Computer Aided Engineering Design

TRANSFORMATIONS AND PROJECTIONS 47

(iv) For α = (90° + β), S 1 * and S 2 are hinged about Q 1 Q 3 and are perpendicular to each other

(Figure 2.19e).

Figure 2.19 Example for positioning two triangles relative to each other using transformations

2

1.5

z 1

0.5

0

2

1

y (^00)
1
2
x
(b) Original positions of the laminae in
Example 2.8
Q 2
Q 1
P 1
Q 3
P 3 P 2
2
1.5
z 1
0.5
0
2
1
y 0 0
1
2
x
(c) Positions for case (i)
0.5
y –0.5 0
1
2
x
(d) Positions for case (ii)
0
1
1.5
2
1.5
z 1
0.5
0
2
P 3 ′
P 1 ′
P 2 ′
2
1.5
z 1
0.5
0
2
1
0
0
y
2
x
(e) Positions for case (iii), figure in right is edge view for Q 1 Q 2 Q 3
1
2
z 1
0
2
1
0
0
1
2
y x
P 1 ′
P 3 ′
P 2 ′
2
1.5
z 1
0.5
0
2
1
y 00
2
x
(f) Positions for case (iv), figure in right is edge view for Q 1 Q 2 Q 3
1 1
2
z 1
0
2
1
00
y
2
x
P 1 ′
P 3 ′
P 2 ′