Muscle moment-arms: a key element in muscle-force estimation

Abstract

A clear and rigorous definition of muscle moment-arms in the context of musculoskeletal systems modelling is presented, using classical mechanics and screw theory. The definition provides an alternative to the tendon excursion method, which can lead to incorrect moment-arms if used inappropriately due to its dependency on the choice of joint coordinates. The definition of moment-arms, and the presented construction method, apply to musculoskeletal models in which the bones are modelled as rigid bodies, the joints are modelled as ideal mechanical joints and the muscles are modelled as massless, frictionless cables wrapping over the bony protrusions, approximated using geometric surfaces. In this context, the definition is independent of any coordinate choice. It is then used to solve a muscle-force estimation problem for a simple 2D conceptual model and compared with an incorrect application of the tendon excursion method. The relative errors between the two solutions vary between 0% and 100%.

Keywords::

• musculoskeletal systems
• moment-arms
• screw theory
• muscle-force estimation

Acknowledgement

This study was supported by the Swiss National Science Foundation (No. K-32K1_122512).

Notes

^1. Email: [email protected]

^2. Email: [email protected]

^3. Email: [email protected]

^4. Notation: bold lower-case letters are vectors, bold upper-case letters are matrices, plain lower-case letters are scalars and plain upper-case letters are geometric points.