# Parameter $r$ of Denavit-Hartenberg

By watching this video which explains how to calculate the classic Denavit–Hartenberg parameters of a kinematic chain, I was left with the impression that the parameter $r_i$ (or $a_i$) will always be positive.

Is this true? If not, could you give examples where it could be negative?

$$a_2 = \vec{{O}_1 {O}_2} \cdot {x}_2$$ Where $$\vec{{O}_1 {O}_2}$$ is the vector between the two frames. The dot product can be negative, but only if the angle is greater than 90 degrees. But because of the strict way you construct the frames, I don't think that can happen.
• While a length is alway positive I think you define a link frame such that the distance to the next link frame was $-a$ or $-d$. Oct 19 '19 at 12:26