CGA FAQ: Joint centre estimation

from BIOMCH-L 15/2/96

Can someone explain or lead me to sources that explain how to locate and
internal joint centers.  The joints I am interested in are the shoulder,
elbow, and wrist
joints.  More specifically:

    1)  I need anthropometric and palpation techniques/rules  used to
estimate the surface
          location of internal joint centers. Joint markers will be placed
at these locations.
          For example, Dempster suggests that the center of rotation of the
humerus is
          located 2 inches inferior to the right acromion on the lateral
surface of the upper

    2)  I also need a mathematical and/or statistical method of calculating
the location of the
          internal joint centers from the location of the surface markers.
I realize that this
          question is more difficult than the first.

I am sure someone out there has tackled these problems before.  I would be
grateful for any

                                  Clifford Larkins
                                  Center for Egronomics
                                  The University of Michigan
                                  Ann Arbor, MI


Subject: Re: Help: Locating and Calculating Internal Joint Centers
X-Sun-Charset: US-ASCII

Dear Clifford Larkins,

I have also the same problems as you. I've done some experimental studies
to locate the average center of rotation of joints, especially
glenohumeral, elbow joints from external surface landmarks. I'm now writing
a paper about this suject. I have intention to submit it to the 4th
symposium of 3d analysis of human movements. By the end of next month, I'll
have finished it. If you give me your mail adresse, I can send you the

Xuguang WANG

Xuguang WANG, PhD
Laboratoire Ergonomie Sante Comfort (LESCO) Institut National de Recherche
sur les
Transports et leur Securite (INRETS)
109, avenue Salvador Allende
69675 BRON
fax: +33 72362437
tel: +33 72362451

 To: clarkins 
From: Gabriel Baud-Bovy  Subject: Re: Help:
Locating and Calculating Internal Joint Centers

There is a third way of locating third joint centers that works with
surface markers which may be arbitrarily located. In my research, I use
three markers for each body segment (body, arm and forarm) and I ask the
subject to do "calibration" movements while keeping the join centers
immobile. For example, to compute the position of the shoulder, the subject
will make circle with the fully extended arm. Each set of three markers
allows to associate a technical system of coordonate (TCS) with each
segment. The calibration allow me to compute the position of the joint
center relatively to the technical system of coordinate of the distal
segment associated the markers. Once I have this information, I can use it
to compute the position of the joint center frame by frame in whatsoever
other movement.

The advantage of this technique is that it allows you to put markers where
they are more visible (I am using a ELITE system). The disadvantages are
that the precision depends upon the quality of the "calibration" and of
course, if the markers are displaced by accident, you have to repeat the

I found your question very interesting. Did you find any paper describing
the "magic formulae" used to compute the position of the joint centers ot
the upper limb from anatomically located surface markers? I did not. I
would very much appreciate if you can communicate to me the list of replies
and the results of your research concerning this question.

Gabriel Baud-Bovy
Université de Genève, FAPSE
9, route de Drize
1227 Carouge - Switzerland

********************************************************** From: (Vaughan Kippers) Subject: Joint Centres

To Clifford Larkins,
In the past I have used information from:

Dempster WT & GRL Gaughran (1967) Properties of body segments based on size
and weight. American Journal of Anatomy 120(1):33-54.

Buseck M, OD Schipplein GBJ Andersson & TP Andriacchi(1988) Influence of
dynamic factors and external loads on the moment at the lumbar spine in
lifting. Spine 13(8):918-921.

Surface markers are:
Ankle - 10 mm proximal to the tip of the lateral malleolus Knee - lateral
femoral epicondyle
hip - superior aspect of the greater trochanter

Of course parallax error is a problem if the camera is not positioned
correctly, related to movement of the subject.

Good luck with your project.


