS_B = COS_A * T[1,1] + SIN_A * T[2,1]
  B = ARCTAN2 (SIN_B, ABS_COS_B); -90 <= B <= +90
  SIN_C =  SIN_A * T[1,3] - COS_A * T[2,3]
  COS_C = -SIN_A * T[1,2] + COS_A * T[2,2]
  C = ARCTAN2 (SIN_C, COS_C)
END

but... 3x3 rotation matrix T[,] has 9 elements and your vector only has 3 elements. that is only one row or column of the rotation matrix. if you know two rows or columns (6 elements) then last row or column can be computed using cross product of the first two.

in other words, you need to know what coordinate system is used as a reference.

Quote from marcalex_savard

Hi there,

I've made a program that helps me do a specific path with the orientation that my tool needs to have on each point on the path. Each point has an X Y Z coordinates, but the orientation of my tool is given by a normal vector. I would like to know if there's a method or something else I can do so I can convert my normal vector to the variables A, B and C.

I will put an image on this thread so you can visualize what I'm saying. Each red line is the orientation my tool needs to have on each point. The orientation is a vector [X; Y; Z] but I need the following variables: A, B, C.

Thanks in advance!

Display More

Dumb question, but in which software did you take the print screen?

This is a function written in krl

Quote from EXOR

Dumb question, but in which software did you take the print screen?

To me it looks like graph was created in MatLab or Octave