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Dear Biomch-L subscribers,
Last Thursday, Thomas Greiner mentioned some problems he had when
trying to estimate an instantaneous center of rotation from 3-D
kinematic data. I do not have the intention (or the time) to
present a complete overview of this topic here, but I could
provide some pointers.
There are two basic problems in your approach. First of all,
estimating an instantaneous center of rotation (ICR) is sensitive
to errors in the kinematic data. In fact, if you try to get a
true ICR (as opposed to a finite center of rotation - FCR) you
will have to use an infinitesimally small change in joint angle
and therefore the error will go to infinity. The only way to
overcome these problems is smoothing of coordinate data, or do an
FCR using a large enough angular movement.
Secondly, you are trying to apply a 2-D method to a 3-D movement.
In 3-D, there is no such thing as a center of rotation. The
corresponding 3-D analysis should give an instantaneous or finite
helical axis (IHA or FHA). Your 2-D projection method will only
produce good results under certain conditions, for example when
your 2-D plane is perpendicular to the IHA or FHA. The 3-D
analysis is quite straighforward, once you are familiar with 3-D
rigid body kinematics.
Some literature pointers:
An FHA analysis of the knee joint was done by Blankevoort et al.,
Journal of Biomechanics 23:1219-1229 (1990).
A theoretical background can be found in the proceedings of the
1986 ESB congress: Woltring et al., in: Biomechanics, Basic and
Applied Research (Bergmann et al., ed.) pp. 121-128 (1987).
This is far from complete, but I hope it helps.
-- Ton van den Bogert
Human Performance Laboratory
University of Calgary
Last Thursday, Thomas Greiner mentioned some problems he had when
trying to estimate an instantaneous center of rotation from 3-D
kinematic data. I do not have the intention (or the time) to
present a complete overview of this topic here, but I could
provide some pointers.
There are two basic problems in your approach. First of all,
estimating an instantaneous center of rotation (ICR) is sensitive
to errors in the kinematic data. In fact, if you try to get a
true ICR (as opposed to a finite center of rotation - FCR) you
will have to use an infinitesimally small change in joint angle
and therefore the error will go to infinity. The only way to
overcome these problems is smoothing of coordinate data, or do an
FCR using a large enough angular movement.
Secondly, you are trying to apply a 2-D method to a 3-D movement.
In 3-D, there is no such thing as a center of rotation. The
corresponding 3-D analysis should give an instantaneous or finite
helical axis (IHA or FHA). Your 2-D projection method will only
produce good results under certain conditions, for example when
your 2-D plane is perpendicular to the IHA or FHA. The 3-D
analysis is quite straighforward, once you are familiar with 3-D
rigid body kinematics.
Some literature pointers:
An FHA analysis of the knee joint was done by Blankevoort et al.,
Journal of Biomechanics 23:1219-1229 (1990).
A theoretical background can be found in the proceedings of the
1986 ESB congress: Woltring et al., in: Biomechanics, Basic and
Applied Research (Bergmann et al., ed.) pp. 121-128 (1987).
This is far from complete, but I hope it helps.
-- Ton van den Bogert
Human Performance Laboratory
University of Calgary