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

McGrath, M; Howard, D; Baker, RJ

Abstract

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.

Citation

McGrath, M., Howard, D., & Baker, R. (2017). A Lagrange-based generalised formulation for the equations of motion of simple walking models. Journal of Biomechanics, 55, 139-143. https://doi.org/10.1016/j.jbiomech.2017.02.013

• Journal Article Type: Article
• Acceptance Date: Feb 11, 2017
• Online Publication Date: Feb 21, 2017
• Publication Date: Feb 21, 2017
• Deposit Date: Mar 17, 2017
• Publicly Available Date: Feb 21, 2018
• Journal: Journal of Biomechanics
• Print ISSN: 0021-9290
• Electronic ISSN: 1873-2380
• Publisher: Elsevier
• Volume: 55
• Pages: 139-143
• DOI: https://doi.org/10.1016/j.jbiomech.2017.02.013
• Publisher URL: https://doi.org/10.1016/j.jbiomech.2017.02.013
• Related Public URLs: https://www.journals.elsevier.com/journal-of-biomechanics/