1. Solids in contact.

2. Introduction.
Solids in contact is in relation to cones, spheres and other cylindrical objects in contact.
Sometimes you can get objects with flat surfaces also in contact. E.G. cubes, prisms, rectangles.
In a question you are usually asked to locate a sphere in contact with a point of contact that you are given or maybe given the point of contact in plan or elevation and obtain it in the other view.

3. Background.
Solids in contact generally work with cylindrical objects. E.G. cones, spheres, hemispheres, cylinders, etc.
Three things you need to understand are:
Points of Contact (POC)
Location of objects when given certain pieces of information
Necessary steps when looking for objects in certain views
There are more but these may be used in Leaving Certificate drawing.

4. Points of contact. (poc)
These are points where two objects meet and are represented by POC on your drawings.
When you have two spheres/sphere and a cone/sphere and a cylinder you get a point of contact.
This is not the case if you have a cylinder or a cone in contact with a cube or a flat surface left against the side of the cone or cylinder.

5. Points of contact (POC)
Below you can see how the point of contact comes about.

6. Point of contact (cone)
On a cone there are a series of lines running up to the top of the cone. These are called GENERATORS. The outer two generators are known as the extreme generators.
These can be obtained by dividing the cone up in plan with your 60/30 set-square, projected to XY line and then joined to the vertex.

7. Example of a cone with generators

8. Establish POC.
This aspect is in relation to establishing a POC between two objects. These can be got between spheres, cones, cylinders, hemispheres.
The general rule is that where two objects touch then a POC is established.

9. Establish poc.
When you require to get the POC you join the two centre points first.
Then drop the POC from elevation until it meets the centre line of the object in plan.
Then swing this point up until it meets the line you used to join the two centre points.
This is then the POC and you bring this point back up to the elevation and bring the initial POC across until it meets this line and this is it in elevation.

10. Establish poc.

11. To draw a sphere in contact with a cone.
Draw a sphere of radius
15mm in contact with
the cone shown below
at point P and is
tangential to cone.

12. To draw a sphere in contact with a cone.
First of all you draw plan
and elevation. The POC is
up 20mm in elevation and
down 25mm in plan. You
project down where the
20mm line in elevation
cuts the edge of the cone
you project this down to
centre line in and swing it
down until it cuts the 25mm
line.

13. To draw a sphere in contact with a cone.
This is then the POC in plan.
Project this back up until it
cuts the 20mm line and this
is it in elevation. Where the
20mm cuts the extreme
generator project out
perpendicular and mark off the
radius of the sphere. We do
this as we can see the cone
and sphere in contact as we look
in at 90˚ to both. Drop
this down to the centre line in
plan.

14. To draw a sphere in contact with a cone.
Project out the generator
that the POC is on past the
cone. Swing the initial centre
down to meet this. This is
then the centre of the sphere
in plan.

15. To draw a sphere in contact with a cone.
Bring the initial centre
horizontally to the left
and project the new centre
up to meet this and this is
the correct centre. The
finished sphere can then be
drawn in.

16. To draw a sphere in contact with a cone.
In a question you may be asked to draw a sphere in contact with a point P and is on the horizontal plane.
This simply means it is on the ground or the XY line.

17. Rolling of solids.
This relates to rolling solids around each other in order to get their finished position.
This is usually done with circular objects.
You add the radius to the object and swing it round about itself in plan.
As mentioned before you get it in elevation as you look in at it and then drop it down to its corresponding centre line and swing it round until it meets the other line you obtained by doing the similar steps.

18. Rolling of solids. This is an example of rolling a sphere into place.
Draw the projections of a sphere radius 15mm which will be in contact with the sphere and the cylinder shown below.

19. Rolling of solids. Firstly draw your plan and
and elevation of the given
solids.

20. Rolling of solids. We know the radius of the sphere is 15mm so we come
up 15mm of the XY line and
draw a line parallel to the XY.

21. Rolling of solids. As the radius is 15mm we add on 15mm to the
radius of the sphere and
swing it until it cuts the
15mm horizontal line.
this is then dropped down
onto the centre line in plan.

22. Rolling of solids. From the centre in plan we
then swing this round in the
direction of the cylinder.
we repeat these steps to the
cylinder, but in elevation there
will be a vertical line out 15mm
from the edge of the cylinder.

23. Rolling of solids. This once again is dropped
down onto the centre line of
the cylinder in plan. Then
swing this down until it cuts
the previous line. This is the
finished centre point for the
sphere in plan.

24. Rolling of solids. To get this in elevation we simply just project it
straight up until it cuts the
15mm horizontal line we
drew earlier.

25. Rolling of solids.
For practice in this area of the topic refer to your workbook.

26. Auxiliaries in solids in contact.
Sometimes, depending on the question we may need to acquire an auxiliary in order to see the necessary information within a question.
By completing an auxiliary we see the component in a different orientation the position of the components will not change.
By doing an auxiliary it allows us to look in at a surface at 90˚ and get and edge view of it. We can work like it was an elevation and start applying heights.

27. Auxiliaries in solids in contact.
An auxiliary which is projected from the plan is an auxiliary elevation.
An auxiliary which is projected from the elevation is an auxiliary plan.

28. Auxiliaries in solids in contact.
A simple auxiliary question:
Draw the given plan and elevation in order to get the sphere in its true position.

29. Auxiliaries in solids in contact.
Draw all the information
that you can from the
question. As the sphere is
radius 25mm, in elevation
you can draw a line parallel
to the XY in construction.

30. Auxiliaries in solids in contact.
We then start the auxiliary
by looking in at 90˚ to the
surface. As the surface in
this question is parallel to
the XY line all our projection
lines are simply horizontal,
but you usually project
parallel to the surface.

31. Auxiliaries in solids in contact.
We then set up a second
XY line and call it X1Y1.
as this is an elevation
because it is being projected
from a plan we can take all
the measurements from the
existing elevation and apply
them over here to get the
pyramid. Now we can see the
edge of the surface.

32. Auxiliaries in solids in contact.
As we did before in an
elevation we apply the
radius of the sphere to the
edge of the pyramid and
on to the X1Y1 line. Where
these cross is the initial
centre of the sphere. This is
then projected back to plan.

33. Auxiliaries in solids in contact.
Where this cuts the centre
line is the centre of the
sphere. This can then be
projected straight up to
elevation and where it cuts
the 25mm line we earlier
applied is the centre of the
sphere in elevation and this
is the drawing finished.

34. Auxiliaries in solids in contact.
For practice in this area of the topic refer to your workbook.