The effect of frequency and mass on stiffness and angular amplitude in unipedal human hopping

The spring-like behavior of the body during bipedal hopping and running has been modeled as a simple mass-spring system. According to this model, spring-like oscillatory behavior can be adequately described using the parameters of mass, stiffness, and frequency. The model has been effective in explaining bipedal hopping behavior but has not been applied to either unipedal hopping or hopping with added mass. Furthermore, the kinematics of unipedal hopping have not been studied. From the model several predictions are made as to unipedal hopping behavior at different frequencies and masses. Therefore, the purpose of this study was to investigate the effect of frequency and mass on average vertical stiffness, cycle period, contact period, flight period, contact amplitude, hip flexion, knee flexion, and ankle dorsiflexion during unipedal hopping. Ten healthy, right leg dominant, males voluntarily participated. In all experiments subjects were videotaped while hopping on the right leg on a force platform. In Experiment 1, subjects hopped at either the preferred frequency (PHF), PHF+20%, or PHF$-$20%. The results demonstrated that hopping frequency is directly related to average vertical stiffness, and inversely related to contact period, flight period, contact amplitude, hip flexion, knee flexion, and ankle dorsiflexion. While average vertical stiffness was linear at both PHF and PHF+20%, it was significantly less linear at PHF$-$20%. In Experiment 2, subjects hopped at the preferred frequency with body mass (Mb), Mb+10%, or Mb+20%. The results demonstrate that with the addition of loads, average vertical stiffness was unchanged and highly linear. Despite increases in ankle dorsiflexion and hip flexion, both knee flexion and contact amplitude were unchanged with the added mass. An increase in the overall cycle period was due to an increase in the contact period as flight period was unchanged across loads. In Experiment 3, conditions consisted of combinations of 2 added mass conditions and the three frequency conditions. The frequency $\times$ mass interaction was not significant, and overall the results are in agreement with the findings of Experiments 1 and 2, although the load increased knee flexion at the higher frequency and hip flexion at the lower frequency.