Predictions of co-contraction depend critically on degrees-of-freedom in the musculoskeletal model

Azim Jinha, Rachid Ait-Haddou, Walter Herzog*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


In biomechanics, the calculation of individual muscle forces during movements is based on a model of the musculoskeletal system and a method for extracting a unique set of muscle forces. To obtain a unique set of muscle forces, non-linear, static optimisation is commonly used. However, the optimal solution is dependent on the musculoskeletal geometry, and single joints may be represented using one, two or three degrees-of-freedom. Frequently, a system with multiple degrees-of-freedom is replaced with a system that contains a subset of all the possible degrees-of-freedom. For example, the cat ankle joint is typically modelled as a planar joint with its primary degree-of-freedom (plantar-dorsiflexion), whereas, the actual joint has three rotational degrees-of-freedom. Typically, such simplifications are justified by the idea that the reduced case is contained as a specific solution of the more general case. However, here we demonstrate that the force-sharing solution space of a general, three degrees-of-freedom musculoskeletal system does not necessarily contain the solutions from the corresponding one or two degrees-of-freedom systems. Therefore, solutions of a reduced system, in general, are not sub-set solutions of the actual three degrees-of-freedom system, but are independent solutions that are often incompatible with solutions of the actual system. This result shows that representing a three degrees-of-freedom system as a one or two degrees-of-freedom system gives force-sharing solutions that cannot be extrapolated to the actual system, and vice-versa. These results imply that general solutions cannot be extracted from models with fewer degrees-of-freedom than the actual system. They further emphasise the need for precise geometric representation of the musculoskeletal system, if general force-sharing rules are to be derived.

Original languageEnglish (US)
Pages (from-to)1145-1152
Number of pages8
JournalJournal of Biomechanics
Issue number6
StatePublished - 2006
Externally publishedYes


  • Agonist
  • Antagonist
  • Force-sharing
  • Movement control
  • Muscle
  • Optimisation

ASJC Scopus subject areas

  • Biophysics
  • Orthopedics and Sports Medicine
  • Biomedical Engineering
  • Rehabilitation


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