To Design a Small Pneumatic Actuator Driven Parallel
Link Mechanism forShoulder Prostheses for Daily Living Use 113
2 2
2
2
2
1
11 1 3 3
' cos sin sin cos
22 2 2 2
13
cos sin sin '
22
PB P P B
PP
rr r r r
rrh
l
2 2
2
3
2
1
11 1 3 3
' cos sin sin cos
22 2 2 2
13 cos sin sin '
22
PB P P B
PP
rr r r r
rrh
l
(9)
Equation (9) is a simultaneous equation with three unknown variables, , , h 1 ’. In the case
that the lengths l 1 ’, l 2 ’, l 3 ’ are given, it is possible to calculate , , h 1 ’ by using the Newton
method (Ku, 1999; Merlet, 1993; Press et al., 1992). Similarly, for the Segment 2 (i.e. in OP 1 -
xP 1 yP 1 zP 1 ), the following equation can be derived. In the case that the length l 4 ’, l 5 ’, l 6 ’, are
given, it is possible to calculate ,, h 2 ’.
2
P P 2
2
P P B
2
P B
2
6
2
P P 2
2
P P B
2
P B
5 2
2 2 2 2
4
'hsinrsincosr
l rcosr' rcosrsinsinr
sincosr 'hsinr
l rcosr' rcosrsinsinr
l' P B P P 2 'hsincosrsinsinrrcosr
2
3
2
1
2
3
2
3
2
1
2
1
2
1
2
3
2
1
2
3
2
3
2
1
2
1
2
1
(10)
The position of the Rod end PRE’ in OP 2 -xP 2 yP 2 zP 2 , i.e. P^2 PRE’ can be defined as:
T
RE R
2PP 00 l , ,'
(11)
Let x, y, z be the coordinate of B^1 PRE’, then end position of the Rod, x, y, z in OB 1 - XYZ can be
described as:
coscossinsincos 'h'hl
cossincossinsin
cos sin
coscossinsincos
cossincossinsin
cos sin
z
y
x
zyx '''
R 2 1
1P
1B
2P
1P
RE
2P
2
2P
1
T 1P
0
0
0
0
0
(^000)
OOPRR
(12)
http://www.ebook3000.com