View Full Version : SUMMARTNormal gait: Are joint angle standard deviations larger atma ximal joint angular velocities?

Forner Cordero, A. (ctw)
04-15-2003, 09:47 PM
First, I apologise for the late summary, but I have problems with my email
Second, there was no agreement in the answers to my question.
It appears that the differences are due to different measurement methods.
Per Slycke from X-sens, Anton van den Bogert and At Hof agreed with my
observations, moreover Dr
van den Bogert proposed a very nice explanation.
Chris Kirtley, on the contrary, provided some data that apparently did not
to suppport my observations.
However, there were important methodological differences with my
The response from Dr Yang, made it very clear how methodological differences

could affect the results.

My conclusion is that I stand on the "Dutch" side this time: My data
supports it and
the explanation is clear. Moreover, I think that the conversion of the
stride time
to percentage and the subsequent averaging introduces this kind of errors.



-----------ORIGINAL QUESTION-------------------
> I measured normal walking on a treadmill, calculated the joint angles
and angular velocities (sagittal plane), converted to stride percentage
and then computed the mean and the standard deviation at every point. I
find that at the hip, knee and ankle joints the maximal standard devations
occurred when the joint angular velocity is maximal.
> I searched the bibliography and Internet resources looking for results
that confirm this observation. I did not find any reference to this
"strange thing". So I ask you if this is a finding or a particular
> My question is: Are standard deviations larger at maximal joint
angular velocities?
> If this is a true repeatable observation of many of you I would like
to discuss about possible causes and different approaches to perform a
"time normalisation" or,... to avoid it definitively.
Your findings correspond to my practical experience when I developed our
speedometer for runners/walkers. It was measured with gyros and
accelerometers on the foot, so its not the joint angles but "absolute"
angles with respect to the surface. However, these findings are not
published etc., so it probably won't help you, but at least you know others
have seen similar things...Good luck.

Best regards,

Per Slycke
The phenomenon you describe has probably been observed by
most people who have performed ensemble averaging of cyclic
gait data. I don't think that the variability of movement is
really larger at those times. It is just a consequence of how you
measure the variability (with a standard deviation, after time
normalization). When the velocity is high, small errors in timing
can easily produce large errors in angle.

I think some people use non-linear time normalization (time warping)
to better align the individual gait cycles before averaging, but I
can't give any references. Hopefully someone else gives you that

Ton van den Bogert
A.J. (Ton) van den Bogert, PhD
Department of Biomedical Engineering
Cleveland Clinic Foundation 9500 Euclid Avenue (ND-20)
Cleveland, OH 44195, USA Phone/Fax: (216) 444-5566/9198

I think there is something wrong here. Actually, the SDs are usually larger
around the peaks of
the angle curves (i.e. when angular velocity is near zero). See some
examples at:


Dr. Chris Kirtley MD PhD
Associate Professor Dept. of Biomedical Engineering
Catholic University of America 620 Michigan Ave NE, Washington, DC 20064
Tel. 202-319-6247, fax 202-319-4287 Email: kirtley@cua.edu

what was the treadmill speed ? Was it a level walking? for normal walking
(around 80m/min to 90m/min) the level path walking is about the same as the
level treadmill walking, but fast than that you might have larger angular

the possibilities are 1) the steps of data measured- the subjects usually
have to catch the speed of treadmill, the steps are not consistent. I took
eight steps data after the subject had about 10 minutes warm up.
For slow walking speed the variation might be larger in your study. You can

check the step length and cadence by placing foot switch to check up.

Dr Yang, SW [SMTP:swyang@bme.ym.edu.tw]

I would suggest that this effect is an artifact of your data analysis.
When angular velocity is high, angles change fast. Minor timing
differences between subjects manifest themselves then in bigger
standard deviations at times when angular velocity is high.
I think this effect can be mathematically proven, but 'leave this as
an exercise to the reader'.
************************************************** *****
At Hof
Institute of Human Movement Sciences &
Laboratory of Human Movement Analysis AZG
University of Groningen
A. Deusinglaan 1, room 321
postal address:
PO Box 196
Tel: (31) 50 363 2645
Fax: (31) 50 363 3150
e-mail: a.l.hof@med.rug.nl
************************************************** *******

PhD Student.
Mechanical Engineering
University of Twente. The Netherlands

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