Exercise 7S

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ENGINEERING GRAPHICS Exercise 7S Student's Name ...............................
Problem 34. Determine the plane tangent to the sphere's surface. Point of
tangency should be one of two points of intersection of sphere pierced by
the straight line m.
34
35
36
m"
Total
Final
O"
x12
m'
O'
Wydział MEiL, ITLiMS, Zakład Podstaw Konstrukcji
ENGINEERING GRAPHICS Exercise 7s Student's Name ...............................
SECTIONS OF CONE'S SURFACE
The cone's axis is perpendicular to
π1-projection plane, but cutting
planes are perpendicular to π2.
φ<α/2
Wh2"
π
2
W"
α/ 2
Wp"
Wh2
φ=α/ 2
W
Wp
A"
Wh1"
φ>α/2
C"=D"=S"
f"
Wh1
m"
A
C
B"
S
D
x12
B
π
1
ellipse
parabola
hyperbola
f
m
Wydział MEiL, ITLiMS, Zakład Podstaw Konstrukcji
ENGINEERING GRAPHICS Exercise 7S Student's Name ...............................
THE PIERCING OF CONE'S SURFACE
t1
π
f||d
W"
2
t2
f"
t1
W
P2"
γ
f
t2
κ"
P1"
m"
P2
2"
x12
S"
d"
α"
P1
1"
m
A"
α
B
κ
S
d
kαγ
1
A
P1'
d'
P2'
S'=W'
π
1
Cone's axis is perpendicular to π1-plane
α − cutting plane α ||π1
γ − additional plane γ(W,d)
A = α I d,
B = α I f,
kαγ(A,B)
kαγ = γ I α,
m = κ I α,
{P ,P } = κ I d
1
2
2
Wydział MEiL, ITLiMS, Zakład Podstaw Konstrukcji
ENGINEERING GRAPHICS Exercise 7S Student's Name ...............................
Problem 35. Determine the
points of intersection of the
cone's surface pierced by
the straight line d.
d"
W"
S"
m"
x12
m'
S'=W'
d'
Wydział MEiL, ITLiMS, Zakład Podstaw Konstrukcji
ENGINEERING GRAPHICS Exercise 7s Student's Name ...............................
Problem 36. Find points of
intersection of the cylindrical
surface pierced by the
straight line m.
Determine the visibility.
m"
1"
x12
m'
1'