10 - mech1009y - intersection.of.solids _stud

8/12/2019 10 - MECH1009Y - Intersection.of.Solids _stud

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10

Curves of

Intersection ofSurfaces


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Introduction

When the surface of one solid meets that of another solid, the

line along which the two surfaces meets is known as the curve

of intersection of the surfaces. Numerous applications (e.g.

ducts, pipe joints etc) involve intersection of surfaces.

Orthographic drawings of lines and curves of intersection of

surfaces must be prepared first for the accurate development of

objects.


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Classification of Intersecting Surfaces

1. Intersection of two plane surfaces

The line of intersection is a straight line.

2. Intersection of two curved surfaces

The line of intersection is a curve.

3. Intersection of a plane surface and a curved surface

The line of intersection is a curve.


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Dissimilar square prisms meeting at 90


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Dissimilar square prisms meeting at an angle


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Square pyramid and a hexagonal prism meeting at an angle


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Cylinder meeting a square pyramid at right angles


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Cylinder meeting a square at an angle


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Intersection of cylinder and cylinder

ExampleA horizontal cylinder of diameter 40 intersects a vertical

cylinder of diameter 60 . The axes of the cylinders cross at

right angles. Draw the curves of intersection when the axis of

the horizontal cylinder is parallel to the VP.

1. Draw the top and front views of the cylinders.2. Draw the left side view of the arrangement.

3. Divide the circle in the side view into number of equal parts

say 12.


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Fillet Curves

ExampleA casting with a rectangular base and a circular-section shaft

is shown in the drawing below. The machining of the fillet

radius in conjunction with the milling of the flat surfaces

produces the curve shown in the front elevation.


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Problem 10.1

A cone (resting on its base) has a base diameter of 60 , an

axis perpendicular to the base and apex point distant by 65

from the base. A horizontal cylinder of 35 diameter

penetrates the cone such that the axis of the cylinder intersects

that of the cone 20 above the base of the cone. Draw the

projections showing the curves of intersection when the axes of

both solids are parallel to the VP.Draw the developments of the lateral surface of the cone.


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Problem 10.2

A square prism with 40 sides at its base and 140 axis

length, is standing on its base with its axis parallel to the VP

and two edges of the base inclined at 30 to the VP. It is

completely penetrated by a square prism with 25 edges at

its base and a 140 long axis. The prism has its axis parallel

to the VP, inclined at 30 to the HP, and its side faces are

equally inclined to the VP. If the two axes bisect each other,draw 3 views of the solids showing the curves of intersection.


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Problem 10.3

A pentagonal pyramid, with 50mm edges at its base and a

100mm long axis, is resting on its base with an edge of itsparallel to the VP. It is penetrated by a cylinder 46mm in

diameter and 100mm in length. The axis of the cylinder is

perpendicular to the VP and intersects that of the pyramid

25mm above its base. Draw 3 views showing the curves of

intersection.Draw the developments of the lateral surface of the pyramid

and the cylinder.


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Problem 10.3

Two elevations of a wheel stop are shown above. Draw, full

size, (a) the given elevations,

(b) a plan looking in the direction of arrow Z.


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Problem 10.4

The above drawing shows the plan and incomplete elevation of

two cylinders. Draw the two views, showing any missing lines.

10 - mech1009y - intersection.of.solids _stud

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