As humans increase walking speed, there are concurrent transitions in the frequency ratio between arm and leg movements from 2:1 to 1:1 and in the phase relationship between the movements of the two arms from in-phase to out-of-phase. Superharmonic resonance of a pendulum with monofrequency excitation had been proposed as a potential model for this phenomenon. In this study, an alternative model of paired pendulums with multiple-frequency excitations is explored. It was predicted that the occurrence of the concurrent transitions was a function of (1) changes in the magnitude ratio of shoulder accelerations at step and stride frequencies that accompany changes in walking speed and (2) proximity of these frequencies to the natural resonance frequencies of the arms modeled as a pair of passive pendulums. Model predictions were compared with data collected from 14 healthy young subjects who were instructed to walk on a treadmill. Walking speeds were manipulated between 0.18 and 1.52 m/s in steps of 0.22 m/s. Kinematic data for the arms and shoulders were collected using a 3D motion analysis system, and simulations were conducted in which the movements of a double-pendulum system excited by the accelerations at the suspension point were analyzed to determine the extent to which the arms acted as passive pendulums. It was confirmed that the acceleration waveforms at the shoulder are composed primarily of stride and step frequency components. Between the shoulders, the stride frequency components were out-of-phase, while the step frequency components were in-phase. The amplitude ratio of the acceleration waveform components at the step and stride frequencies changed as a function of walking speed and were associated with the occurrence of the transitions. Simulation results using these summed components as excitatory inputs to the double-pendulum system were in agreement with actual transitions in 80% of the cases. The potential role of state-dependent active muscle contraction at shoulder joints on the occurrence of the transitions was discussed. Due to the tendency of arm movements to stay in the vicinity of their primary resonance frequency, these active muscle forces were hypothesized to function as escapements that created limit cycle oscillations at the shoulder’s resonant frequency.
['Masayoshi Kubo', 'Robert C. Wagenaar', 'Elliot Saltzman', 'Kenneth G. Holt']
Biomechanical mechanism for transitions in phase and frequency of arm and leg swing during walking