Walking, running or jumping are special cases of articulated motions which rely heavily on contact forces for their accomplishment. This central role of the contact forces is widely recognized now, but it is rarely connected to the structure of the dynamics of articulated motion. Indeed, this dynamics is generally considered as a complex nonlinear black-box without any specific structure, or its structure is only partly uncovered. We propose here to precise this structure and show in details how it shapes the movements that an articulated system might realize. Some propositions are made then to improve the design of control laws for walking, running, jumping or free-floating motions.