Biomedical Engineering Reference
In-Depth Information
assume for example in the case of the upper limbs, that the
thorax, arm, forearm and hand are rigid bodies articulated
by the shoulder, elbow and wrist respectively, if an overall
analysis of the gesture is desired, or analyze in more detail
the different bone segments and joints of the shoulder or
hand, in other cases.
By definition, a body segment will therefore be considered
as a set of material points rigidly linked to one another, that
is to say that the distances between these points are
constant irrespective of the movement of the segment.
A rigid body (also called a solid) can move freely in space
with six degrees of freedom; in other words, its movement
can be entirely described by six independent parameters
corresponding to elementary movements: three translation
parameters of a particular point of the solid, and three
rotation parameters of the solid about this point. When we
are interested in an articulated system of rigid bodies, also
called a kinematic chain, the joints represent links between
solids that block or restrict some of their degrees of freedom.
To form equations of this problem, we associate an
orthonormal coordinate system to each rigid body. An
orthonormal coordinate system is a mathematical tool
composed of an origin (a specific point) and three unit vectors
(with a norm or length equal to one) in orthogonal pairs.
Later, we will describe how to form such a coordinate system
using a minimum of three markers per segment. To
characterize the attitude of a rigid body, it involves defining
that of the coordinate system that is attached to it compared
to another coordinate system, considered to be fixed. In this
case, where the latter is fixed, i.e. attached to the Earth on a
scale that interests us and therefore typically denoted as R
0
,
we refer to absolute parameterization; when the coordinate
system considered fixed is that attached to the rigid body
