Biomedical Engineering Reference
In-Depth Information
Plane of motion
X
0
q
1
y
2
y
1
x
2
y
0
q
2
x
1
FIGURE 4.2
A 2-DOF planar arm model restricted to move in a planar motion and showing the DH
coordinate systems.
Table 4.1
Parameters for the 2-DOF Arm
Length:
L
5
L
0
:
4
m
5
1
2
Mass:
m
1
5
m
2
5
0:5kg
Inertia:
1 kgm
2
I
1
5
I
2
5
0
:
Center of Mass of Link 1:
1
r
1
5
ð
2
L
1
=
2
;
0Þ
Center of Mass of Link 2:
2
r
2
5
ð
2
L
2
=
2
;
0Þ
Torque upper bound:
τ
U
5
10 Nm
Torque lower bound:
τ
L
52
10 Nm
4.6.1
The DH parameters
The DH parameters of the planar two-link arm are shown in
Figure 4.3
and pre-
sented in
Table 4.2
.
The transformation matrices are:
0
@
1
A
0
@
1
A
cos
θ
1
2
sin
θ
1
0
L
1
cos
θ
1
cos
θ
2
2
sin
θ
2
0
L
2
cos
θ
2
sin
θ
1
cos
θ
1
0
L
1
sin
θ
1
sin
θ
2
cos
θ
2
0
L
2
sin
θ
2
T
1
5
T
2
5
(4.60)
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
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