Vaughan Kippers PhD
Functional Musculoskeletal Anatomy Group Department of Anatomical Sciences
The University of Queensland 4072
Voice-Mail +61 (0)7 33652704
FAX     +61 (0)7 33651299
WWW University Location WWW Department Location -

To: clarkins 
From: (Jonathan Dingwell)
Subject: Re: Help: Locating and Calculating Internal Joint Centers

Mr. Larkins -

Finding the instantaneous joint center for the shoulder joint is indeed
quite a task, and potentially not one that's as straight forward as your
question appears to be. It may depend quite a bit on the type of dat you're
collecting. You may want to check out some good papers on shoulder joint
biomechanics by A.E. Engin in the ASME Journal of Biomechanical Engineering
(circa 1980-1985). I can get you specific references if you need, but these
give a good description of the biomechanics and some good sdetails about
measurement techniques as well.

Good luck,

| Jonathan Dingwell, M.S.       |
| Center for Locomotion Studies |
| Penn State University |
| University Park, PA 16802     |
| Ph #: 1-814-865-1972  |
| Email:     |

To: clarkins 
From: Laboratorio Biomeccanica  Subject: Re: Help:
Locating and Calculating Internal Joint Centers

We work on the knee joint, but the following two papers can be useful to
answer you second question, which is a general one and apply to many joints
(essentially of "spherical" type):

Holzreiter ST (1991): "Calculation of the instantaneous center of rotation
for a rigid body", J. Biomechanics v.24,n.7,pp.643-647

Spoor CW, Veldpaus FE (1980): "Rigid Body motion calculated from spatial
coordinates of markers", J. Biomechanics, v.13,pp.391-393

The classical mathematical method to compute the center of rotation is
geometrical (follow at leat two points on Xrays and find the intersection
of the axes of the obtaine segments) or "statistical" (use least square fit
algorithm to find the fixed point of a succession of transformations or a
3D trajectory).
These methods are numerically unstable and result in inaccurate tracking of
the instantaneous center of rotation in the knee or in joints in which this
center is expected to move and the natural flexion is almost planar. It
might be a reliable measurement on the wrist, but be careful with it!

Good luck, Sandra and Luigi.

Lab. Biomeccanica
via di Barbiano 1/10    fax: (+39).51.583 789
I-40136 Bologna



To: clarkins 
Subject: Re: Help: Locating and Calculating Internal Joint Centers
Mime-Version: 1.0

I don't have the answers to your questions, but I'm interested in what your
application is. I'm about to start a motion analysis of four activities of
daily-living: standing up from a chair, lifting a box, carrying a suitcase
and walking with a cane. I will be putting markers on the arm. I need the
kinematics of the arm plus the forces in order to determine the
bone-on-bone forces at the shoulder (using a separate program). I need that
information for setting load levels in mechanical testing of shoulder

I am not too concerned about getting the exact internal joint centres since
I am only looking for the approximate kinematics. The people here who do
gait analysis take X-rays with lead beads in the place of the markers. This
means that they can get exact vectors to the internal joint centre, but
this is only justified if the X-rays are already being taken for another

I'm interested to hear from you,

Carolyn Anglin
Dept. of Mechanical Engineering
Queen's University
Kingston, Ontario, Canada

Date:          Tue, 30 Jan 1996 10:37:11 -0500
Subject:       Internal from External Landmarks
Priority: normal

Hi Cliff,

I'm one of Don Chaffin's Ph.D. students, although you don't see me around C4E
much because I work and do my research at UMTRI.  I'm currently working on a
set of equations to calculate joint center locations from external landmarks.
I'm drawing primarily on three sources:

Dempster (1955).  Space requirements of the seated operator.

McConville et al. (1980).  Anthropometric relationships of body and body
segment moments of inertia.

Reynolds et al. (1981).  Spatial geometry of the human pelvis.
and a record of a selection of joint center locations for crash dummy design

Schneider et al. (1983).  Anthropometry of motor vehicle occupants, Vol.1
Robbins et al. (1983). Anthropometry of motor vehicle occupants, Vols.2&3

Let me know if you need complete references.  It seems that someone must have
published a summary paper on this problem, since it's ubiquitous in
biomechanics research.  Please let me know if you find other useful

Matt Reed
Senior Research Associate
University of Michigan
Transportation Research Institute

From: "Johan Molenbroek " 
Subject: Re: Help: Locating and Calculating Internal Joint Centers
To: clarkins 

