# How to determine x-axis if the two z-axis are intersecting in Denavit Hartenberg representation

Suppose I have a 3 link(1 dimensional) chain in which all the joints are revolutes, the axis of first revolute joint is along Z-axis(global) and axis of second joint is along X-axis(global). The first link is along X-axis(global) and second link is along Z-axis(global).

Now in order to use DH representation I introduced a local frame for link 1 at joint 1(z axis along Z and x axis along X) and another frame at joint 2.Here z-axis is along axis of rotation(global X) and here I am clueless how to determine x-axis for joint 2 because the two z axis are intersecting.(standard procedure is to find common normal between two z axis) Thanks for your time.

Regarding your question, I believe if you try crossing your z-axes, $z_1 \times z_2$, you'll get the x-axis you're looking for (orthogonal to both axes). Because the two z axes intersect, your $r$ or $a$ value, depending on your notation, will be zero because the new x-axis lies on your previous z-axis.