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.