View Full Version : Replies about Lombard's paradox

Michel Pillu
04-27-2004, 06:11 PM
Replies about Lombard's paradox

Hi, Dear All,
Would you find enclosed all the replies I had concerning the Lombard's
paradox. I would like to thank everybody. Alle the responses helped me a
Nice day to everybody

You might be interested in the work Felix Zajac has done concerning the role
of biarticular muscles, for example: Journal of Biomechanics 35(8) 1011-8

Dear Michel,

I have Lombard's original paper somewhere in my archives, but I will not get
to my office for a few days. Please let me know if you get it from somewhere
else in the meantime. Otherwise, I will scan it and email it to you.
In terms of a more recent explanation of antagonistic activity in squatting,
please have a look at this link:
and feel free to ask any
questions you may have.
Best regards,

John Rasmussen, Assoc. Prof., Ph.D., The AnyBody Group, www.anybody.aau.dk
Institute of Mechanical Engineering, Aalborg
www.ime.aau.dk/~jr jr@ime.aau.dk
Tel. +45 9635 9307
We had a discussion about this some time ago:

Dr. Chris Kirtley MD PhD
Associate Professor
Dept. of Biomedical Engineering
Catholic University of America
620 Michigan Ave NE, Washington, DC 20064
Tel. 202-319-6134, fax 202-319-4287
Email: kirtley@cua.edu

Arthur Kuo has published recently a nice paper on L. paradox in Classics in
Human Science (edited by Latash and Zatsiorsky)
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
References: 1)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 . 2) 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. 3) Rasch, P.J., & Burke, R.K. (1978). Kinesiology and applied
anatomy. (6th ed.). Philadelphia: Lea & Febiger.

STEPHAN PICKERING / Chofetz Chayim ben-Avraham
The Dinosaur Fractals Project
2333 Portola Drive # 4
Santa Cruz, California 95062-4250 USA
website: http://groups.yahoo.com/group/paleo_bio_dinosaur_ontology

theropod research summarized:
see under PICKERING at their Reference Base

Andrews, James G. The functional roles of the hamstrings and quadriceps
during cycling: Lombard's paradox revisited. Journal of Biomechanics 1987;
20(6): 565-575.
Gregor, RJ, Cavanagh, PR, and Lafortune M. Knee flexor moments during
propulsion in cycling- A creative solution to Lombard's paradox. Journal of
Biomechanics 1985; 18: 307-316.
Lombard WP. The action of two-joint muscles. Am. phys. Educ. Rev. 1903; 8:

G Robert Colborne, PhD
Equine Centre
Faculty of Medical & Veterinary Sciences
University of Bristol
Langford, N. Somerset
BS40 5DU

Phone: Int +44 (0)117 928 9363
Email: Bob.Colborne@bristol.ac.uk

Hi Michel,
Lombard's paradox is discussed in a text called Kinesiology and Applied
Anatomy written by Philip Rasch and Roger Burke. The reference in the
1971 4 th edition is on page 357 and the text was published by Lea &
Febiger. I would suspect that it would be referenced in later editions
but Burke was dropped from the authorship in the later editions. This
concept is very important in understanding the mechanics of rising from
a seated position and also jumping.
I hope this has helped.

Al Finch
Biomechanics Lab
Indiana State University
tel: 812-237-3927
Email: pmfinch@scifac.indstate.edu

Bonjour Michel,

J'ai attaché à ce courriel un papier de Art Kuo concernant ce paradox.

Martin Simoneau
Université Laval, PEPS
Faculté de Médecine, Division de Kinésiologie
Groupe de Recherche en Analyse du Mouvement et Ergonomie
Québec, Qc, CANADA
G1K 7P4
Phone: 418-656-2131 ext. 7788
Fax : 418-656-2441
Dear Michael

I have never read the Lombard´s paradox but I think that the explanation is
possible on the base of 1)open/closed kinetic chaims and/or 2)punctum fixum
versus punctum mobile. The result of single muscle activity in complex of
movement system depends on the given postural situation and is determined by
the other forces too e.g. gravity, aktivity of the other muscles etc., etc.
In the case of biarticular muscles is important how are the joints " locked
" by monoarticular muscles. That means in case of " locked " hip (e.g. m.
iliopsoas) the hamstring activity will result in knee flexion, in case of "
locked " knee (e.g. mm. vasti)the result will be a hip extension. Thinking
this way you can not see any paradox. But tell me if I am wrong.

Dear Michel,

You should find the following article relevant for your question. Good
Luck. FB

J Biomech. 1985;18(5):307-16.
Knee flexor moments during propulsion in cycling-a creative solution to
Lombard's Paradox.
Gregor RJ, Cavanagh PR, LaFortune M.
The function of two joint muscles in the human lower extremity was studied
during a cycling task with efficiency of their action discussed in light of
Lombard's Paradox. Special pedals were designed to monitor reaction forces
parallel to the sagittal plane of the body. Net moments of force about the
hip, knee and ankle and EMG patterns in selected lower extremity muscles
were recorded in five subjects pedalling against a constant load. The most
original aspect of this study was the clear difference in hip and knee
action during the propulsive phase of the pedalling cycle. A knee flexor
moment was consistently observed in all subjects starting approximately half
way through the propulsive phase of crank rotation (0-180 degrees) and
presented as a creative solution to Lombard's Paradox.
Frank L Buczek, Jr, PhD
President-Elect, GCMAS
Director, Motion Analysis Laboratory
Shriners Hospitals for Children
1645 West 8th Street, Erie PA, 16505, USA
(814) 875-8805 voice, (814) 875-8756 fax
On the following homepage I found a paper of Kuo (pdf file) about Lombards
paradox and the action of two-joint muscles:



Huub Maas
There is a two-page explanation of Lombard's Paradox in ...
Rasch, Philip J., and Roger K. Burke
Kinesiology and Applied Anatomy: The Science of Human Movement.
Lea and Febiger

I have the third edition, which was published in 1967. It may be out of
print now, but it was used extensively in the 70's and 80's and you may be
able to find a copy in your library. It was first printed in 1959.
Rasch and Burke provide the following citation for the original work by
Lombard, W.P. and Abbott, F.M. The Mechanical Effects Produced by the
Contraction of Individual Muscles of the Thigh of the Frog. American
Journal of Physiology, Volume 20, Pages 1-60, 1907.
If your own school library doesn't have this journal, it should be fairly
easy to obtain from another library.

I don't have the original reference, but there is been some talk of this in
cycling research for some years.
Gregor, Komi and Lafortune wrote a paper in 1958 (Journal of Biomechanics)
and work by van Ingen Schenau and his colleagues will be worth looking
Nick Brown

Michel PILLU
PhD Biomécanique
La Renaissance Sanitaire
Tél : 03 23 70 75 38
06 23 89 84 06
Fax : 03 23 70 53 24
E-mails : michel.pillu@hlrs-villiers.net


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