View Full Version : The Wobbling Mass Model

Herman J. Woltring
02-21-1991, 09:33 AM
Dear Biomch-L readers,

While the title is not new (the Zurich group at Professor Stuessi's lab has
been concerned with the topic for some time), I think that it is worth-while
to mention one specific poster from the Nice meeting that was announced on
this list last week:

At the Department of Theoretical Astrophysics, Division for Biomechanics at
the University of Tuebingen in Germany, the Wobbling Mass Model accomodating
the non-rigid nature of body segments in human movement is a focal point of
interest. The introductory part of the poster goes as follows:

To calculate the mechanical loads to and in the human locomotor
system during movements, it is necessary to provide simplified
mechanical computer models. Analysis of load and overload is
interesting for clinical as well as for sports application. The
models normally used in biomechanics for this purpose consist of
several movable connected rigid bodies. Up to now such models have
served for the investigation of a variety of human movements such
as walking, stair climbing, slow running. If the external forces,
acting during the movement, show fairly smooth time histories, these
simulation models give satisfying results. However, they fail as
soon as there are higher accelerations or even impacts. In these
cases it is important to consider that most of the body mass is not
located in the skeleton but in the w o b b l i n g m a s s e s
of the body such as fat, connecting tissue, and muscles. At high
accelerations, the wobbling masses shift with respect to the skeleton
and provide time histories of the external reaction forces and of the
resulting forces acting in the joints as they can never be simulated
correctly with a model that only consists of rigid bodies connected with
joints to one another. By means of high speed filming the shift between
skeleton and wobbling mass can clearly be seen. We have developed the
Wobbling Mass Model in order to take into account the tremendous influen-
ces of the wobbling masses. At the present state of the investigation
it is a five link 2D-model (...)

The authors (F. Hospach, H. Ruder, J. Subke & K. Widmayer) provide some
graphical results suggesting that, a.o., the horizontal constraint force
component in the knee joint for a rigid-body model ranges between -850 N
and + 1 kN, and between -250 N and + 50 N in their wobbling mass model, for
what appears to be a vertical jump at landing. Thus, conventional rigid-body
models may substantially overestimate internal joint forces. With the
advantage of hindsight, this seems quite obvious; it is, therefore, rather
astonishing that this has (to my knowledge) never been reported or even
suggested before in the literature!

Since the authors model their skeletal joint as fixed pivots, it would be
interesting to see which assumption has the stronger influence: the rigid-
body model for the body segments, or the fixed hinge assumption for the body

The authors provided their email address on their poster; they can be reached
at PEHP001@tat.physik.uni-tuebingen.de.

Herman J. Woltring,