Ability of the planar spring–mass model to predict mechanical parameters in running humans

SUMMARYKinematic and kinetic parameters of running gait were investigated through growth in the ostrich, from two weeks up to 10 months of age, in order to investigate the effects of increasing body size. Ontogenetic scaling relationships were compared with published scaling relationships found to exist with increasing body size between species to determine whether dynamic similarity is maintained during growth. During the study, ostrich mass ( ), significantly exceeding the close to geometric scaling observed between mammalian and avian species of increasing body size. Scaling of kinematic variables largely agreed with predicted scaling for increasing size and demonstrated relationships close to dynamic similarity and, as such, ontogenetic scaling of locomotor parameters was similar to that observed with increasing body mass between species. However, the ways in which these scaling trends were achieved were very different, with ontogenetic scaling of locomotor mechanics largely resulting from simple scaling of the limb segments rather than postural changes, likely to be due to developmental constraints. Small deviations from dynamic similarity of kinematic parameters and a reduction in the predicted scaling of limb stiffness (ϰM b 0.59 ) were found to be accounted for by the positive allometric scaling of the limb during growth.

Section: Methodsmentioning

confidence: 99%

Ontogenetic scaling of locomotor kinetics and kinematics of the ostrich (Struthio camelus)

Smith

Jespers

Wilson

2010

“…In contrast to simplified, single-mass models (Blickhan, 1989;Blum et al, 2009;Farley and Gonzalez, 1996;McMahon and Cheng, 1990;Silder et al, 2015), which are incapable of capturing the high-frequency, impact-phase components of the waveform (Bullimore and Burn, 2007;Shorten and Mientjes, 2011), and multi-mass models that do not account for the whole waveform and are too theoretical and complex for practical application, the two-mass model requires only body mass and very limited motion data in order to predict the waveform in full. These attributes enable indirect assessment of impact forces, limb loading rates, and other informative, force-based outcomes using video or other inexpensive motion-sensing technologies.…”

Section: General Considerations Applications and Concluding Remarksmentioning

confidence: 99%

A general relationship links gait mechanics and running ground reaction forces

Clark

Ryan

Weyand

2016

The relationship between gait mechanics and running ground reaction forces is widely regarded as complex. This viewpoint has evolved primarily via efforts to explain the rising edge of vertical forcetime waveforms observed during slow human running. Existing theoretical models do provide good rising-edge fits, but require more than a dozen input variables to sum the force contributions of four or more vague components of the body's total mass (m b ). Here, we hypothesized that the force contributions of two discrete body mass components are sufficient to account for vertical ground reaction forcetime waveform patterns in full (stance foot and shank, m 1 =0.08m b ; remaining mass, m 2 =0.92m b ). We tested this hypothesis directly by acquiring simultaneous limb motion and ground reaction force data across a broad range of running speeds (3.0-11.1 m s −1) from 42 subjects who differed in body mass (range: 43-105 kg) and foot-strike mechanics. Predicted waveforms were generated from our two-mass model using body mass and three stride-specific measures: contact time, aerial time and lower limb vertical acceleration during impact. Measured waveforms (N=500) differed in shape and varied by more than twofold in amplitude and duration. Nonetheless, the overall agreement between the 500 measured waveforms and those generated independently by the model approached unity (R 2 =0.95 ±0.04, mean±s.d.), with minimal variation across the slow, medium and fast running speeds tested (ΔR 2 ≤0.04), and between rear-foot (R 2 =0.94±0.04, N=177) versus fore-foot (R 2 =0.95±0.04, N=323) strike mechanics. We conclude that the motion of two anatomically discrete components of the body's mass is sufficient to explain the vertical ground reaction force-time waveform patterns observed during human running.

“…However, this classic model was formulated largely for broad evaluative purposes, not specific quantitative ones. Accordingly, the perfectly symmetrical force-time waveforms the model predicts (Bullimore and Burn, 2007;Robilliard and Wilson, 2005) cannot account for the non-symmetrical components that the force-time waveforms inevitably contain. These include, but are not limited to, heel-strike impacts at slow speeds and extremely rapid rising edges at faster ones (Kuitunen et al, 2002;Weyand et al, 2009;Weyand et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…The single-mass approach models running and hopping animals as a lumped point-mass mass bouncing on a massless leg spring. This single-mass model explains many aspects of running and hopping gaits with remarkable accuracy given its mechanical simplicity (Bullimore and Burn, 2007;Farley et al, 1993;Ferris and Farley, 1997;McMahon and Cheng, 1990). However, this classic model was formulated largely for broad evaluative purposes, not specific quantitative ones.…”

Section: Introductionmentioning

confidence: 99%

Foot speed, foot-strike and footwear:linking gait mechanics and running ground reaction forces

Clark

Ryan

Weyand

2014

Running performance, energy requirements and musculoskeletal stresses are directly related to the action-reaction forces between the limb and the ground. For human runners, the force-time patterns from individual footfalls can vary considerably across speed, footstrike and footwear conditions. Here, we used four human footfalls with distinctly different vertical force-time waveform patterns to evaluate whether a basic mechanical model might explain all of them. Our model partitions the body's total mass (1.0M b ) into two invariant mass fractions (lower limb=0.08, remaining body mass=0.92) and allows the instantaneous collisional velocities of the former to vary. The best fits achieved (R 2 range=0.95-0.98, mean=0.97±0.01) indicate that the model is capable of accounting for nearly all of the variability observed in the four waveform types tested: barefoot jog, rear-foot strike run, fore-foot strike run and fore-foot strike sprint. We conclude that different running ground reaction force-time patterns may have the same mechanical basis.