>> In this lecture, we're going to talk about auxiliary views.
Let's start by recalling that for the principal planes,
the frontal, horizontal, and the profile planes,
when you make those principal projections,
you use those principal projection planes
and project points perpendicular to those planes.
They will give you the principal orthographic views of front,
top and right side views respectively.
On the other hand, an auxiliary plane is a plane that is used
as a projection plane but it's not parallel to any
of the front, top or the right profile planes, OK.
And as a result of projection in--
projecting into this auxiliary plane,
we will get what's called auxiliary views.
And auxiliary views are used to show true sizes of planes
that are either oblique or inclined.
Here's an illustration of an auxiliary view.
We are given the top, front
and right side views of these solid here.
And take note that plane A, B, C is an inclined plane
because it's shown as foreshortened in the top
and also foreshortened in the right side view
and an edge view and the front view.
So, none of these two views here that show plane A, B, C,
D as planes, it's the true size.
If you want to see the true size of this plane, what we need
to do is make a line of sight
from up here along the direction that's perpendicular
to the plane.
So as illustrated here, this is the direction of line
of sight exactly perpendicular to the edge view
of the inclined plane in the front,
you will see the true size and shape of this plane.
And that view-- resulting view is an auxiliary view.
So you're looking along a direction that is perpendicular
to this reference plane that is parallel
to the edge view and the front view.
Here's an illustration of how
that develops using glass box model.
Recall for the six principal views.
We have the glass box.
We put the object inside and then we project
into the surfaces of this glass box, the features
of your object, and then you open the box
to get view the top view, front, right,
as well as the other views.
For an auxiliary view on the other hand,
instead of having a regular rectangular box,
one of the faces of our glass box is intentionally constructed
parallel to this inclined plane.
And then what we do is project the features
of the object orthographically, so perpendicular
to this auxiliary reference plane, OK.
That corresponds to taking a line of sight
that is perpendicular to the auxiliary reference plane
and hence perpendicular to this inclined plane,
and then we open it to give us the auxiliary view.
So, we're going to start
in what's called primary auxiliary views which just
like the previous example.
It's one in which the--
it is projected from a principal orthographic view using a
primary auxiliary plane.
So it could be from the top-- projected from the top,
the front, or the right side view.
A primary auxiliary reference plane is perpendicular to one
of the principal planes but inclined with the other two.
So in this case here, this auxiliary reference plane here
that is inclined is perpendicular to the front view,
to the frontal plane and inclined relative
to the other two planes.
And we can use the folding-line method
to construct our auxiliary view.
Think of auxiliary planes as planes that fold
from the principal planes, just like a glass box model.
Here it is an illustration.
So, very similar to the objects
that we had inside the glass box here, OK.
Here's the top, front, right side view and you can think
of the auxiliary reference plane as in this case,
being folded off of the frontal plane.
So in this case, this auxiliary view is projected off
of the front view because this primary auxiliary reference
plane was perpendicular
to the frontal plane before we unfolded the box.
And the key here is, in finding locations of this--
any point in the auxiliary view, we take measurements
from the existing view.
So for instance, here, this distance here M
which is a measure of how far the object is behind the frontal
plane, is really the depth of the object
and that depth is shown both in the top view
and the right side view.
So in locating this edge of the blue plane, we simply borrow
or transfer the depth of the top view
or over the right side view,
because this distance M represents how far this edge
of the plane is relative to or behind the frontal plane.
And that distance behind the frontal plane is the same
as seen from the top view, as seen from the right side view,
and consequently as seen from the auxiliary view.
So there's three types of a primary auxiliary views.
Again, primary auxiliary views are views that are projected off
of one of the three principal planes, front, top, and right.
So the first one is called the auxiliary view
and it's projected from the top view.
It's called a height auxiliary view because the dimension
of height is perpendicular to the top view.
And the idea is you take a fold line right here up on the top,
and what we see is the heights
of objects below the top plane is the same whether you're
looking it from the front or you're looking it
from the right side view or looking at it
from the height auxiliary view.
So what we do is to locate the details of the points here,
the bottom of this here, OK, has a depth--
has a height of H below the top horizontal planes.
So this fold line here separates the top and the frontal planes,
the top horizontal plane.
This fold line here between the top view
and the auxiliary view represents the fold line
between the top horizontal plane and the primary reference plane.
And take note that it's very useful to label your planes--
your projection planes.
It's H on this side.
It's giving you the top view here.
It's F on this side giving the front view here.
And one here or auxiliary reference plane number 1
to give you the primary auxiliary view.
Again, this height here is the same as this height, OK.
And then if you want to look at this part here,
this height here, it should be the same as this height.
Here are the steps for creating the height auxiliary view.
So let's say that this inclined plane here, I've labeled 1, 2,
3, 4, 1 and 4 over here, 2 and 3 over here.
And we're interested in finding the two sides
of that inclined plane.
