INTERPENETRATIINTERPENETRATIONON

OF SOLIDSOF SOLIDS

INTERPENETRATIONINTERPENETRATION

By definition, is: the intersection of By definition, is: the intersection of two bodies of similar or different two bodies of similar or different form, resulting in a regular or form, resulting in a regular or irregular figure.irregular figure.

Can you think of any simple Can you think of any simple examples? They are evident in examples? They are evident in everyday life.everyday life.

Two triangular Two triangular based prisms. based prisms. (Tetrahedron)(Tetrahedron)

Can you think any Can you think any examples of examples of interpenetration in interpenetration in our daily our daily environment?environment?

Interpenetration of two Interpenetration of two cylindrical objects.cylindrical objects.

The skewer cuts The skewer cuts the sausage the sausage centrally to give a centrally to give a similar effect to similar effect to the two pipes the two pipes below.below.

What kind of effect would we get if What kind of effect would we get if the cylinders cut each other off the cylinders cut each other off

centre?centre?

>>Visualise and sketch!!>>Visualise and sketch!!

We can see the two We can see the two surfaces curving to surfaces curving to a point as one a point as one protrudes through protrudes through the other.the other.

Now we see the Now we see the effect of them effect of them being cut acutely being cut acutely to each other.to each other.

Cylinder and a cut Cylinder and a cut surfacesurface

What shape will be What shape will be cut in the ground cut in the ground where the post where the post penetrates the penetrates the ground surface?ground surface?

Supposing the post Supposing the post was leaning to one was leaning to one side, what would be side, what would be the resultant the resultant shape? Would it be shape? Would it be the same?the same?

How can we prove that How can we prove that this is the case?this is the case?

There are two main ways we do this There are two main ways we do this in drawing…in drawing…

Can you think what they might be?Can you think what they might be?

Horizontal Cuts orHorizontal Cuts orSectional ViewsSectional Views

1) Take a section, or 1) Take a section, or sectional view.sectional view.

We make a horizontal We make a horizontal cut through the solid cut through the solid to give us a true to give us a true shape, or to enable us shape, or to enable us to visualise what it to visualise what it looks like at a certain looks like at a certain point or level.point or level.

Look down or along the Look down or along the object object

to see its true shape.to see its true shape. Enables us to Enables us to

develop an develop an understanding of understanding of its true shape, and its true shape, and in terms of in terms of interpenetration, it interpenetration, it allows us to see allows us to see how the object how the object affects another affects another object in its object in its context.context.

These two methods are the medium These two methods are the medium by which we solve problems on by which we solve problems on interpenetration. By understanding interpenetration. By understanding how it is done in principle provides how it is done in principle provides us with a more complete us with a more complete understanding and appreciation in understanding and appreciation in theory.theory.

IndexingIndexing

Is a key principle in drawing, but Is a key principle in drawing, but especially in interpenetration. If a especially in interpenetration. If a mistake is made it is very difficult to mistake is made it is very difficult to trace if indexing is not used. (see trace if indexing is not used. (see next slide)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 StepsKey Steps

1)1) Project the orthographic views Project the orthographic views neatly and accurately, including neatly and accurately, including true shape of cutting prism at true shape of cutting prism at aligned angle, given.aligned angle, given.

2)2) Project an auxiliary elevation to Project an auxiliary elevation to view the face of the cutting prism.view the face of the cutting prism.

3)3) Index auxiliary including where the Index auxiliary including where the cutting prism protrudes around the cutting prism protrudes around the corners of the other prism.corners of the other prism.

Key StepsKey Steps

4) Project these points back to find 4) Project these points back to find corresponding point in elevation and corresponding point in elevation and drop to plan. (indexing)drop to plan. (indexing)

5) Join points over the surfaces in 5) Join points over the surfaces in elevation and plan taking note of elevation and plan taking note of which lines can and cannot be seen which lines can and cannot be seen in different views.in different views.

6) Follow same procedure for points 6) Follow same procedure for points which are ‘round the back’.which are ‘round the back’.