I had all the DH parameters and calculated transformation matrix. From that I know the end-effector value position. But I don't understand how to integrate orientation.


1 Answer 1


Orientation is already integrated in the transfomration matrix. A transformation matrix is a $4x4$ matrix, which can be written as:

$$\begin{pmatrix}R_{3x3} & P_{3x1}\\\ 0_{1x3} & 1\end{pmatrix}$$

$R_{3x3}$ represents a $3x3$ matrix, the upper left part of the transformation matrix which is the describes the rotation. For the 6 DoF inverse kinematics, you can build up such a transformation matrix by multiplying pure transfomration matrices. This will result in a matrix with know values which then equals the DH chain of unkown values.

$T_{TCP} = X_{trans}(x)\cdot Y_{trans}(y)\cdot Z_{trans}(z)\cdot X_{rot}(\alpha)\cdot Y_{rot}(\beta)\cdot Z_{rot}(\gamma)$

You can plug in here the end-effector coordinats, translations $x, y, z$ and orientation $\alpha, \beta, \gamma$. You can also change the types of rotations to XYX or ZYZ if it better suits your application, see here.

Plaese see also this R.SE question and answer here.


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