Dear Clifford,
Did you try Biomechanics of Human Motion from Williams and Lisner
Saunders Philadelphia 1962.
The data on page 133 are based on Dempster(1955) and the paper of
Trotter and Gleser in Am J of Phys Anthropology nr 10 p 463-514,1952
Also I remember a book of Stanley Plagenhoef which we use in our lab for
such purposes.
with kind regards
Johan F.M.Molenbroek,PhD
Associate Professor Engineering Anthropometry
Deputy Subdepartment Physical Ergonomics
Faculty Industrial Design Engineering
Delft University of Technology
Jaffalaan 9
2628 BX Delft, The Netherlands
voice + mailbox:+31-152783086
voice secr      +31-152783029

Date: Wed, 31 Jan 1996 18:07:48 +0100
Subject: Re:  Help: Locating and Calculating Internal Joint Centers

        I wrote a paper, that should be published soon on the J. of B.
Basically, I used 3D data reported by Chandler et al. to compute
joint center LONGITUDINAL POSITIONS, relative to neighboring
anthropometric landmarks.

        Title: "Joint center longitudinal positions computed from
a subset of Chandler's data".

        The transverse and sagittal positions are not given.
For the Hip joint center, several articles have been published on
the J. of Biomechanics (latest on August 1995, if I remember well)
about 3D position relative to pelvis landmarks.

        Let me know if you need more info.

     __________ _________ ___________~___ ________ _________________~___
   /           ~         ~               ~        ~                      \
 /______________~______~__________ _______~_____~______________~_____~_____\
| Paolo de Leva                   ~      \      Tel.+ FAX: (39-6) 575.40.81 |
| Istituto Superiore di Educazione Fisica >     other FAX: (39-6) 361.30.65 |
| Biomechanics Lab                      /                                   |
| Via di Villa Pepoli, 4              <   INTERNET e-mail address:          |
| 00153 ROME - ITALY                    \   deLEVA@RISCcics.Ing.UniRoma1.IT |
|_____________________~________~____________________________________   _____|
                                      challenging entropy           :-)

Date: Thu, 1 Feb 1996 20:04:15 +0100
Subject: Re:  Help: Locating and Calculating Internal Joint Centers

        You are welcome.

        I suggest you not to use Chandler's data directly. Some of his
numbers are clearly wrong. I discovered the errors by checking Chandler's
3D data against his 2D data (measured on the same subjects with
different instruments). THen I devised a method to purge Chandler's data
from inconsistencies.

        Chandler's data are not extremely accurate, but they are the
only COMPLETE set of joint center positions ever published, as
far as I know. If you need my final data I can give them to you by

        I guess you know that the concept of joint center is questionable
for at least two reasons: it does not work in 3D, unless you have a
perfect ball-and-socket joint, and it does not even work in 2D,
unless you have a perfect hinge or ball-and socket joint, which is
not true at all for the human joints. Instantaneous joint helical
axes are known to change their position relative to both the sergments
that form the joint, throughout the joint range of moption.

Good luck,

     __________ _________ ___________~___ ________ _________________~___
   /           ~         ~               ~        ~                      \
 /______________~______~__________ _______~_____~______________~_____~_____\
| Paolo de Leva                   ~      \      Tel.+ FAX: (39-6) 575.40.81 |
| Istituto Superiore di Educazione Fisica >     other FAX: (39-6) 361.30.65 |
| Biomechanics Lab                      /                                   |
| Via di Villa Pepoli, 4              <   INTERNET e-mail address:          |
| 00153 ROME - ITALY                    \   deLEVA@RISCcics.Ing.UniRoma1.IT |
|_____________________~________~____________________________________   _____|
                                      challenging entropy           :-)

From: ""  (by way of (Clifford Larkins))
Subject: Re: Help: Locating and Calculating Internal Joint Centers

  Dear Clifford,
  Using a pointer, the position of bony landmarks can be determined with
  respect to surface markers. In our laboratory we use a 3-D digitizer called
  'the palpator', but any 3-D tracking device can be used for this purpose.

