Biomedical Engineering Reference
In-Depth Information
s y 52 sin q 1 cos ðq 2 1 q 3 1 q 4 Þ
(2.66)
s z 52
sin
ð
q 2 1
q 3 1
q 4 Þ
(2.67)
a x 5
sin q 1
(2.68)
a y 52
cos q 1
(2.69)
a z 5
0
(2.70)
p x 5
cos q 1 ð 2
3 sin
ð
q 2 1
q 3 1
q 4 Þ 1
9 cos q 2 1
11 cos
ð
q 2 1
q 3 ÞÞ
(2.71)
p y 5
sin q 1 ð 2
3 sin
ð
q 2 1
q 3 1
q 4 Þ 1
9 cos q 2 1
11 cos
ð
q 2 1
q 3 ÞÞ
(2.72)
(2.73)
e. To determine the orientation of the 4 th coordinate system with respect to the
hip, we substitute q 1 5
p z 5
9 sin q 2 1
11 sin
ðq 2 1 q 3 Þ 1
3 cos
ðq 2 1 q 3 1 q 4 Þ
0 into 0
0, q 2 5
0, q 3 5
0, and q 4 5
T 4 and the
T
T
orientation is identified as
n 5
001
,
s 52
100
, and
.
In order to determine the position of the point Q , defined with respect to
the 4 th coordinate system, we shall use the extended vector equation as
T
a 5
0
10
2
5
0
4
1
1
0
T 4 ð q Þ
(2.74)
T
The position of a point on the foot is given by
v Q 5
000
.Forthe
initial posture of the lower limb, the joints are q 1 5
0, q 2 5
0, q 3 5
0, and q 4 5
0.
In order to calculate the new posture given the change in joint variables,
we substitute into 0
T 4
2
3
0
1
0
11
2
4
5
0
0
10
2
90
90
0
T 4 ð
0
;
; 2
;
0
Þ 5
(2.75)
1
0
0
12
0
0
0
1
The position is calculated as
90 ; 2
90 ;
v Q ð
0
;
0
Þ 5
12
0
11
(2.76)
2
and the orientation is calculated as
T
n 5
100
(2.77)
T
s 5 001
(2.78)
T
a 5
0
10
(2.79)
2
as shown in Figure 2.24 .
Search WWH ::




Custom Search