I spoke with airman00 and he said he gave you some basic kinematics code.
It appears you want to put basic walking into equations instead of preprogrammed motions. Its been done quite a lot before, search the various science papers on walking robots.
Also, a leg is actually no different from an arm. This is a 3 DOF robot arm . . . What you want to do is called 'trajectory following' - where you don't really care what the joints are doing, as long as the foot (end effector) is following a desired trajectory.
If I were to do it I wouldn't bother with the equations. I'd put a lot of preprogrammed motions in, and set them up with a fuzzy-based controller that modifies/selects the kinematics based on sensor data.
For example, a human has a limited set of gaits preprogrammed into our head: walk, run, jog, climb, jump. Using sensor data in our brain/body, we tweak the gait in real-time (so that we don't fall or whatever).
If you went with equations, you'd still need a different equation for each gait.