Denavit-Hartenberg Parameters for a Quadruped Robot

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I am trying to find Denavit-Hartenberg Parameters for a 12 dof quadruped robot. Every leg is similar having three joints hip, thigh and calf. The main issue I am having about the procedure is the axis, i.e. in my scenario hip joint rotate around x-axis, thigh and calf joint rotate about y-axis(Can be seen in the image below). However Denavit-Hartenberg method says to start defining rotation axis by z. Quoting from Wikipedia "the z-axis is in the direction of the joint axis". So in this way all 4 paramters are defined.

I have looked on the internet and in several articles. They follow the same convention.

Anyone who have some leads or can suggest me a way out of this.