CGA FAQ: Variability in joint moments & powers

from BIOMCH-L 4-21/5/96

I've spent quite a bit of time lately developing a nice multimedia tool for
analysing gait. It does the full inverse dynamics analysis to derive joint
moments and powers. The joint (resultant) moments
and powers during push-off (around 55% of cycle) peak at the following

               Moment                    Power
Knee     0.85 Nm/kg extensor        4.8 W/kg eccentric
Hip      1.35 Nm/kg flexor          1.45 W/kg concentric

For comparison, Winter reports:

               Moment                    Power
Knee     0.16 Nm/kg extensor        0.76 W/kg eccentric
Hip      0.4 Nm/kg flexor           0.67 W/kg concentric

I have found only one other set of normal curves, from Kabada's (1989)
study, which I took from Dwight Meglans's chapter in "Human Walking". There
are no powers quoted (Dwight seems to use Winter's data for these), and
unfortunately his units are rather obscure, since he normalises for leg
length (LL) as well as body weight:

Knee     8 Nm/kg.LL extensor
Hip      14 Nm/kg.LL flexor

I don't know how to convert these values to Nm/kg, but scaling for the
ankle moments (which all our results seem to agree on!) indicate dividing
by a factor of about 10:

Knee     0.8 Nm/kg extensor
Hip      1.4 Nm/kg flexor

i.e. the same as our results (and different from Winter's).

Our results are quite repeatable - we so far have not examined anyone who
gives curves like Winter's. At this point in time I still feel reluctant to
criticise Winter, since his normal data is the gold standard. But since we
seem to agree with Kabada, I now have the confidence to ask you all:


What values are you getting?


By the way, this experience has highlighted to me the need for more
published data on normal joint kinetics. I even traced back through all the
ISB proceedings and found very little except for Winter's reports. Does
this mean that there's noone else doing joint kinetics? I'm sure there must

I'll send a summary of responses.

Many thanks,


I want to thank everyone who responded to my query about knee and hip
moments during push-off. It certainly has stimulated an intriguing
discussion. I feel somewhat embarrassed now, however, since I discovered
that my own results were erroneous!

I am using a Macintosh computer to grab the video directly to computer, and
had assumed it was recording at the frame rate indicated. Unfortunately, it
was dropping three frames in every 25 (due simply to the grabber board not
beingfast enoough). The effect of this was that the force data were
incorrectly synchronised with the kinematics, to an increasing degree as
the subject advanced through the cycle. Thus the discrepancy was maximal at
toe-off, with early-mid stance being relatively unaffected and swing, of
course, totally unaffected. This explains why my results were not in
agreement with Winter's data. I have corrected the problem and my results
now agree.

Concerning the discussion raised by Chris Kirtley I would like to add that
we in our research group have obtained joint moments by inverse dynamics
very comparable to the data of David Winter. However, we have also noted
large differences between individuals regarding the time course of the
moment patterns (Simonsen et al. 1995), which corresponded well with the
data of Pedotti (1977). These differences are so pronounced (and
reproducible) that it is questionable to average joint moments from several
subjects. A better solution is probably to group individuals according to
different dynamic strategies before normalization and averaging. 

I feel sure that all David Winters data are correct since we have also tried
to implement joint moment formulas given by Pedotti (1977) and Mann (1980)
resulting in similar moments.  

I do not completely agree with prof. Hatze that 2. derivative data have
tremendous influence on the joint moments during human walking. I have
examined the contribution from each term of the formula for the moment
calculation and found that during the stance phase the ground reaction
forces represent the dominant contributor, not only for the foot but also
for the shank and the thigh. The ground reaction forces are simply much
larger than the linear forces calculated from acceleration of the segments.
Also the contribution coming from the moment of inertia and the angular
acceleration of the segment is very small. This is, however, NOT an argument
for the use of the more simple "floor reaction force vector" approach, which
to my experience only works for the ankle joint moment. For the knee and hip
it often gives erroneus results mainly because the point of force
application is incorrect. 

To my experience the most critical part of the procedure for obtaining joint
moments by inverse dynamics during walking is to get the center of pressure
(COP) correctly alligned to the foot. Small errors in this synchronization
between force plate and movement data may result in very different joint

Erik B. Simonsen


Mann R. & Sprague P. 1980. A kinetic analysis of the ground leg during
sprint running. Research Quarterly. 51, pp 334-348.

Pedotti A. 1977. A study of motor coordination and neuromuscular activities
in human locomotion. Biol. Cybern. 26, pp 53-62.

Simonsen E. B., Dyhre-Poulsen P., Voigt M., Aagaard P., Sjøgaard G. &
Bojsen-Møller F. 1995. Bone-on-Bone Forces during Loaded and Unloaded
Walking. Acta Anatomica. 152, pp 133-142.

