Skip to main content

Research Repository

Advanced Search

Modelling of the human quiet stance with ankle joint complexity

Ganguly, Amartya


Amartya Ganguly


Ming Hou

Catherine Anne Dobson


This study derives an inverted pendulum model for quiet stance in humans around the ankle joints with 4×9-element mass-spring-damper (MSD) units as the musculoskeletal connections between the shank and foot bilaterally. The model focuses on the role played by both the stiffness and the damping parameters of muscles, tendons and ligaments about the ankle complex. This model partitions muscles, tendons and ligaments functionally. This novel model is used to study the behaviour of individual components in relation to quiet standing. The Lagrange d’ Alembert principle has been used to derive the equations of motion of the system and resulted in eighteen 2nd order differential equations with nine constraints. Four MSD units connects with the shank (tibia and fibula) and foot bilaterally. The units function passively and are representative of the mechanical functionality of muscles, tendons, and ligaments about the ankle complex. The dynamics of the MSD units are considered linear in nature and their stiffness and damping parameters are calculated by finding the slope of the force vs. deformation length curve and force vs. velocity curve reported in the literature.

The simulation results revealed that the torques generated by the internal constraints through the MSD units are significantly greater than the gravitational torque. A case study has been conducted for eyes open vs. eyes closed conditions. It was found that the angular displacement of the shank varied but the overall range of motion of the ankle joint remained constant at 0.6. This was expected as there was no external perturbation applied to facilitate any amount of plantarflexion or dorsiflexion at the point of articulation of the ankle joint.

In conclusion, the model derived and analysed in this study explains that the human body was able to maintain its upright posture mechanically during unperturbed quiet standing without the use of an active control system emphasising the importance of damping and its influence on postural balance. Furthermore, this sophisticated model is not limited to only considering the muscle-tendon unit and ligaments play an important role in maintaining balance during quiet stance and are therefore included in the model. This model is physiologically more realistic than previously developed postural models thus providing a deeper insight towards the passive mechanism of postural balance and providing a new approach towards future postural models.


Ganguly, A. (2014). Modelling of the human quiet stance with ankle joint complexity. (Thesis). University of Hull. Retrieved from

Thesis Type Thesis
Deposit Date Oct 2, 2015
Publicly Available Date Feb 23, 2023
Keywords Engineering
Public URL
Additional Information Department of Engineering, The University of Hull
Award Date Aug 1, 2014


Thesis (2 Mb)

Copyright Statement
© 2014 Ganguly, Amartya. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.

You might also like

Downloadable Citations