A simple model of human walking


  • Leonardo Campanelli All Saints University School of Medicine, Toronto, Canada



Human Locomotion, Gait, Inverted Pendulum Model, Modelling


Objectives. We investigate the Alexander's inverted pendulum model, the simplest mathematical model of human walking. Although it is successful in explaining some kinematic features of human walking, such as the velocity of the body's center of mass, it does not account for others, like the vertical reaction force and the maximum speed of walking. The aim of this paper is to minimally extend the Alexander's model in such a way to make it a viable and quantitative model of human walking for clinical biomechanics.

Material and Methods. In order to compare the predictions of the Alexander's model with experimental data on walking, we incorporate in it a robust phenomenological relation between stride frequency and stride length derived in the literature, and we introduce a step-angle dependent muscle force along the pendulum. We then solve analytically the equation of motion of the pendulum and nd the corresponding analytical expression for the average speed of walking.

Results. The values of the average speed of walking for dierent heights predicted by our model are in excellent agreement with the ones obtained in treadmill experiments. Moreover, it successfully predicts the observed walking-running transition speed which occurs when the stride length equals the height of an individual. Finally, our extended model reproduces the experimentally observed ground reaction forces in the midstance and terminal stance phases in a satisfactory way. As a consequence, the predicted value of the (height-dependent) maximum speed of walking is in reasonable agreement with the one obtained in more sophisticated models of human walking.

Conclusions. Augmented with our minimal extensions, the Alexander's model becomes an eective and realistic model of human walking which can be used in clinical investigations of the human gate.


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How to Cite

Campanelli L. A simple model of human walking. JMS [Internet]. 2023 Mar. 1 [cited 2023 Mar. 20];:e817. Available from:



Original Papers
Received 2023-02-10
Accepted 2023-03-01
Published 2023-03-01