  We determine the positions of the following landmarks :
  Thorax : Insisura Jugularis, Processus Xyphoideus, sterno-clavicular joint,
           Dorsal spine of the 7th cervical vertebra and the 8th thoracic
  Scapula: acromio-clavicular joint, angulus acromialis, trigonum spinae
           and the angulus inferior.
  Humerus: medial and lateral epicondyles.

  As the glenohumeral joint can be modelled as a spheric joint (with a fixed
  poin of rotation with respect to both the scapula and the humerus) the
  position of this third humerus landmark can be derived from a regression
  equation using the scapular landmarks and calculating the centre of
  rotation from the shapes of the articulating surfaces. My colleage Leonard
  Rozendaal applied this method for 14 cadaver specimen with accurate results.

  The axial direction of the clavicle is determined by the sternal and
  scapular joint (NB: palpated points, not the accurate rotation centers).

  The bony landmarks are used to calculate the local coordinate systems
  of the four bony elements of the shoulder and relative rotations can be
  calculated from the position matrices.

  The position of the scapula cannot be measured by using skin fixed markers
  as the position of the scapula is not related to the skin. Palpation of
  the positions of the bony landmarks at different postures seems inevitable.

  Pronk GM, Van der Helm FCT (1991), The palpator, an instrument for
    measuring the 3-D positions of bony landmarks in a fast and easy way.
    J.Med.Eng.Techn. 15(1):15-20.

  Van der Helm FCT et al. (1992), Geometry parameters for musculo-skeletal
    modelling of the shoulder system. J.Biomechanics 25(2) 129-143.

 Jurriaan de Groot,
  Lab. of Measurement and Control  |Tel : -31-(0)15-2782156
  Fac. Mechanical Engineering      |Fax : -31-(0)15-2784747
  Delft University of Technology   |E-mail : GROOT@TUDW03.TUDELFT.NL
  Mekelweg 2                       |  |____/(O======================
  2628 CD Delft                    |  |:::::/
  The Netherlands                  |  |:::/    DUTCH SHOULDER GROUP
                                   |  |:/


We are using an ELITE motion analysis system to collect whole-body, 3D
kinematic data, although we are performing 2D, sagittal plane analysis of
pulls made while standing.  Because we study whole-body movements, we deal
with many joints including the ankle, knee, hip, lumbar spine, shoulder,
elbow, wrist, and neck.  Currently, we palpate bony landmarks in order to
estimate the location of each joint's center of rotation and then place
reflective markers directly over these estimated joint centers.   We are
concerned about the accuracy of this method, however, and are looking for a
more precise approach.

Recently, several questions have been posted to BIOMCH-L regarding the best
way of estimating specific joint center locations from anatomical landmarks.
It is clear from the responses to these postings, as well as from our search
of the literature, that there are several ways to approach the problem of 2D
joint center identification.  These include:

(1) Putting markers directly on the estimated joint center locations;
(2)  Putting markers on various anatomical landmarks and then using them to
infer a  joint center location;
(3) Using an array (rigid or not) of at least 2 markers on each segment and
rigid body analysis to compute  joint center locations from "calibration
movements", performed before the start of the experiment, that involve
substantial changes in joint angles;
(4) Using an array on each segment and rigid body analysis on the movements
in the experiment to determine the instantaneous center of rotation.

It seems that many labs use a combination of these methods due to the
limitations of the various techniques (solutions breaking down when changes
in joint angle are small, peculiarities of a particular joint, etc.).

While we realize that it is difficult to generalize across joints, we are
wondering if anyone has compared the errors in 2D joint center estimation
for these different techniques.  We are aware of an article by Spiegelman
and Woo (1987) which compares a geometric (Reuleaux) approach with a rigid
body analysis approach and another by Crisco et al. (1994) who did a more
extensive error analysis of a similar rigid body method.

Crisco, J., Chen, X., Panjabi, M., Wolfe, S.  (1994).  Optimal marker
placement for calculating the instantaneous center of rotation.  Journal of
Biomechanics  27(9): 1183-1187.
Spiegelman, J., Woo, S.  (1987).  A rigid-body method for finding centers of
rotation and angular displacements of planar joint motion.   Journal of
Biomechanics  20(7): 715-721.

