Elastic energy in locomotion: Spring-mass vs. poly-articulated models

• A poly-articulated system (PAM) can behave as a spring mass (SMM).
• Elastic energy (SMM) equals internal kinetic energy minus internal forces work (PAM).
• The coordination of the internal forces work produces a global stiffness.
• The equality is verified over a wide range of running speeds.
• Walking does not verify the equality at high speed.

The human is often modeled as a Poly-Articulated Model (PAM) with rigid segments while some authors use a Spring Mass Model (SMM) for modeling locomotion. These two models are considered independent, and the objective of this study was to link them in order to enlighten the origin of the elasticity in locomotion.Using the characteristics of the two models, a theoretical relationship demonstrates that the variation of elastic energy of the SMM equals the variation of the internal kinetic energy minus internal forces work of the PAM. This theoretical relationship was experimentally investigated among 19 healthy participants walking and running on a treadmill.The results showed that the equality is verified except during the double support phase at 0.56 m s−1, at high walking speeds (1.67 and 2.22 m s−1) or during the aerial phase of running.The formal relationship showed that the global stiffness of the SMM is directly related to the work of the internal forces of the PAM, and thus, to the characteristics of the musculoskeletal system. It also showed the relevance of taking into account the participation of each joint in the global stiffness. Finally, the coordination of internal forces work to produce a global stiffness may be considered as a new criterion of movement optimization for clinical purposes or motion planning for humanoid robots.