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

,
,
,
,
(3)
where is the 5-order vector of coefficients: , , , , .
This polynomial was defined as class
, because the second derivatives is linked to
each other for every subset i, as follows:
,1 ,0 2 ,
,1 ,0 ,1 ,0 (4)
Furthermore, we set:
1,
,0 ,1 (5)
,0
,1
respecting the link relation:
1, 1, ,1 ,0 0 (6)
Whereas (3) denoted 5n coefficients, equations (4) and (5) led us to 5N-1 linear
equations. As a consequence, a cubic spline 0 was used on the last interval . Then, considering that joint coordinates provided from the measurement, the
coefficients appeared as a function of a vector to optimize which collects the joint
accelerations:
, , … , 0, … , , … , (7)
The coefficients were deduced from the linear resolution of:
Φ (8)
Finally, over the interval [0,T], we wrote the following approximations:
,
,
,
which led to the rewriting criterion:
(9)
∑ , , , , ,
(10)
Accounting that polynomial coefficients involve measured joint coordinates, the
parametric optimization stayed unconstrained and timeless consuming consequently.
3.2. Experimentation and inverse dynamics
Our approach was tested using a flexion-entension movement performed at self-selected
velocity on a force plate (Kistler, Switzerland) setting at 1000Hz. Kinematic data were
recorded at 50Hz using a motion analysis system (Biogesta, France). The joint
coordinates were provided from sixteen markers (top of head, spinous process of
the 7 th cervical vertebrae, acromio-clavicular joint, lateral elbow epicondyle, radius
styloid, great trochanter, lateral knee epicondyle, lateral maleous, second metatarsal
head). Their positions were low-pass filtered at 6Hz with a zero-lag Butterworth fourorder
filter. A finite centred differentiation was used to determine the first ( ) and