When setup properly this should be good for mechanical kind of motion. Circular motion, number 8 kind of motion, bouncing ball, all can be put together easily with math functions.

I am using Animation Nodes for this example, and you can see how easy we can use a running frames to generate wave functions for animation of position XYZ and rotation euler XYZ.

Now, see if you can improve the walk cycle based on this! A more complex and challenging setup would be to recreate the motion based on IK and FK control for bipedal or quadruple creatures.

Enjoy!