Lombard's paradox

Palpate the quadriceps and hamstring muscles as you arise to standing from sitting. These muscle groups are simultaneously active as a subject arises from sitting, even though the rectus femoris and the hamstrings are antagonistic. This very real coactivation of two antagonistic muscles during the activity of standing from a sitting position has been known for many years as Lombard's paradox (Lombard & Abbott, 1907).

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.

How does a net hip extension moment result when antagonistic muscles develop both extensor and flexor moments at the same time? All that is necessary is for the hip extensor moment to exceed the hip flexor moment. Two antagonistic muscles can produce such a net moment, even if they develop identical forces, if their moment arms around the hip are unequal. In this standing activity, the hamstrings' moment arm with respect to the hip joint's lateral axis exceeds that of the rectus femoris.

Similarly, a net knee extensor moment results at the knee even though the hamstrings and rectus femoris develop simultaneous and antagonistic moments. All that is necessary is for the knee extensor moment to exceed the knee flexor moment. The antagonists produce a net knee extension moment, even if they develop identical forces, because their moment arms around the knee are unequal; the rectus femoris' moment arm at the knee exceeds that of the hamstrings.

The phenomenon still interests students of biomechanics (Gregor, Cavanagh, & LaFortune, 1985). Whatever its explanation, the fact that the hamstrings and quadriceps are simultaneously active at the knee during closed chain activities is a factor in the design of rehabilitation programs.


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 .

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.

Rasch, P.J., & Burke, R.K. (1978). Kinesiology and applied anatomy. (6th ed.). Philadelphia: Lea & Febiger.

Last updated 2-8-01 ©Dave Thompson PT