Please send any responses to and we will post a
summary of responses.  Thanks in advance.

Wynne Lee, Ph.D.
Jim Patton, M.S.
Julie Steege, M.S.

Motor Control and Learning group
Programs in Physical Therapy
Northwestern University
Chicago, Illinois, USA

************************ RESPONSES **********************

FROM: Rebecca A. States, Ph.D.                  276H Read Building
Dept. of Health & Kinesiology                   (409) 862-3229
Texas A & M University, M.S. 4243               (409) 847-8987 (fax)
College Station, Texas 77843          

I would like to respond to your post about the accuracy of various
methods for estimating joint centers for 2D movements, in particular
about your question ...

> While we realize that it is difficult to generalize across joints, we are
> wondering if anyone has compared the errors in 2D joint center estimation
> for these different techniques.  

Last fall, I presented a poster on this topic at the Society for 
Neurosciences meeting, "Comparison of three methods for locating joint 
centers during planar arm motion" (#174.15).  The work was designed to 
introduce a simple measure of the reliability of joint center estimates,
and to compare three methods for estimating the axes of rotation during
2D movements. A summary, written for a broad audience, follows.  I will 
also send you a copy of the poster by overground mail.

        Becky States

        Reliability of Three Methods for Measuring Joint Angles

                College of Education Seed Grant
                        3/1/95 - 12/31/95

                        Rebecca A. States
                Department of Health & Kinesiology
                        College of Education
                        Texas A & M University

