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I am trying to set up a generalized approach to generate DH parameters for my simulated robot arms, but I am having trouble setting up the frames. To find the X axis of each joint I read that I have to find a line orthogonal to both Z axes of the previous and current joint. e.g. as explained in this video around 0:40 https://www.youtube.com/watch?v=rA9tm0gTln8

However, in some cases I find that a line orthogonal to both Z axes does not seem to exist. So how do I then determine the X-axis direction of subsequent joints. Are there configurations for which DH-parameters simply do not exist? or is there some other rule tied to this? Or does this orthogonal line exist somewhere but I'm simply failing to find it? I can't find my specific case online. I have enclosed a picture with the two Z axes drawn in the axis of revolution for 2 joints. the Z axes are not intersecting anywhere, not parallel and not perpendicular.two joints with Z axes pictured in axis of rotation

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  • $\begingroup$ DH is not unique. Which one you are using? $\endgroup$
    – CroCo
    Jul 13, 2022 at 18:04

2 Answers 2

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Given two linearly independent (read: not parallel) vectors, you can always find a vector which is perpendicular to both of them using the cross product: https://en.wikipedia.org/wiki/Cross_product.

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Absolutely. Depending on which version of D-H you are using, look at the $d$ and $r$ terms to accommodate the offsets.

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