# Finding the DH parameters from Transformation Matrices

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

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

equation taken from here