Walking dynamic similarity induced by a combination of Froude and Strouhal dimensionless numbers: Modela-w

Evaluating dynamic similarity of fixed, self-selected and anatomically scaled speeds in non-linear analysis of gait during treadmill running

“…Studies considering the use of Froude numbers within walking and running trials using linear measures also found dynamic similarity in each case when compared with fixed speeds (Delattre et al, 2009;Villeger et al, 2014;Villeger et al, 2015). Our research has also evaluated Froude speeds for non-linear measures when running and found this to be less variable, also suggesting that scaled speeds are a legitimate alternative to create similar conditions between participants within non-linear analysis of movement variability.…”

“…Where previous studies have considered using Froude numbers to evaluate dynamic stability in running, the comparison has been done with fixed speeds and linear measures (Delattre et al, 2009;Villeger et al, 2014). Other studies have considered walking (Villeger et al, 2015), or walk-run transitions (Kram et al, 1997) again considering linear measures. In each case using a scaled speed resulted in apparent dynamical similarity, but there is a gap in the research considering how the Froude number affects non-linear analysis and comparing this to self-selected speeds.…”

“…Like the Froude number, the Strouhal number is a dimensionless number, in this case representing the frequency of the gait pattern (Alexander, 1989). However, previous studies including the Strouhal number have focused on linear measures (Delattre et al, 2009;Villeger et al, 2015), and research suggests that fixing stride frequency affects non-linear measures (Terrier and Deriaz, 2013;Terrier, 2019), so we excluded it from this analysis to avoid introducing a confounding variable.…”

Simulation of human gait with body weight support: benchmarking models and unloading strategies

“…In the context of BWS, the level of dynamic similarity between the unloaded walking task and the eventual task to be trained, namely walking without support, is crucial. In order to quantify this dynamic similarity, we first represented the gait dynamics for each condition by a dimensionless number, modela-w [27]:…”

“…Dynamic similarity [24,25], based on the Froude number, has been previously used for investigating the effect of BWS on gait [26]. However, a recent work [27] suggested the Froude number alone to be inadequate and proposed a new metric called Modela-w. We thus use the change in Modela-w caused by the different BWS Fig. 1 The three gait models considered in this paper: (1) Simplest Walking (SW) model [21] where M is the mass of the body, m of each foot and m is assumed to be negligible as compared to M, θ is the stance leg angle w.r.t.…”