        In many studies that measure joint motion, video or 
other optical systems are used to track the positions of 
markers attached to the body as they move about in 3-D 
space.  Several problems limit the reliability of this 
approach.  Markers are generally placed on or near bony 
landmarks so one can judge their location relative to the 
positions of the underlying bones, and relative to the 
center of joint rotation.  Locating the center of joint 
rotation is crucial for measuring joint angles and forces 
that act on the joint.  Judging the center of rotation from 
bony landmarks is not easily accomplished however, since the 
shapes and sizes of individuals' bones differ.  An 
additional problem arises in that skin and soft tissue 
motion may cause the markers to move in relation to the 
bones, further distorting estimates of the center of joint 
        This study seeks to improve reliability of systems that 
use surface markers to measure joint angles in humans by 
introducing a new method for evaluating the reliability with 
which joint centers are located.   Segment length 
variability is suggested for this purpose since under ideal 
measurement conditions, an individual's segment lengths 
should remain precisely constant within and between 
measurement sessions.  A clear advantage of this technique 
is that segment length variability can be easily assessed 
from data collected during the experimental procedures.  
Hence, it can provide an indicator of measurement problems, 
such as particular types of soft tissue motion, that only 
occur during the experimental procedures.  Moreover, this 
technique is ideally suited to the many studies where 
multiple joints are measured.  For example, in studies that 
record motion of the arm, one might place markers at the 
shoulder, elbow, wrist and tip of the index finger.  
Comparing the variability in segment lengths for the hand, 
forearm and upper arm can help pinpoint measurement errors 
linked to one of the joints.  If the marker over the elbow 
were out of place, then the variabilities for the forearm 
and upper arm segments would be especially large. 
        This study also compared two methods for making post-
hoc adjustments to data from surface markers to see if 
either one improved reliability beyond that seen in the raw 
data.  Both of these methods are limited to situations where 
motion stays predominantly within a single plane.  In those 
circumstances, the joint is said to have one and only one 
axis of rotation (AoR).  Hence, the rest of this write-up is 
concerned only with planar arm movements.  
        Data from planar arm movements that go through a large 
range of motion can be used to mathematically estimate the 
location of the true AoR relative to the positions of 
surface markers.  If the calculated AoR differs from the 
position of the marker which is supposed to track that 
joint, an adjustment factor can be determined and applied to 
subsequent data.  The adjusted data can then give a better 
estimate of the AoR.  Reliability studies on such post-hoc 
methods have generally been performed using an ideal 
mechanism like a mechanical hinge joint (Walter & Panjabi, 
1988; Fioretti et al., 1990; Bell et al., 1990; Hart et al., 
1991) so they can verify the effectiveness of the adjustment 
method.  This study takes a different approach by testing 
two post-hoc methods in a real-world setting where soft 
tissue motion and small amounts of out-of-plane motion may 
occur.  This more ecologically valid approach is only 
possible given the novel technique introduced above for 
measuring reliability.
        Four subjects performed a series of single and multi-
joint movements.  This series was repeated five times during 
each of five sessions.  Joint motion was measured during 
these movements by collecting 3-D position data from 18 
active markers using an Optotrak 3020 infrared measurement 
system running at 100 Hz.  Markers were placed at the 
apparent axes of joint rotation for the right wrist, elbow, 
and shoulder, as well as for the left shoulder.  In 
addition, markers were placed on splints which were attached 
to the hand, forearm, upper arm, and on a harness attached 
to the torso.  The splints were designed to track the motion 
of the limb segments rather than to restrict joint motion.  
Data from the single-joint elbow movement trials were used 
to find post-hoc adjustment factors for the elbow using two 
methods - Speigelman & Woo's (1987) 2D method, and a novel 
3D method described in States (1995).  The adjustment 
factors were applied post-hoc to data from the multi-joint 
movement trials, a procedure which increases the rigor of 
the reliability test.  Results showed that both post-hoc 
methods improved within-session reliability, reducing 
segment length standard deviations by about 50% compared to 
the raw data.  This verifies the usefulness of post-hoc 
adjustment procedures even under conditions  where there may 
have been significant soft tissue or out-of-plane motion.  
These results also demonstrate that the reliability of 2-D 
data can be equivalent to 3-D data, at least for the 
movements tested.  Neither post-hoc method was found to 
improve between-session reliability, supporting the common 
practice of making critical comparisons within a single 
testing session.
        This study also examined a related problem, that 
markers sometimes can not be placed near the apparent AoRs 
since doing so would occlude them from the view of the 
camera or other sensing device.  In those circumstances, 
markers are placed at a distance from the joint, and some 
type of post-hoc adjustment procedure is used to calculate 
AoR.  The abilities of the two post-hoc procedures 
investigated here to cope with this problem were examined.  
Each post-hoc procedure was used to locate the AoR for the 
shoulder joint from markers placed on a shoulder harness. 
Variability in upper arm and torso segment lengths were 
compared to those obtained for data from an observational 
condition where markers were placed directly over the joints 
for those same trials.  Both post-hoc methods were found to 
be as reliable as the unadjusted raw data from the 
observational condition, though they were not as reliable as 
data from the observational condition after it had been 
adjusted.  These results show the post-hoc methods can be 
used to successfully accommodate for situations where 
markers must be placed at a distance from the joint, even 
when there is soft-tissue or limited out-of-plane motion. 
        The methods described here will be applied in future 
studies investigating joint coordination during skilled 
movement tasks which are planned by the PI.  This study was 
presented as a poster (#174.15) at the 25th Annual Meeting 
of the Society for Neuroscience in San Diego, CA, November, 


Bell, A.L., Pedersen, D.R. & Brand, R.A. (1990).  A 
comparison of the accuracy of several hip center 
location prediction methods.  J. Biomechanics, 23, 617-
Fioretti, S., Jetto, L. & Leo, T. (1990).  Reliable in vivo 
estimation of the instantaneous helical axis in human 
segmental movements. IEEE Trans. on Biomedical 
Engineering, 37, 398-409.
Hart, R.A., Mote, C.D.Jr. & Skinner, H.B. (1991).  A finite 
helical axis as a landmark for kinematic reference of 
the knee.  J. Biomedical Engineering, 113, 215-222.
Spiegelman, J.J. & Woo, S.L.-Y. (1987).  A rigid-body method 
for finding centers of rotation and angular 
displacements of planar joint motion.  J. Biomechanics, 
20, 715-721.
Walter, S.D. & Panjabi, M.M. (1988).  Experimental errors in 
the observation of body joint kinematics.  
Technometrics, 30, 71-78.

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