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My questions is the following: How do I find the DH values of a given transformation matrix? Or a set of transformation matrices if one is not enough? I can assume that the angle theta is known for each of them and all other DH parameters are the same accross transformation matrices.

thank you guys, Alex

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Consider the expression at the bottom as the transformation between one system and the next.

If you have the numeric values of this transformation (from coordinate system $i$, to coordinate system $i+1$) you could use the elements of the matrix in equation 3.10 as follows:

$$\theta_i = \arctan \left(\frac{A_{2,1}}{A_{1,1}} \right)$$

$$\alpha_i = \arctan \left(\frac{A_{3,2}}{A_{3,3}} \right)$$ Knowing $\theta_i$, you can then find $a_i$ easily as:

$$a_i=\frac{A_{1,4}}{\cos(\theta_i)}$$

Finally, $d_i=A_{3,4}$

D-H matrix equation taken from here

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