Biomedical Engineering Reference
In-Depth Information
TABLE 10-1
Denavit-Hartenberg Parameters for the Human Arm
Joint
β
i
No
α
i
a
i
d
i
θ
i
0
◦
Base
0-1
0
a
0
d
0
0
90
◦
medial rotation to
90
◦
lateral rotation
90
◦
90
◦
Shoulder
−
+
1-2
−
00
β
1
+
−
180
◦
abduction to
+
50
◦
adduction
+
90
◦
00
β
2
+
90
◦
Shoulder
2-3
−
180
◦
flexion to
+
80
◦
extension
β
3
+
90
◦
Shoulder
3-4
0
l
1
0
−
10
◦
flexion to
+
145
◦
extension
+
90
◦
00
β
4
+
90
◦
Elbow
4-5
−
90
◦
pronation to
+
90
◦
supination
+
90
◦
β
5
+
90
◦
Elbow
5-6
0
l
2
−
90
◦
flexion to
+
90
◦
extension
+
90
◦
00
β
6
+
90
◦
Wrist
6-7
−
15
◦
abduction to
+
40
◦
adduction
Wrist
7-8
0
l
3
0
β
7
Source
: Pons, J. (Ed.),
Wearable Robots—Biomechatronic Exoskeletons
, Chichester, UK: John Wiley & Sons, 2008.
θ
i
around axis
Z
i
corresponds to the variable around the
i
-th DoF of the model. The range of
motion depends on the physiological limits of that joint,
The D-H parameters for the human arm are defined in Table 10-1 where the angle
β
i
(deg), as listed Table 10-1. The
parameters
a
i
and
d
i
are the body segment lengths that remain constant for each human
being, but they vary from individual to individual (generally as a function of their height
and sex).
Using the D-H convention, the general form of the transformation matrix between
two consecutive coordinate systems is described by
⎡
⎣
⎤
⎦
cos
θ
i
−
cos
α
i
sin
θ
i
sin
α
i
sin
θ
i
a
i
cos
θ
i
sin
θ
i
cos
α
i
cos
θ
i
−
sin
α
i
cos
θ
i
a
i
sin
θ
i
T
i
−
1
=
(10.1)
sin
α
i
cos
α
i
0
d
i
0
0
0
1
The position and orientation of the terminal device can be determined by developing a
single transformation matrix as a combination of the transformations of each successive
joint.
T
0
T
0
T
1
T
7
=
...
(10.2)
In the case of most prosthetic arms, only a subset of the complete transformation would
be applied depending on the position of the amputation.
From a dynamic perspective, the movement of each joint can be related to the external
forces transmitted to the joint, the inertia of the body in motion, and the torque at each
joint actuator.
10.4
STRUCTURE OF THE LEG
As shown in Figure 10-9, the leg consists of three segments: (1) the thigh; (2) shank and
foot; and (3) three joints—hip, knee, and ankle.
10.4.1 The Hip Joint
The hip joint consists of the cup-shaped acetabulum on the pelvis and the spherical head
of the femur. It functions as a spherical joint allowing three degrees of freedom: flexion-
extension, abduction-adduction, and medial-lateral rotation. The first allows rotation in