Erik B. Simonsen, Msc. Ph.D.
Institute of Medical Anatomy section C.
Panum Institute. University of Copenhagen
Blegdamsvej 3., DK-2200 Copenhagen N
Phone:  +45 35 32 72 34 (work)   Fax: +45 35 32 72 17
Phone:  +45 42 89 45 86 (home)     

  Here at Queen's our lab is using and Optotrack, an AMTI force plate 
and custom written software to compute the forces and moments at the 
knee in 3D. When looking at the sagittal plane our results are similar 
to Winter's. We have found that skin marker placement, or more 
precisely, the correction of the skin marker placement is important. As 
well we find that the segment masses, their exact position, and the 
inertial properties are less important than the application of the 
external forces. For more details please see our paper: 

Li,J.; Wyss,U.P.; Costigan,P.A.; Deluzio,K.J.
An integrated procedure to assess knee-joint kinematics and kinetics 
during gait using an optoelectric system and standardized X-rays. 
J.Biomed.Eng.  15:392-400 (1993. 

Good luck with your work.
Pat Costigan

Let me preface my comments by saying that I am a biomedical engineer with
graduate training in neurophysiology.  I have only observed 3-D kinematic
analysis in the past but intend to perform experiments in the area soon.  

It appears to me that one major area for potential inherent "variations"
is in that knee and hip joint centers share a common sagittal plane.  This
approximation presumes that everyone is, given small biological
variability, neither "bow-legged" nor "knock-kneed" (i.e., that no one has
significant knee varus/valgus morphologies).  

Since we know this is not the case, perhaps here we find a major problem
in the 3-D analysis.  Mechanically speaking, knee varus or valgus
morphology will be translated into the floor ground reaction force as a
variation in 3-D force vector (and therefore ankle or knee moment vector)
during the stance phase and likely heel strike as well.  Given that a knee
varus/valgus deformity could be as large as a few centimeters out of the
sagittal plane containing the hip center, one could be looking at
significant errors in values for moments at the hip, knee, and ankle.  

Although, as I mentioned above, I am a novice at this form of analysis, I
wonder if the algorithms for moment calculation might be altered to
include some accounting for how coplanar (the amount or degree of non-
coplanar positioning?) the knee and hip actually are.  Such considerations
only make the math more difficult, but it appears to me that knee
varus/valgus morphologies vary between subjects as much, perhaps, as
intersegmental limb lengths or normal stride length.

The human body must interact with and locomote within a 3-D environment,
yet we tend to utilize 2-D assumptions to get at these 3-D questions.  It
may be naive for me to say, but maybe we need to bite the bullet and
collect a third degree of parameters to get more accurate 3-D movement data.

Good luck with your investigation!

J. H. Lawrence, Ph.D.
Center for Biomedical Engineering
University of Kentucky
Lexington, KY 40506-0070


In Chris Kirtley's letter (parts deleted):
> There's little doubt in my mind now that the knee and hip moments
> (especially around push-off) reported in this study are inaccurate, since
> most other labs (including ours now, after correction!) agree with 
> curves. I simply can't believe (despite Herbert Hatze's stirring remarks)
> that our systems have such a large inherent variability (if they do, I
> wonder what we are all doing in biomechanics!). The SD bars in the Kadaba
> curves are actually quite narrow, incidentally.

   Our gait analysis programs have been running for two decades now. 
Originally they were written for 2-D, but for the last 5 years have been 
able to do 3-D. They have been used by hundreds of students and faculty, 
and the algorithms have been written separately by about 100 grad students 
(as part of their training) so if there was anything wrong with the code 
(or concept), we would have seen it long ago. I wish you had contacted my 
lab directly, then this could have been issue could have been easily 
  Now, about the high variability, especially at the hip and knee.... This 
was reported in one of our original papers twelve years ago (Winter D.A., 
"Kinematic and kinetic patterns in human gait:Variability and Compensating 
Effects",Human Movement Science, 3:51-76, 1984). We illustrated that 
variability by 10 repeat trials across days and 10 repeat trials within the 
hour showed a major co-variance between hip and knee moment patterns, and 
that the sum of the two came out with much smaller variability. All this 
information appears in the text I published on gait which is in its second 
edition (" The Biomechanics and Motor Control of Human Gait: Normal, 
Elderly and Pathological "). We've used this covariance measure as one of 
the degenerative measures for the elderly population: "Winter et al., 
"Biomechanical walking pattern changes in the fit and healthy elderly", 
Physical Therapy, 70:340-347, 1990. The major cause of this variability 
starts with the hip moment during stance, which has the major 
responsibility of balance and posture of the trunk (head and arms). This 
varies on repeat trials (especially across days),but because the hip moment 
is part of the  total support against gravity, there is an almost equal and 
opposite trade-off with the knee moment. This is the covariance we 
originally calculated.

Dr. Dave Winter

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