CONE STANDING &

CYLINDER PENETRATING

h

a

b

c

d

e

g

f

a’ b’h’ c’g’ d’f’ e’ g” g”h” a”e” b”d” c”

12

3

45

6

7

8

X Y

o”o’

1

3,7

5

2,8

4,6

Problem: A vertical cone, base diameter 75 mm and axis 100 mm long, is completely penetrated by a cylinder of 45 mm diameter. The axis of thecylinder is parallel to Hp and Vp and intersects axis of the cone at a point 28 mm above the base. Draw projections showing curves of intersection.

2

Intersection of a square prism and a hemisphere

30o

T

F

•Draw concentric circles in the TV on the hemispherical surface to represent different heights in the FV

•One circle should touch the inner corners of the prism in order to get the end points of the intersection curves

•3 faces of the cube intersect the surface of the hemisphere

•Join corresponding intersection points of the prism and concentric circles

Intersection curves shown in RED

Draw the curves of intersection of the hemisphere intersected by a pentagonal pyramid as shown. The axis of the prism is 10mm due south-east of the center of the hemisphere. Assume a suitable height of the prism.

S. E.

Mark other curves similarly

4

X Y

CYLINDER STANDING &

CONE PENETRATING

Problem: A cylinder of 80 mm diameter and 100 mm axis is completely penetrated by a cone of 80 mm diameter and 120 mm long axis horizontally.Both axes intersect & bisect each other. Draw projections showing curve of intersections.

1

2 8

3 7

4 6

5

7’

6’ 8’

1’ 5’

2’ 4’

3’

5

Triangular and hexagonal prisms- lines of intersection will be straight lines

Parallel

Draw generator lines (pink) on the surface, parallel to the edges, passing through the points of intersection

Project the points of intersection from TV to FV.

Join them

T

F

Draw the curves of intersection of the hexagonal and triangular prism as shown.

A cylinder with base diameter of 55mm and height 110mm is standing with its base on the horizontal plane. A triangular prism with a base side of 40mm and a height of 110 mm penetrates the cylinder completely. The axes intersect at their midpoints but are inclined at 60o to each other. Draw the curves of intersection on both sides of the cylinder.

Mark other curves similarly

7

Draw generator lines along the conical surface in the 3 views

The point of intersection of the cylinder base circle with the generator lines gives the points of intersection

Project the points in TV and FV

Cylinder joining cone at an angle

Draw an auxiliary view in order to get the true shape of the cylinder base. The points of intersection will lie around the periphery

T

F

PRIMARY AUXILIARY VIEW

Point of inflectionNot visible below this line in TV

Draw a generator line through this point in order to get the point where curve changes direction

o

o

a

a

a

o

Draw the curves of intersection, in the top and the front view, of the cone intersected by a cylinder as shown in the fig.