Biomedical Engineering Reference
In-Depth Information
We shall use this method to develop a complete model of the human, always
maintaining a serial link approach to facilitate a computational approach. As will
be seen in later chapters, this approach enables us to address problems in simula-
tion and ergonomics.
2.10
Establishing coordinate systems
In order to obtain a systematic method for generating the (4
4) homogeneous
transformation matrix between any two links, it is necessary to follow a conven-
tion in establishing coordinate systems on each link. This can be accomplished by
implementing the following rules. It should be emphasized that a suitable
home
configuration
must first be established before applying these rules. A home con-
figuration denotes the start configuration of the serial chain (segmental links). It
is customary to start from a well-known position where the user indicates that this
posture is the home configuration.
The procedure for establishing coordinate frames at each link is as follows:
1.
Name each joint starting with 1,2,
3
...
up to
n
-degrees of freedom.
z
i
2
1
axis along the axis of motion of the
i
th
joint.
2.
Embed the
3.
Embed the
x
i
axis normal to the
z
i
2
1
(and of course normal to the
z
i
axis).
4.
Embed the
z
i
subject to the
right hand rule. However, on the kinematic skeleton, it is customary not to
show the
y
i
axis such that it is perpendicular to the
x
i
and
y
i
axis so as not to clutter the drawing and since it is not needed for
determining the DH parameters.
The location of the origin of the first coordinate frame (frame 0) can be cho-
sen to be anywhere along the
z
0
axis. In addition, for the
n
th
coordinate system, it
can be chosen to be embedded anywhere in the
n
th
link subject to the above four
rules. In order to generate the matrix relating any two links, four parameters are
needed. The four parameters are:
1.
θ
i
is the joint angle, measured from the
x
i
2
1
to the
x
i
axis about the
z
i
2
1
(right hand rule applies). For a prismatic joint
θ
i
is a constant. It is basically
the angle rotation of one link with respect to another about the
z
i
2
1
.
1
)
th
coordinate frame to the
2. d
i
is the distance from the origin of the (
i
2
intersection of the
z
i
2
1
axis. For a revolute
joint,
d
i
is a constant. It is basically the distance translated by one link with
respect to another along the
z
i
2
1
axis with the
x
i
axis along
z
i
2
1
axis.
3. a
i
is the offset distance from the intersection of the
z
i
2
1
axis with the
x
i
axis
to the origin of the
i
th
frame along
x
i
axis. (Shortest distance between the
z
i
2
1
and
z
i
axis).
4.
α
i
offset angle from
z
i
2
1
axis to
z
i
axis about the
x
i
axis (right hand rule).
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