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Kuo - 1993 - A biomechanical analysis of muscle strength as a limiting factor in standing posture


Kuo A, Zajac F. A biomechanical analysis of muscle strength as a limiting factor in standing posture. J Biomech. 1993;26 Suppl 1:137-50. PUBMED

10 Word Summary

Joint acceleration limits show that individual segments do not move independently.
Hip strategy is imposed for greater accelerations.


We developed a method for studying muscular coordination and strength in multijoint movements and have applied it to standing posture. The method is based on a musculoskeletal model of the human lower extremity in the sagittal plane and a technique to visualize, geometrically, how constraints internal and external to the body affect movement. We developed an algorithm to calculate the set of all feasible accelerations (i.e., the 'feasible acceleration set', or FAS) that muscles can induce. For the ankle, knee, and hip joints in the sagittal plane, this set is a polyhedron in three dimensions. Using the volume of the FAS as an indicator of overall mobility, we found that strengthening muscles on the posterior side (as opposed to the anterior) of the body would cause greater increases in mobility. Employing the experimental observations of others, we also found that acceleration constraints greatly reduce the range of feasible accelerations. We then defined a set of four basic acceleration vectors which, when used in various combinations, can produce the repertoire of postural movements. We used linear programming to find the maximum magnitudes of these vectors, and the sensitivity of these magnitudes to muscle strength, thereby delineating those muscles which, if strengthened, would cause the greatest increase in the body's ability to generate the basic acceleration vectors. For our particular model, those muscle groups were found to be hamstrings, tibialis anterior, rectus femoris, and gastrocnemius. These muscle groups would be of great importance in cases involving severely reduced muscle strength. This methodology may therefore be useful for purposes such as design of functional electrical stimulation controllers or exercises for persons at risk for falling.


  • The mass matrix is near rank one, showing that all segments are coupled.  Muscles showing the most sensitivity to the change in acceleration were associated with hip and ankle flexors.  The extensors did not drastically change the feasible acceleration set with varying amplitude.