Biomedical Engineering Reference
In-Depth Information
q
1
z
0
q
3
z
2
z
1
q
2
z
1
z
0
z
2
Point of
Interest P
FIGURE 3.3
The upper extremity modeled as 3 DOF and restricted to planar motion.
Table 3.1
DH Table
θ
i
d
i
α
i
a
i
1
q
1
0
0
4
2
q
2
0
0
2
3
q
3
0
0
1
2.
If this point is reachable and it is required to reach the point with the
orientation a
5
[1 0], it is necessary to calculate a posture of the upper
extremity.
The DH table is readily determined and presented in
Table 3.1
.
Substituting each row into the general DH matrix representation, Equation
(2.49) yields the following (4
3
4) transformation matrices
2
3
cos
θ
2
sin
θ
00
4
5
sin
θ
cos
θ
00
T
z
;θ
5
(3.4)
0
0
1
0
0
0
0
1
Performing the multiplication and obtaining the position vector yields
4cos q
1
1
2cos
ð
q
1
1
q
2
Þ
1
cos
ð
q
1
1
q
2
1
q
3
Þ
n
x
0
ð
q
Þ
5
(3.5)
4sin q
1
1
2sin
ð
q
1
1
q
2
Þ
1
sin
ð
q
1
1
q
2
1
q
3
Þ
We shall also impose ranges of motion on each joint as
2
π=
3
q
i
#
π=
3;
#
i
1
3.
We now answer the two objectives:
;
2
;
5
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