The mechanics of running: How does stiffness couple with speed?

McMahon, Thomas A.; Cheng, George

doi:10.1016/0021-9290(90)90042-2

Cited by 925 publications

(932 citation statements)

References 8 publications

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“…The peak ground reaction force occurs at the same time as the centre of mass reaches its lowest point during running (McMahon & Cheng 1990;He et al 1991;Farley & Gonzalez 1996). On a non-compliant surface, the combination of leg sti¡ness and half the angle swept by the leg during ground contact ( ) establishes a runner's e¡ective vertical sti¡ness (McMahon & Cheng 1990).…”

Section: Methodsmentioning

confidence: 99%

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Running in the real world: adjusting leg stiffness for different surfaces

Ferris

Louie

Farley

1998

Proc. R. Soc. Lond. B

486

394

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A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal's leg sti¡ness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg sti¡ness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered di¡erent surfaces in the natural world. We found that human runners adjust their leg sti¡ness to accommodate changes in surface sti¡ness, allowing them to maintain similar running mechanics on di¡erent surfaces. These results provide important insight into the mechanics and control of animal locomotion and suggest that incorporating an adjustable leg sti¡ness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.

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Section: Methodsmentioning

confidence: 99%

“…In fact, the simplest model of a running animal is a spring^mass system consisting of a linear spring representing the stance limb (i.e. the leg spring) and a point mass equivalent to body mass (Blickhan 1989;McMahon & Cheng 1990) (see ¢gure 1).…”

Section: Introductionmentioning

confidence: 99%

Running in the real world: adjusting leg stiffness for different surfaces

Ferris

Louie

Farley

1998

Proc. R. Soc. Lond. B

486

394

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“…Although this includes both energy production (muscle fibers) and absorption (soft tissue, ligaments, muscles) the leg stiffness is surprisingly constant during the stance time. Blickhan (1989) and McMahon and Cheng (1990) introduced a simple spring-mass model to approximate this generally observed force pattern. This representation of the leg by a linear spring was successfully applied by biologists (Blickhan and Full, 1993;Farley et al, 1993;Farley and Gonzalez, 1996), sport scientists (Arampatzis et al, 1999;Seyfarth et al, 1999), and bioengineers (Herr, 1998) to describe and predict animal and human locomotion.…”

Section: Introductionmentioning

confidence: 99%

“…An approach to predict the leg spring adjustment in running was made by Blickhan (1989) and McMahon and Cheng (1990), which showed that for given parameters (running speed, leg stiffness, angle of attack) the spring-mass model might produce symmetric trajectories of the center of mass. Nevertheless, they did not prove whether the predicted solutions are stable with respect to deviations in landing conditions or leg stiffness.…”

Section: Introductionmentioning

confidence: 99%

A movement criterion for running

Seyfarth

Geyer

Günther

et al. 2002

Journal of Biomechanics

425

382

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The adjustment of the leg during running was addressed using a spring-mass model with a fixed landing angle of attack. The objective was to obtain periodic movement patterns. Spring-like running was monitored by a one-dimensional stride-to-stride mapping of the apex height to identify mechanically stable fixed points.We found that for certain angles of attack, the system becomes self-stabilized if the leg stiffness was properly adjusted and a minimum running speed was exceeded. At a given speed, running techniques fulfilling a stable movement pattern are characterized by an almost constant maximum leg force. With increasing speed, the leg adjustment becomes less critical. The techniques predicted for stable running are in agreement with experimental studies.Mechanically self-stabilized running requires a spring-like leg operation, a minimum running speed and a proper adjustment of leg stiffness and angle of attack. These conditions can be considered as a movement criterion for running. r

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“…In particular, on the mechanical level, the planar spring-mass model for bouncing gaits (Blickhan, 1989;McMahon and Cheng, 1990) has drawn attention since, while advocating a largely reductionist description, it retains key features discriminating legged from wheeled systems: phase switches between flight (swing) and stance phase, a leg orientation, and a repulsive leg behavior in stance. In consequence, not only biomechanical studies investigating hopping (Farley et al, 1991;Seyfarth et al, 2001) or running (He et al, 1991;Farley et al, 1993), but also fast legged robots driven by model-based control algorithms (Raibert, 1986;Saranli and Koditschek, 2003) rely on this plant.…”

Section: Introductionmentioning

confidence: 99%

Spring-mass running: simple approximate solution and application to gait stability

Geyer

Seyfarth

Blickhan

2005

Journal of Theoretical Biology

249

232

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The planar spring-mass model is frequently used to describe bouncing gaits (running, hopping, trotting, galloping) in animal and human locomotion and robotics. Although this model represents a rather simple mechanical system, an analytical solution predicting the center of mass trajectory during stance remains open. We derive an approximate solution in elementary functions assuming a small angular sweep and a small spring compression during stance. The predictive power and quality of this solution is investigated for model parameters relevant to human locomotion. The analysis shows that (i), for spring compressions of up to 20% (angle of attack X60 ; angular sweep p60 ) the approximate solution describes the stance dynamics of the center of mass within a 1% tolerance of spring compression and 0:6 tolerance of angular motion compared to numerical calculations, and (ii), despite its relative simplicity, the approximate solution accurately predicts stable locomotion well extending into the physiologically reasonable parameter domain. (iii) Furthermore, in a particular case, an explicit parametric dependency required for gait stability can be revealed extending an earlier, empirically found relationship. It is suggested that this approximation of the planar spring-mass dynamics may serve as an analytical tool for application in robotics and further research on legged locomotion. r

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The mechanics of running: How does stiffness couple with speed?

Cited by 925 publications

References 8 publications

Running in the real world: adjusting leg stiffness for different surfaces

Running in the real world: adjusting leg stiffness for different surfaces

A movement criterion for running

Spring-mass running: simple approximate solution and application to gait stability

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