A MOVEMENT CRITERION FOR RUNNING
A. Seyfarth *°, H. Geyer *°, R. Blickhan *
*Biomechanics Lab, Friedrich-Schiller-Universität Jena, Germany
°Leglab, MIT, Cambridge MA, USA
Introduction
Spring-like leg behaviour is present in many types of fast animal and human locomotion. One typical
example is human running which was addressed by Blickhan (1989) and McMahon and Cheng (1990).
Although the representation of the leg by a linear spring is widely used by biologists and bioengineers
there is only little known about the advantages of this type of locomotion. In this study the stability of
spring-like leg operation during running is addressed.
Methods
Running was investigated by a stride-to-stride analysis of the spring-mass model (Fig. 1). At given initial
conditions (forward speed v0, apex height during flight phase y0) we identified appropriate leg
adjustments (leg stiffness kLEG, leg angle of attack D0, initial leg length "0 at touch-down) resulting in a
periodic running pattern. Touch-down occured if the centre of mass reaches the critical height yTD which
is a consequence of the fixed angle of attack D0 and the initial leg length "0 at touch-down:
yTD = "0 sin D0.
(1)
Take-off occured if the initial leg length is reached again "(tTO) = "0. During the flight phase the centre of
mass trajectory is simply determined by the gravitational acceleration. The leg movement is not described
by the model during this period.
Fig. 1 The spring-mass model for running. The leg spring is characterised by the stiffness
kLEG and the nominal length "0 which is the leg length at touch-down and take-off. In our
approach the leg orientation at touch-down is characterised by a given angle of attack D0.
During the flight phase the horizontal velocity is constant. One stride can be defined as the
movement from one apex to the next one.
The number of successful steps served as a measure for periodicity. The predicted leg operation for
running was compared to an experimental study on human running at moderate speed (v = 4.6r0.5 m/s;
12 students: body weight m = 69.5r9.8 kg, height 1.77r0.08 m).
Results
The analysis of the spring-mass system revealed that there exist leg adjustments (leg stiffness, angle of
attack: Fig. 2) which lead into periodic limit cycles in the movement pattern. These solutions proved to be
robust with respect to adjustment errors and variations in kinematic parameters (speed, initial apex
height). Small variations in the leg stiffness kLEG (ca. r3 kN/m at D0 = 68°) and angle of attack D0 (ca. r1°
at kLEG = 20kN/m) were tolerated by the system without leaving the periodic running pattern (Fig. 3).
The experimental data (circles in Fig. 2)showed a good coincidence with the predicted leg adjustments.
Different strategies were used by the subjects: either stiff legs with steep angles of attack or more
compliant legs with flatter angles.
Fig. 2 Predicted steps to fall (v=5m/s).
Fig. 3 Trajectories of the centre of mass for different
angles of attack D0 but the same leg stiffness kLEG.
Discussion
Adaptations in the chosen angle of attack similar to our findings have been observed during running for
largely different animals (Farley et al., 1993) and humans (Farley and Gonzalez, 1996). The experimental
evidences of the model predictions lead to the conclusion that self-stabilised running requires a springlike leg operation with a minimum running speed as well as a proper adjustment of the leg stiffness and
the angle of attack. These conditions can be considered as a movement criterion for running.
On the musculo-skeleton level elastic properties of the leg can be found if proprioceptive feedback
mechanisms are included (Seyfarth et al. #890 at this conference). Using the movement criterion for
running this resulted in running patterns similar to Fig. 3.
References
Blickhan, R. J. Biomech. 22, 1217-1227, 1989.
Farley, C. T., Glasheen, J., and McMahon, T. A. J. Exp. Biol. 185, 71-86, 1993.
Farley, C. T. and O. Gonzalez. J. Biomech. 29(2): 181-6, 1996.
McMahon T. A. and Cheng, G. C. J. Biomech. 23, Suppl. 1, 65-78,1990.
Acknowledgements
This work was supported by the German Science Foundation (DFG) within the “Innovationskolleg
Bewegungssysteme” (INKA22 project C1) and by a DFG “Emmy Noether” grant (SE1042/1-1) to Andre
Seyfarth.