INTERPENETRATION
OF SOLIDS
INTERPENETRATION

By definition, is: the intersection of two bodies
of similar or different form, resulting in a
regular or irregular figure.

Can you think of any simple examples? They are
evident in everyday life.

Two triangular based
prisms. (Tetrahedron)

Can you think any
examples of
interpenetration in our
daily environment?
Interpenetration of two cylindrical
objects.

The skewer cuts the
sausage centrally to give
a similar effect to the two
pipes below.
What kind of effect would we get if the
cylinders cut each other off centre?
>>Visualise and sketch!!

We can see the two
surfaces curving to a
point as one protrudes
through the other.

Now we see the effect of
them being cut acutely to
each other.
Cylinder and a cut surface

What shape will be cut in
the ground where the
post penetrates the
ground surface?

Supposing the post was
leaning to one side, what
would be the resultant
shape? Would it be the
same?
How can we prove that
this is the case?

There are two main ways we do this in
drawing…

Can you think what they might be?
Horizontal Cuts or
Sectional Views

1) Take a section, or
sectional view.

We make a horizontal cut
through the solid to give
us a true shape, or to
enable us to visualise
what it looks like at a
certain point or level.
Look down or along the object
to see its true shape.

Enables us to develop an
understanding of its true
shape, and in terms of
interpenetration, it allows
us to see how the object
affects another object in
its context.

These two methods are the medium by which
we solve problems on interpenetration. By
understanding how it is done in principle
provides us with a more complete understanding
and appreciation in theory.
Indexing

Is a key principle in drawing, but especially in
interpenetration. If a mistake is made it is very
difficult to trace if indexing is not used. (see
next slide)
This is a typical solution at mid
completion. Points need to be located in
an auxiliary and transferred back to the
orthographic views. You need to be able
to follow and read the drawing.
Key Steps
1)
2)
3)
Project the orthographic views neatly and
accurately, including true shape of cutting
prism at aligned angle, given.
Project an auxiliary elevation to view the face
of the cutting prism.
Index auxiliary including where the cutting
prism protrudes around the corners of the
other prism.
Key Steps
4) Project these points back to find corresponding
point in elevation and drop to plan. (indexing)
5) Join points over the surfaces in elevation and
plan taking note of which lines can and cannot
be seen in different views.
6) Follow same procedure for points which are
‘round the back’.