A Lagrange-based generalised formulation for the equations of motion of simple walking models

McGrath, M, Howard, D and Baker, RJ ORCID: https://orcid.org/0000-0003-4759-4216 2017, 'A Lagrange-based generalised formulation for the equations of motion of simple walking models' , Journal of Biomechanics, 55 , pp. 139-143.

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Simple 2D models of walking often approximate the human body to multi-link dynamic systems, where body segments are represented by rigid links connected by frictionless hinge joints. Performing forward dynamics on the equations of motion (EOM) of these systems can be used to simulate their movement. However, deriving these equations can be time consuming. Using Lagrangian mechanics, a generalised formulation for the EOM of n-link open-loop chains is derived. This can be used for single support walking models. This has an advantage over Newton-Euler mechanics in that it is independent of coordinate system and prior knowledge of the ground reaction force (GRF) is not required. Alternative strategies, such as optimisation algorithms, can be used to estimate joint activation and simulate motion. The application of Lagrange multipliers, to enforce motion constraints, is used to adapt this general formulation for application to closed-loop chains. This can be used for double support walking models. Finally, inverse dynamics are used to calculate the GRF for these general n-link chains. The necessary constraint forces to maintain a closed-loop chain, calculated from the Lagrange multipliers, are one solution to the indeterminate problem of GRF distribution in double support models. An example of this method's application is given, whereby an optimiser estimates the joint moments by tracking kinematic data.

Item Type: Article
Schools: Schools > School of Health and Society > Centre for Health Sciences Research
Journal or Publication Title: Journal of Biomechanics
Publisher: Elsevier
ISSN: 0021-9290
Related URLs:
Depositing User: Prof Richard Baker
Date Deposited: 17 Mar 2017 14:52
Last Modified: 16 Feb 2022 18:17
URI: http://usir.salford.ac.uk/id/eprint/41598

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