Angular momentum in human walking

Abstract

SUMMARY: Angular momentum is a conserved physical quantity for isolated systems where no external moments act about a body's center of mass (CM). However, in the case of legged locomotion, where the body interacts with the environment(ground reaction forces), there is no a priori reason for this relationship to hold. A key hypothesis in this paper is that angular momentum is highly regulated throughout the walking cycle about all three spatial directions [\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(|{\vec{L}}(t)|{\approx}0\) \end{document}], and therefore horizontal ground reaction forces and the center of pressure trajectory can be explained predominantly through an analysis that assumes zero net moment about the body's CM. Using a 16-segment human model and gait data for 10 study participants, we found that calculated zero-moment forces closely match experimental values (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(R_{x}^{2}=0.91\) \end{document}; \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(R_{y}^{2}=0.90\) \end{document}). Additionally, the centroidal moment pivot (point where a line parallel to the ground reaction force, passing through the CM, intersects the ground) never leaves the ground support base,highlighting how closely the body regulates angular momentum. Principal component analysis was used to examine segmental contributions to whole-body angular momentum. We found that whole-body angular momentum is small, despite substantial segmental momenta, indicating large segment-to-segment cancellations (∼95% medio-lateral, ∼70% anterior–posterior and∼80% vertical). Specifically, we show that adjacent leg-segment momenta are balanced in the medio-lateral direction (left foot momentum cancels right foot momentum, etc.). Further, pelvis and abdomen momenta are balanced by leg,chest and head momenta in the anterior–posterior direction, and leg momentum is balanced by upper-body momentum in the vertical direction. Finally, we discuss the determinants of gait in the context of these segment-to-segment cancellations of angular momentum.