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

elative motion of the corresponding bodies. For example, in the spherical joint at the
pelvis, accuracy in determining the position of the hip joint center (HJC) affects both
kinematics and dynamics (Stagni et al. 2000). There are two main methods for the
estimation of the HJC: the functional method that is based on the relative motion between
the pelvis and the femur for its estimation, such as in (Halvorsen 2003); and the prediction
method, that is based on the size of the pelvis and the femur from the anatomical
landmarks, (Bell et al. 1990; Davis et al. 1991). The last method corresponds to higher error
levels (Leardini et al. 1999). As a result, the functional method has received more attention
recently (Shea et al. 1997; Amis and Jakob 1998; Halvorsen 2003; Siston and Delp 2006).
In this study, we introduce a method for the reduction of the STA magnitude. This method
is based on obtaining the orientation of a rigid body from landmark trajectories. (Sommer
1992) introduced a method for the determination of the first and second order instant screw
parameters from landmark trajectories, i.e. angular velocities and accelerations from
position, velocity and acceleration of individual landmarks of the body. Here, a local
reference frame was attached to each body and from these parameters its orientation was
determined by integration after an adequate transformation, from which position, velocity
and acceleration could be recalculated for each landmark. This also guarantees that the
integrated trajectory of each body matches the calculated velocity and acceleration.
With respect to the HJC, it was estimated using the functional method presented by
(Halvorsen 2003) with the protocol proposed by (Camomilla et al. 2006). This method was
verified using a simulated model of the pelvis and the femur created in MSC-ADAMS
dynamic simulation software.
3. METHODOLOGY:
From the position, velocity and acceleration of skin landmarks of the body, its angular
velocity and acceleration for a rigid body is estimated using the linear procedure introduced
by (Sommer 1992).
A local reference frame is attached to the body at the centroid. Initially it has the same
orientation as the global one. The orientation of this frame is represented by three
successive rotations by angles (γ,β,α) around fixed global axis XYZ, respectively. The
resulting rotation matrix is,
R
cici cisi sisici sisi cisici
cs c c s ss s c c ss
si
s i ci cic
i
G i
L i i i i i i i i i i i i
G i
where for a given time instant of the trajectory (i): R L is the rotation matrix between the
global (G) and local (L) reference frames, and cαi and sαi are shorthand for cos(αi) and
sin(αi), respectively, etc.
(1)