We review the mechanical components of an approach to motion science that enlists recent progress in neurophysiology, biomechanics, control systems engineering, and non-linear dynamical systems to explore the integration of muscular, skeletal, and neural mechanics that creates effective locomotor behavior. We use rapid arthropod terrestrial locomotion as the model system because of the wealth of experimental data available. With this foundation, we list a set of hypotheses for the control of movement, outline their mathematical underpinning and show how they have inspired the design of the hexapedal robot, RHex.