For examples if i have this robotic arm: Example, for the base rotation (5th DOF in the clip at 0:58), we know that the Z axis for that joint will be the same as the Z axis for the base frame{0}, but I don't know about Y and Z axises of the base rotation respects to the base frame, should they be the same or not ?

And one more thing, for defining the frame of the base rotation (at 0:58 in the clip), the vertical arm pitch (at 0.47 in the clip) and the horizontal arm pitch (at 0:46 in the clip), it's pretty easy, but I don't know how to continue for defining the frame of wrist roll (at o.12 in the clip) and wrist pitch (0.23 in the clip) since the angle between the Z axis of wrist roll and the wrist pitch is now 90o.
Thank you very much.

  • $\begingroup$ I've no idea what you're on about but my 2p is, my triangle insect will trounch your infertile worm... super dudes ;) $\endgroup$
    – MadusDogus
    Dec 6, 2013 at 14:43

1 Answer 1


Follow the Denavit-Hartenburg parameters, and you'll get easy equations for the transformation matrices between each frame.

  • The $z_n$-axis is in the direction of the $(n+1)^{th}$ joint axis
  • The $x_n$-axis is collinear to the common normal: $x_n = z_n × z_{n-1}$ If there is no unique common normal (parallel $z$ axes), the direction of $x_n$ is from $z_{n-1}$ to $z_n$.
  • The $y$-axis follows from the $x$- and $z$-axis by choosing it to be a right-handed coordinate system.

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