So what we do is we take a fold line here or a reference plane
that is parallel to 1, 2, 3, 4 at its edge view, OK.
This fold line here corresponds to H or horizontal top plane
on this side and first auxiliary reference plane on this side,
in the same way that this fold line here corresponds to H
above here and F below.
And since its height auxiliary view, when trying to locate 0.1,
0.1 can be anywhere along this projection.
So I create a construction lines from 0.1 perpendicular
to my reference plane, construction line from 0.2,
perpendicular to the reference plane.
And then to find the location of 1, we say that the height of 1,
how far it is below the horizontal plane.
Remember, this is the horizontal plane?
So this distance here represents how far below you are
from the top horizontal plane before you unfolded the
glass box.
It must be the same as this height here in the front view.
Same thing along the projection of 2,
the height of 2 here is transferred from the height
of 2 given in the front view.
And then project 3 also perpendicular
to the reference plane and 4 perpendicular
to the reference plane.
Take note that the projection line--
construction line for 3 is exactly the same as 2
because they are exactly the same location here.
Projection for 4 is the same as 1.
And then to find the location of 3 and 4,
this height here should be the same as the height
of 3 below the horizontal plane.
We transfer that, same thing with 4 over here.
And then that gives you the two sides of the plane, OK.
In this example here, we only are focusing on how a plane,
1 here, 2, 3, 4, appears in the auxiliary reference plane.
Take note that the other features
of the 3D object, right?
You have other objects here, OK, need to be shown here as well,
as you will see in our lab.
And the second type of primary auxiliary view is the depth
auxiliary view and it's projected off of the front view.
It's called the depth auxiliary view because the dimension
of depth is perpendicular to the front view.
And we're going to use the depth of--
look at locations of points to construct the auxiliary view.
And here's an illustration.
Here's the front view.
And I want to find the true size of this inclined plane here,
so what I do is I take a fold line off of the front view
that is parallel to that inclined plane.
Take note that this reference plane is perpendicular
to the front view.
In locating points in my auxiliary reference plane,
what I do is project points from the existing front view, OK,
along construction lines.
All construction lines need to be constructed perpendicular
to the reference plane.
And just to help us, it's a good idea
to always label your projection planes on both sides.
So this side here, this is the fold line between the top
and the front, and it's F on this side and H on that side.
This is the fold line between the front
and the right profile plane, F on this side and P on that side.
This is the fold line between the front
and the first auxiliary view.
So this is front here and ARP,
auxiliary reference plane number 1 here.
And then to find locations
of points along the projection construction lines,
you borrow the depth of points.
So depth D for instance here,
represents how far this object here is,
this point in the object is behind the frontal plane,
and that distance depth behind the frontal plane
of course we knew from before, is shown both in the top view
and the right side view.
However, that distance behind the frontal thing is also the
same in the primary auxiliary view.
So we measure this distance here, that will be the location
of this point and that point is along this projection.
Take note that when measuring away from F, OK,
all the depths are measured away from the frontal plane.
Here's an illustration of the depth auxiliary construction.
Here is the top view and here is the front view.
And I see the edge view of the inclined plane.
What I do is I want to find the two sides
of that inclined plane.
So I take a reference plane that is parallel to that edge view.
That reference plane is F on this side and ARP1,
auxiliary reference plane number 1 on this side, the same way
that this is F here and H here.
Take projection lines from the points here of the plane,
perpendicular to the reference plane.
Whenever a line of sight or the projection lines,
construction lines cause a reference plane,
they should be perpendicular to the reference plane.
So, how do I know how far the points are?
So I'm calling this 0.1 here, 0.2 here, OK?
How do I know the location of 0.1?
This is 0.1.
It's going to be in anywhere along this--
actually the 0.1 is over here.
So let's start with this corner here.
OK. It's along this projection.
How far along that projection?
You measure this depth.
That depth there defines the depth of 1.
Here's the other point here corresponding to this, OK.
It's along this line.
And take note that it's also depth D. So transfer the depths
of points measured away from this fold line.
It should be the same as depths measure for this fold line
and laid out along the corresponding
construction lines.
Do the same thing for the two points here
that are closer to the front.
This depth here is the same as the depth here
to give you the true sizes.
This is an error.
This D here should be over here.
Now the third type of primarily auxiliary view
in the width auxiliary view.
It's the one that's projected off of the right side view.
Take note that the right profile plane is perpendicular
to the dimension of width, OK.
Width is a measure of how far you are
to the left of the right plane.
So use width measurements of points with respect
to the profile plane as basis for finding locations of points.
So here, if you take this as your fold line, it will be front
on this side and P on this side.
You take this fold line here.
It's going to be P on this side and ARP1 on this side.
So this is P and this is also P, distances away
from the right plane which we call width is the same
as the distances here away from the corresponding P here
when constructing the auxiliary view.
Secondary auxiliary views, this will be in lab number 12.
Lab number 11 will be primary auxiliary views.
And you will understand it more when we do lab number 11.
