Metabolic cost of human hopping.

To interpret the movement strategies employed in locomotion, it is necessary to understand the source of metabolic cost. Muscles must consume metabolic energy to do work, but also must consume energy to generate force. The energy lost during steady locomotion and, hence, the amount of mechanical work muscles need to perform to replace it can be reduced and, in theory, even eliminated by elastically storing and returning some portion of this energy via the tendons.

The apparently contradictory energetics of hopping and running: the counter-intuitive effect of constraints resolves the paradox.

Metabolic rate appears to increase with the rate of force application for running. Leg function during ground contact is similar in hopping and running, so one might expect that this relationship would hold for hopping as well. Surprisingly, metabolic rate appeared to decrease with increasing force rate for hopping.

The dynamic limits of hop height: Biological actuator capabilities and mechanical requirements of task produce incongruity between one- and two-legged performance.

The maximum hop height attainable for a given hop frequency falls well below the theoretical limit dictated by gravity, h = g/8f(2). However, maximum hop height is proportional to 1/f(2), suggesting that ground reaction force and, hence, force production capabilities of the leg muscles limit human hopping performance. Curiously, during one-legged hopping, subjects were able to produce substantially more than 50% the ground reaction force produced during two-legged maximum height hopping-66% on average and as much as 90% the total force produced during two-legged hopping.

Collision-based mechanics of bipedal hopping.

The muscle work required to sustain steady-speed locomotion depends largely upon the mechanical energy needed to redirect the centre of mass and the degree to which this energy can be stored and returned elastically. Previous studies have found that large bipedal hoppers can elastically store and return a large fraction of the energy required to hop, whereas small bipedal hoppers can only elastically store and return a relatively small fraction. Here, we consider the extent to which large and small bipedal hoppers (tammar wallabies, approx.

Constrained optimization of metabolic cost in human hopping.

Constrained optimization of metabolic cost/distance travelled largely predicts the gait parameters selected by humans during walking and running. This study evaluates whether this is also the case for human hopping. Hop frequency (f), height (h) and metabolic energy expenditure were measured in partly constrained (f, h or hop speed, s ≡ fh, specified), fully constrained (both f and h specified) and unconstrained conditions (neither f nor h specified) for 4 min trials.

Constrained optimization in human running.

Walking humans spontaneously select different speed, frequency and step length combinations, depending on which of these three parameters is specified. This behavior can be explained by constrained optimization of cost of transport (metabolic cost/distance) where cost of transport is seen as the main component of an underlying objective function that is minimized within the limitations of specified constraints. It is then of interest to ask whether or not such results are specific to walking only, or indicate a more general feature of locomotion control.