There are many mathematical perspectives one could take on running, many of them I think are more interesting than the narrow question you posed. (Since it's a graphics question another SX site might have been better.)
(The second one is more about swimming than running.)
You might want to (or not) think about putting a sensor on each knee, each foot, each toe, etc., and consider the paths traced out by each sensor. You could use the language of diffeomorphisms and elastic deformations to talk about "small" (or large) deviations. You could also invoke some functional analysis to be a bit more specific about how the paths can deform.
There are a lot of other perspectives you could take--like what about the forces that come up through the heels/metatarsals/toes and travel through both bone and soft matter? Or, finally getting back to what you brought up: the Lie algebra of parameter space which all the angles of the joints. There you're interested in questions that might be answered—or perhaps they'll lead you toward new questions instead—in an introductory differential-geometry or algebraic-topology text. (Spivak DG v1 or Hatcher AT will do.)
But really what you want, I think, are some practical measurements—science derived from kinesiology—rather than pure-mathematics stuff. Ball-and-socket joints move in like a deformed disk; elbows and knees allow motion in a unit interval; and all of this is tied together with a product that's more complicated than Cartesian (you can't put your hand through your chest, for example). Sort of boring, mathematically; that's the stuff I mentioned above that's covered in an introductory DG or AT text. The more relevant information for you, maybe, will be in empirical/scientific specifics of real bodies.