ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

configuration.[4] have explained how the forces that constrain the movement of the
knee joint, and infinitesimal displacement, are interlinked in terms of reciprocal
conditions. They have located the instantaneous axes of the knee (IAK) which is
reciprocal to five constraints−the anterior cruciate ligaments (ACL), the posterior
cruciate ligament (PCL), the medial collateral ligament (MCL), and articular contact in
both the medial (P1) and lateral (P2) compartments. The reaction of the five constraints
which limit the motion of the knee will neutralise every wrench on a screw reciprocal to
the IAK as workless constraints that do not work.
In this paper, we apply the principle of virtual work for static equilibrium [5] to
add a new dimension to current research regarding the connection between the foot and
IAK. The virtual work involves equilibrating the externally applied forces of the knee
joint with the workless constraints.
3. METHODOLOGY
The foundation of the framework is a reciprocal configuration model connecting knee
kinematics to the ground reaction vector in the sense of “reciprocal connection”,
utilising the fact that the virtual work in equilibrium with workless constraints is equal
to zero. [4] indicated that the ligaments and cartilage contacts of the knee joint
contribute to its mechanical constraints (Figure 1).
$´3
$´4
$´2
$´1
$´5
Figure 1: Five constraints $ s are
collectively reciprocal to the instantaneous
screw$ . The instantaneous motion of the
knee is guided by the constraints of the
anterior cruciate ligaments (ACL), posterior
cruiciate ligament (PCL), medial collateral
ligament (MCL), and articular contact in the
medial (P1) and lateral (P2) compartments.
Note that no combination of the constraint
$ forces that might be generated at the $ will
result in a turning at the $ and no angular
velocity at the $ will cause the constraint
force to do any work at the points on medial
and lateral contacts. (The figure was
originally published by Kim and Kohles
(2011)).
We thus have to prove (Figure 2) that if a knee has a freedom of the first order, then
there is always one −and only one −screw, , for the GRF that determines the freedom
of the knee, such that an impulsive wrench on it makes a given screw, , the
instantaneous screw for the IAK. The reaction of the constraints which limit the motion
of the knee will neutralise every wrench on a screw reciprocal to the given IAK . We
may, therefore, discard all the wrenches except those on the muscle and GRF .
Draw the cylindroid ( , ), and determine there on the screw which is reciprocal to
. The body will not be in equilibrium unless the wrenches about and constitute a
resultant wrench on and hence the ratio of the wrench intensities about and is