Trying to look for a more mathemathical, vectorized summarized idea of Drawing correctly all the frames involved in the walk cycle

From the idea that it is looping to maintaining constant balance between on step or cycle to another. But generally it needs to be summarized into a shape or curves or something easily read, mathemathically, that will tell where the pose go so to define the motion that is predetermined... which includes variety of things limping, running, crowling... assortments of so.

The prioritt idea is the balance and the repeat, so much less than abstract characteristic but rather the correct physics in accordance to the asked body motion