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Hiroaki Hobara, Yoshiyuki Kobayashi, Emika Kato, and Toru Ogata

Although many athletic activities and plyometric training methods involve both unilateral and bilateral movement, little is known about differences in the leg stiffness (K leg) experienced during one-legged hopping (OLH) and two-legged hopping (TLH) in place. The purpose of this study was to investigate the effect of hopping frequencies on differences in K leg during OLH and TLH. Using a spring-mass model and data collected from 17 participants during OLH and TLH at frequencies of 2.0, 2.5, and 3.0 Hz, K leg was calculated as the ratio of maximal ground reaction force (F peak) to the maximum center of mass displacement (ΔCOM) at the middle of the stance phase measured from vertical ground reaction force. Both K leg and F peak were found to be significantly greater during TLH than OLH at all frequencies, but type of hopping was not found to have a significant effect on ΔCOM. These results suggest that K leg is different between OLH and TLH at a given hopping frequency and differences in K leg during OLH and TLH are mainly associated with differences in F peak but not ΔCOM.

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Hiroaki Hobara, Koh Inoue, and Kazuyuki Kanosue

Understanding the degree of leg stiffness during human movement would provide important information that may be used for injury prevention. In the current study, we investigated bilateral differences in leg stiffness during one-legged hopping. Ten male participants performed one-legged hopping in place, matching metronome beats at 1.5, 2.2, and 3.0 Hz. Based on a spring-mass model, we calculated leg stiffness, which is defined as the ratio of maximal ground reaction force to maximum center of mass displacement at the middle of the stance phase, measured from vertical ground reaction force. In all hopping frequency settings, there was no significant difference in leg stiffness between legs. Although not statistically significant, asymmetry was the greatest at 1.5 Hz, followed by 2.2 and 3.0 Hz for all dependent variables. Furthermore, the number of subjects with an asymmetry greater than the 10% criterion was larger at 1.5 Hz than those at 2.2 and 3.0 Hz. These results will assist in the formulation of treatment-specific training regimes and rehabilitation programs for lower extremity injuries.

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Sean J. Maloney, Joanna Richards, and Iain M. Fletcher

determine if a task can be deemed an appropriate representation of a simple spring-mass model. While various active (typically muscular) and passive (typically tendinous) components contribute to summative stiffness, 2 this investigation will focus on the global measure of vertical stiffness. Modeling

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Justin P. Waxman, Kevin R. Ford, Anh-Dung Nguyen, and Jeffrey B. Taylor

, et al . Leg stiffness and sprint ability in amputee sprinters . Prosthet Orthot Int . 2012 ; 36 ( 3 ): 312 – 317 . PubMed doi:10.1177/0309364612442121 10.1177/0309364612442121 22918908 8. Dalleau G , Belli A , Bourdin M , Lacour JR . The spring-mass model and the energy cost of

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Simon A. Rogers, Chris S. Whatman, Simon N. Pearson, and Andrew E. Kilding

speeds during competition. Various approaches to quantify stiffness have been reported in the literature, including both global 12 – 14 and component stiffness. 6 , 15 Derived from the spring-mass model originally presented by Alexander, 16 global stiffness measures comprise of vertical ( k vert

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Sean J. Maloney, Iain M. Fletcher, and Joanna Richards

The assessment of vertical leg stiffness is an important consideration given its relationship to performance. Vertical stiffness is most commonly assessed during a bilateral hopping task. The current study sought to determine the intersession reliability, quantified by the coefficient of variation, of vertical stiffness during bilateral hopping when assessed for the left and right limbs independently, which had not been previously investigated. On 4 separate occasions, 10 healthy males performed 30 unshod bilateral hops on a dual force plate system with data recorded independently for the left and right limbs. Vertical stiffness was calculated as the ratio of peak ground reaction force to the peak negative displacement of the center of mass during each hop and was averaged over the sixth through tenth hops. For vertical stiffness, average coefficients of variation of 15.3% and 14.3% were observed for the left and right limbs, respectively. An average coefficient of variation of 14.7% was observed for bilateral vertical stiffness. The current study reports that calculations of unilateral vertical stiffness demonstrate reliability comparable to bilateral calculations. Determining unilateral vertical stiffness values and relative discrepancies may allow a coach to build a more complete stiffness profile of an individual athlete and better inform the training process.

