Biomedical Engineering Reference
In-Depth Information
FIGURE 2.3
Modeling of a human using a series of rigid links connected by joints, also called
kinematic skeleton.
within the joint while taking into consideration muscle action, ligaments, and
other effects that are not considered in the DH representation method.
This chapter will begin with the fundamental theories required to understand
motion in 3D. The general translational and rotational motion of an object will
first be presented, followed by a standardization of a method for embedding coor-
dinate systems (also called triads) in each segmental link. We will then develop a
formulation that relates any two segmental links in this chain.
2.2
General rigid body displacement
We define the word
configuration
as denoting the position and orientation of a
rigid body. Consider the gene
ral
motion of the hand, now considered as a rigid
body, where the line segment
OW
embedded in the hand is shown in
Figure 2.4
.
The motion will carry the rigid body from its initial configuration in
coordi-
nate system
A
to a different configuration indicated by the line segment
O
.
This
mo
tion can be described in vector notation as a translation along the vector
p
5
v
W
v
OO
0
and a rotation about
O
0
prescribed by the rotation matrix
A
R
B
, where this
rotation matrix rotates the
A
-coordinate system from its orientation to the orienta-
tion shown in the
B
-coordinate system. In vector notation, this motion can be
described as
A
x
ð
W
vÞ
OO
0
1
O
0
W
v
(2.1)
where
A
as seen
by the
A
-coordinate system. A superscript to the left of the letter denotes
x
ð
W
vÞ
denotes the vector extending from the origin O to
W
v
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