The paradox is classically explained by noting the relative moment arms
of the hamstrings and rectus femoris at either the hip or
the knee, and their effects on the magnitude of the moments produced by either muscle group at each of the two joints (Rasch
& Burke, 1978, pp. 296-7).
Muscles cannot develop different amounts of force in their different parts. The hamstrings, for instance, cannot selectively extend the hip without acting with equal force at the knee. Thus, the only way for hip extension and knee extension to occur simultaneously in the act of standing (or eccentrically in the act of sitting) is for the net moment to be an extensor moment at both the hip and knee joints. Lombard suggested three necessary conditions for such paradoxical co-contraction:
we said on the CGA list
Andrews J G (1985) A general method for determining the functional role of a muscle J Biomech Eng 107: 348-353.
Bobbert MF, van Soest AJ (2000) Two-joint muscles offer the solution - but what was the problem? Motor Control 4: 48-52 & 97-116.
Gregor, R.J., Cavanagh, P.R., & LaFortune, M. (1985). Knee flexor moments during propulsion in cycling--a creative solution to Lombard's Paradox. Journal of Biomechanics, 18, 307-16 .
Ingen-Schenau GJv (1989) From rotation to translation: constraints on multi-joint movement and the unique action of bi-articular muscles. Hum. Mov. Sci. 8:301-37.
Lombard, W.P., & Abbott, F.M. (1907). The mechanical effects produced by the contraction of individual muscles of the thigh of the frog. American Journal of Physiology, 20, 1-60.
Mansour J M & Pereira J M (1987) Quantitative functional anatomy of the lower limb with application to human gait J Biomech 20: 51-58.
Park S, Krebs DE, Mann RW (1999) Hip muscle co-contraction: evidence from concurrent in vivo pressure measurement and force estimation. Gait & Posture 10: 211-222.
Rasch, P.J., & Burke, R.K. (1978). Kinesiology and applied anatomy. (6th ed.). Philadelphia: Lea & Febiger.
Visser JJ, Hoogkamer JE, Bobbert MF & Huijing PA (1990) Length and Moment Arm of Human Leg Muscles as a Function of Knee and Hip Angles. Eur. J Appl Physiol 61: 453-460.
Zajac FE & Gordon MF (1989) Determining muscle's force and action in multi-articular movement Exerc Sport Sci Revs 17: 187-230.
FE, Neptune RR, Kautz SA (2003) Biomechanics and muscle coordination of
human walking - Part II: Lessons from
dynamical simulations and clinical implications, Gait & Posure 17 (1): 1-17.
Back to Teach-in page