Spin Angular Momentum in Human Walking: Magnitude, Dimensionality and Distribution

Short Title: Angular momentum in human walking Summary In this study we examine the relative size of whole-body spin angular momentum in human walking, and the dimensionality and distribution of intersegment angular momentum. Using a 16-segment human model and kinetic and kinematic gait data, we examine whole-body rotational dynamics for ten study participants walking at self-selected speeds. Across the gait cycle, we find that spin angular momentum remains small, () Velocity Height Mass Spin < 0.03, whole-body angular excursions are negligible, <3 o , and whole-body rotational kinetic energy is a small fraction of center of mass (CM) kinetic and gravitational potential energies, <3%. Assuming zero net moment about the body CM, we derive a relationship ()(CP CM CM z r r z F F r r r − =). These zero-moment forces closely match experimental forces (R 2 x = 0.94; R 2 y =0.91), indicating that horizontal ground reaction forces in steady state walking can be explained predominantly by spin angular momentum conservation. Principal component analysis is used to examine the dimensionality and distribution of intersegment angular momentum in walking. we find that only three principle components are required to explain greater than 90% of angular momentum data in medio-lateral and vertical directions, whereas four principle components are necessary in the anterior-posterior direction, suggesting a greater rotational dimensionality in the coronal plane compared to sagittal and transverse planes. In addition, we find that whole-body spin angular momentum is small not because of negligible intersegment angular momentum but because of substantial intersegmental cancellations (~95% medio-lateral cancellation; ~70% anterior-posterior cancellation; ~80% vertical cancellation).