Lab number 12 deals with secondary auxiliary views.
These are projected from a primary auxiliary view.
So you have an existing primary auxiliary view
or it could be a depth or height or a width auxiliary view.
And then you take another reference plane perpendicular
to that primary auxiliary view.
It gives you a secondary auxiliary reference plane
that gives you the secondary auxiliary view.
And these are-- the secondary auxiliary view are used
to show the true size of oblique planes.
Primary auxiliary views are used
to find the true size of inclined planes.
Inclined plane is inclined only with respect
to two principal planes and perpendicular to the third.
On the other hand, an oblique plane is actually rotated
directed to all three principal planes.
That's why you need two auxiliary reference planes
to find the true size of this oblique plane.
Secondary auxiliary reference plane that is used
to find the secondary auxiliary view is constructed
perpendicular to an existing ARP1.
And we use distance from point--
of a point from the ARP1 in the same secondary auxiliary view
as in the principal orthographic view.
So let's illustrate this.
And again, you will understand it more
when you do lab number 12.
We're given the top and the front view of this 3D object.
This is the top plane or H, you will see the label in this H
and this is the front, OK.
Let's focus on the plane.
This triangle 1, 2, 3 shown in the top, 1, 2,
3 shown in the front, and it's inclined.
What we do is-- That's not inclined.
It's oblique.
OK. I give you this first auxiliary reference plane.
So this type here, this is projected off from the front,
which means that this is a depth auxiliary reference plane.
So what we do is we take a construction line perpendicular
to the auxiliary reference plane here.
Take note, the auxiliary reference plane was actually
constructed perpendicular to line 1, 3.
So when we project 1, 1 would be anywhere along this projection.
We project 2, 2 would be anywhere along this projection.
And when we project 3, OK, the projection
for 3 is exactly the same as that for 1 because line 1
and 3 here in the front is perpendicular
to the auxiliary reference plane.
Now to-- so I labeled this as ARP1 over here.
And to locate 0.1, I will use the depth here.
So this distance here from F--
behind F, that's the depth of 0.1, OK.
Since this is also F, 1 is along this projection.
This distance here also is the depth of 1.
So this distance of 1 is exactly the same
as the distance of 1 giving you 0.1.
To locate 0.2, 0.2 is anywhere along this projection
and I measure the depth of 2.
So this distance here from here to the fold line here
of F is the same as this distance of 2 here
to the fold line of F. That's how we located 0.2.
Now 0.3 is exactly in the same projection
as 1 is also exactly the same depth as 1.
This distance here is the same as this distance so that 1
and 3 actually end up being at the same point,
which means that when you construct the plane 1, 2, 3,
and the first auxiliary view is actually an edge view.
So this one here is the edge view of 1, 2, 3, OK?
Since in this example we're only focusing on triangle 1, 2, 3,
I'm going to not show you the construction
of the other points of this solid object.
So once we have 1, 2, 3 in the first auxiliary view,
the primary auxiliary view,
we take a secondary auxiliary reference plane,
this fold line here parallel to the edge view of 1, 2, 3.
So this fold line here corresponds on this side ARP1,
this whole thing is the primary auxiliary view.
So this side of the fold line here is ARP1,
on this side here would be ARP2.
That will give you auxiliary view secondary.
Let's try and locate 1, 2 and 3 in the secondary auxiliary view
by projecting 1 and 3 will be along this projection, OK.
The projection line is perpendicular
to the reference plane
and 2 will be anywhere along this projection.
The question now is how do we find the location of 1
and 3 along this line, and location of 2 along this line?
What we do is we borrow distances.
So this distance is here, this distance is away
from auxiliary 1 and we already have that here
because this is auxiliary 1.
This whole thing, this current central view is the first
auxiliary plane.
And distances away from that plane
in this direction should be the same as distances
from aux 1 in this plane.
So for instance, in locating 0.1 along this projection,
we notice that 0.1 is this distance away from ARP1.
So this distance here which we call X, is the distance
of 0.1 away from ARP1.
So what we do is we borrow that distance of X-- that's X--
and lay it out along the projection of 1
to give you location of 1.
Same thing for 2, 2 is anywhere along this projection,
but how far along this distance?
Well, we notice that distance of 2
from ARP1 is this distance Y. OK.
That's how far 2 is from ARP1.
It's the same distance Y that we construct away
from ARP1 or aux 1.
That will give you 2.
Similarly for 3, distance of 3 is this
from auxiliary reference.
This is auxiliary reference 1.
The perpendicular distance here
which we call Z should be the same as the distance
from perpendicular distance for this corresponding ARP1
and that's Z. So the X here, distance for 1 is the same
as distance from 1 here.
They're both measured from the same auxiliary reference A1
and 1 here.
Y here for 2, Y for 2, and Z here for 3 and Z here
for 3, give you 1, 2, 3.
And you will understand this when you look at the video
for Lab 12 and also complete that lab.