The Force Driven Harmonic Oscillator as a Model for Human Locomotion

Holt, Kenneth G.; Hamill, Joseph; Andres, Robert O.

doi:10.1249/00005768-198004001-00576

Cited by 33 publications

(64 citation statements)

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“…Wagenaar and van Emmerik (2000) found that the observed frequency of arm swing at slow walk- 92 ing speeds (about 0.5 m/s) coincided with the estimated resonant frequency of the arm, using a pendulum and spring model (see Holt et al 1990). Using a simple pendulum model, it was found that both frequency ratio and phase transitions occurred when the stride frequency was decreased to slightly lower than the arm's estimated natural pendular frequency (Webb and Tuttle 1989;Webb et al 1994).…”

Section: Introductionmentioning

confidence: 64%

Biomechanical mechanism for transitions in phase and frequency of arm and leg swing during walking

et al. 2004

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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.

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Section: Introductionmentioning

confidence: 64%

Biomechanical mechanism for transitions in phase and frequency of arm and leg swing during walking

et al. 2004

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“…In this model, lower limbs are presented as a pendulum (leg)/mass-spring (muscles and connective tissue) system. (Holt et al 1990(Holt et al , 1991.…”

Section: Introductionmentioning

confidence: 99%

Comparison of the metabolic energy cost of overground and treadmill walking in older adults

et al. 2011

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We assessed whether the metabolic energy cost of walking was higher when measured overground or on a treadmill in a population of healthy older adults. We also assessed the association between the two testing modes. Participants (n = 20, 14 men and 6 women aged between 65 and 83 years of age) were randomly divided into two groups. Half of them went through the overground-treadmill sequence while the other half did the opposite order. A familiarization visit was held for each participant prior to the actual testing. For both modes of testing, five walking speeds were experimented (0.67, 0.89, 1.11, 1.33 and 1.67 m s(-1)). Oxygen uptake was monitored for all walking speeds. We found a significant difference between treadmill and track metabolic energy cost of walking, whatever the walking speed. The results show that walking on the treadmill requires more metabolic energy than walking overground for all experimental speeds (P < 0.05). The association between both measures was low to moderate (0.17 < ICC < 0.65), and the standard error of measurement represented 6.9-15.7% of the average value. These data indicate that metabolic energy cost of walking results from a treadmill test does not necessarily apply in daily overground activities. Interventions aiming at reducing the metabolic energy cost of walking should be assessed with the same mode as it was proposed during the intervention. If the treadmill mode is necessary for any purposes, functional overground walking tests should be implemented to obtain a more complete and specific evaluation.

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“…1a. This simplistic model has previously been used to describe a variety of biological movements and has been shown to sufficiently represent the dynamics of a one-degree-of-freedom system (Winters and Stark 1987;Holt et al 1990;Long and Nipper 1996;Halaki et al 2006). As such, the motion of the mechanical subsystem is governed by…”

Section: The Mechanical Subsystemmentioning

confidence: 99%

“…In particular, sensory feedback facilitates the convergence of both the CPG and movement frequencies to the resonant frequency (ω r ) of the mechanical dynamics, a phenomenon called resonance tuning. Combined experimental and theoretical studies suggest that resonance tuning occurs during numerous biological rhythmic movements, including leg and arm swinging in humans (Holt et al 1990;Hatsopoulos and Warren 1996;Jeng et al 1997;Abe and Yamada 2003) and swimming in jellyfish and scallops (Demont and Gosline 1988;Demont 1990). There are several advantages to moving at ω r ; these advantages include maximization of the movement predictability as well as minimization of the degrees of freedom, the variability, and the energy associated with the movement Pabst 1996;Goodman et al 2000).…”

Section: Introductionmentioning

confidence: 99%

A comparison of resonance tuning with positive versus negative sensory feedback

Williams

DeWeerth

2007

Biol Cybern

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We used a computational model of rhythmic movement to analyze how the connectivity of sensory feedback affects the tuning of a closed-loop neuromechanical system to the mechanical resonant frequency (omega(r)). Our model includes a Matsuoka half-center oscillator for a central pattern generator (CPG) and a linear, one-degree-of-freedom system for a mechanical component. Using both an open-loop frequency response analysis and closed-loop simulations, we compared resonance tuning with four different feedback configurations as the mechanical resonant frequency, feedback gain, and mechanical damping varied. The feedback configurations consisted of two negative and two positive feedback connectivity schemes. We found that with negative feedback, resonance tuning predominantly occurred when omega(r) was higher than the CPG's endogenous frequency (omega(CPG)). In contrast, with the two positive feedback configurations, resonance tuning only occurred if omega(r) was lower than omega(CPG). Moreover, the differences in resonance tuning between the two positive (negative) feedback configurations increased with increasing feedback gain and with decreasing mechanical damping. Our results indicate that resonance tuning can be achieved with positive feedback. Furthermore, we have shown that the feedback configuration affects the parameter space over which the endogenous frequency of the CPG or resonant frequency the mechanical dynamics dominates the frequency of a rhythmic movement.

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The Force Driven Harmonic Oscillator as a Model for Human Locomotion

Cited by 33 publications

References 0 publications

Biomechanical mechanism for transitions in phase and frequency of arm and leg swing during walking

Biomechanical mechanism for transitions in phase and frequency of arm and leg swing during walking

Comparison of the metabolic energy cost of overground and treadmill walking in older adults

A comparison of resonance tuning with positive versus negative sensory feedback

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