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Hiroaki Hobara, Koh Inoue, Yoshiyuki Kobayashi, and Toru Ogata

Despite the presence of several different calculations of leg stiffness during hopping, little is known about how the methodologies produce differences in the leg stiffness. The purpose of this study was to directly compare K leg during hopping as calculated from three previously published computation methods. Ten male subjects hopped in place on two legs, at four frequencies (2.2, 2.6, 3.0, and 3.4 Hz). In this article, leg stiffness was calculated from the natural frequency of oscillation (method A), the ratio of maximal ground reaction force (GRF) to peak center of mass displacement at the middle of the stance phase (method B), and an approximation based on sine-wave GRF modeling (method C). We found that leg stiffness in all methods increased with an increase in hopping frequency, but K leg values using methods A and B were significantly higher than when using method C at all hopping frequencies. Therefore, care should be taken when comparing leg stiffness obtained by method C with those calculated by other methods.

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Michael S. Cherry, Sridhar Kota, Aaron Young, and Daniel P. Ferris

Although there have been many lower limb robotic exoskeletons that have been tested for human walking, few devices have been tested for assisting running. It is possible that a pseudo-passive elastic exoskeleton could benefit human running without the addition of electrical motors due to the spring-like behavior of the human leg. We developed an elastic lower limb exoskeleton that added stiffness in parallel with the entire lower limb. Six healthy, young subjects ran on a treadmill at 2.3 m/s with and without the exoskeleton. Although the exoskeleton was designed to provide ~50% of normal leg stiffness during running, it only provided 24% of leg stiffness during testing. The difference in added leg stiffness was primarily due to soft tissue compression and harness compliance decreasing exoskeleton displacement during stance. As a result, the exoskeleton only supported about 7% of the peak vertical ground reaction force. There was a significant increase in metabolic cost when running with the exoskeleton compared with running without the exoskeleton (ANOVA, P < .01). We conclude that 2 major roadblocks to designing successful lower limb robotic exoskeletons for human running are human-machine interface compliance and the extra lower limb inertia from the exoskeleton.

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Gaspare Pavei, Elena Seminati, Jorge L.L. Storniolo, and Leonardo A. Peyré-Tartaruga

We compared running mechanics parameters determined from ground reaction force (GRF) measurements with estimated forces obtained from double differentiation of kinematic (K) data from motion analysis in a broad spectrum of running speeds (1.94–5.56 m⋅s–1). Data were collected through a force-instrumented treadmill and compared at different sampling frequencies (900 and 300 Hz for GRF, 300 and 100 Hz for K). Vertical force peak, shape, and impulse were similar between K methods and GRF. Contact time, flight time, and vertical stiffness (kvert) obtained from K showed the same trend as GRF with differences < 5%, whereas leg stiffness (kleg) was not correctly computed by kinematics. The results revealed that the main vertical GRF parameters can be computed by the double differentiation of the body center of mass properly calculated by motion analysis. The present model provides an alternative accessible method for determining temporal and kinetic parameters of running without an instrumented treadmill.

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Kurt L. Mudie, Amitabh Gupta, Simon Green, Hiroaki Hobara, and Peter J. Clothier

This study assessed the agreement between Kvert calculated from 4 different methods of estimating vertical displacement of the center of mass (COM) during single-leg hopping. Healthy participants (N = 38) completed a 10-s single-leg hopping effort on a force plate, with 3D motion of the lower limb, pelvis, and trunk captured. Derived variables were calculated for a total of 753 hop cycles using 4 methods, including: double integration of the vertical ground reaction force, law of falling bodies, a marker cluster on the sacrum, and a segmental analysis method. Bland-Altman plots demonstrated that Kvert calculated using segmental analysis and double integration methods have a relatively small bias (0.93 kN⋅m–1) and 95% limits of agreement (–1.89 to 3.75 kN⋅m–1). In contrast, a greater bias was revealed between sacral marker cluster and segmental analysis (–2.32 kN⋅m–1), sacral marker cluster and double integration (–3.25 kN⋅m–1), and the law of falling bodies compared with all methods (17.26–20.52 kN⋅m–1). These findings suggest the segmental analysis and double integration methods can be used interchangeably for the calculation of Kvert during single-leg hopping. The authors propose the segmental analysis method to be considered the gold standard for the calculation of Kvert during single-leg, on-the-spot hopping.