Mega May PDF Sale - NOW ON! 25% Off Digital Certs & Diplomas Ends in : : :
Claim My Discount!
Video:
Hello everyone, welcome to our NPTEL online certification courses on Engineering Drawing and
Computer Graphics. We are learning Isometric Projections.
(Refer Slide Time: 00:24)
So, in the earlier classes, we have seen a different kind of projections as orthographic oblique and
perspective projections. In that, a very popular method what we are learning is isometric projections.
(Refer Slide Time: 00:38)
So, isometric projections come under the part of axonometric projections with parallel lines we use
it. And the main concept of isometric projections is, with the horizontal one of these base will be at
30 degrees on both sides and the principal axis makes 120 degrees angle with each other. And
especially we will learn this isometric box method in using an example. Where the views are
embedded in a box and try to rotate so that, we will see isometric projections.
(Refer Slide Time: 01:41)
So, let us take the first example of three different views using the 1st angle method. We have
something like a front view, having certain dimensions like steps kind of architecture, some 30, 20
units and its right side view is given with total height 70 units and the top view is given with
dimensions 50, 20 and 20. The remaining dimensions we can get it from the other views.
So, if these views are given, can we guess how an object in three dimensions looks like and especially
can we draw that object using the isometric projection method. Can you take a look at it how it might
be in three dimensions?
(Refer Slide Time: 02:49)
So, the object looks like a staircase step. So, these stairs, we can see it in the front view when we are
looking at it. These are the steps and the box goes all the way in this way, that is the front view what
we are discussing.
Similarly, in top view, the object what we can see in this block. Similarly, this block is that and this
one is that and right side view if you are looking at it, from right side dimensions we will try to look
at. So, this one is this, this one is this and this part is that. Now, how to draw such kind of isometric
projections?
(Refer Slide Time: 03:59)
First thing, what we have to do? Enclose your front view. Whatever the dimensions give you a
maximum idea about the object that one we will take it and start constructing these isometric views.
So, from the front view, there is an object with steps. So, first, we have to enclose this entire object
in a rectangle, that rectangle is shown in this way.
And for isometric projections, what we have to do? First draw a horizontal line, with respect to that
horizontal line, construct a 30 degrees line that line matches with this blue line. So, first, draw that
one in that way. Now transfer this point A B to A B these lengths are the same because these are the
principal axis lines parallel to principal axis lines we are picking.
So, A B here at the isometric view A B here from the front view remains the same. Now from B drop
a vertical line, that is this one let us call C. The length C we will get it from the right side view, 70
units which have been given. So, whatever the B C length is there the same B C length we will draw
it.
Now, parallel to B C from A draw one more line D and connect C and D. On this box, the 30 degrees
angle whatever it is making, measure this point 1 C to 1 and locate that point 1. Similarly, measure
this 2 point from B to 2, whatever B to 2 points first locate B 2 point.
Similarly, from B locate the third point. So, somewhere locate the third point. So, here 3 we have,
here we have 2. Now drop a vertical passing through this 3 point and similarly drop a parallel line
parallel to A B from point 2.
So, wherever it is intersecting connect those lines so that, we will have this block. So, from C we
have located 1 drop a perpendicular line, from 2 drops one more parallel line to A B so that it goes
intersect here. Similarly, it goes intersect therefrom 3 drops a perpendicular line in the vertical
direction so it is going to intersect here, it is going to intersect at this point from B. Measure this
length call this one as 4th point.
So, let me write these numbers 3 B in isometric is equal to 3 B in that view, in the front view.
Similarly, 4 B in the isometric view is equal to 4 B or B 4 in the frontal view. Similarly, we have to
track it each of these points so that, we will be in a position to join that by a line. This is the way we
transform that entire front view into isometric projections.
(Refer Slide Time: 08:37)
Once that is done we will pick the right side view. So, from the rightward direction, we are trying to
locate it in this way. So, already it is a rectangle, transfer this rectangle onto a 30 degrees line. Again
this is a 30 degrees line, this point we called A, this point we called this is A, this is B. When we are
looking at this point and B point coincides, let us call B prime.
So, using B prime, whatever the length in the right side view we have that length first we have to
transfer it, complete the rectangle measure length of this line; similarly, measure lengths of that line.
So, at those locations draw two lines parallel to this one, let us call this point as something E. So, B
prime and this is E prime. So, whatever the length of B prime, E prime, that is same as B E. In that
way construct this rectangle.
(Refer Slide Time: 10:14)
Along with these lines, once it is done we can use the other view top view to construct the top side of
this box. So, let us look at the top view.
(Refer Slide Time: 10:30)
So, as I said we have this kind of blocks, transfer this entire thing using our isometric axis. Now, this
point comes at the top side, we are looking from the top side of that. So, these are the points what we
are going to see, the points which are going to match with our earlier P point is this.
So, B here B double prime matches on the top side; so, with respect to that draw a rectangle. We have
to turn this rectangle parallel to these lines so whatever, this initial line we have parallel to that we
have to draw it. Similarly, parallel to this line we have to draw this one.
On the top side is basically, if I am going to complete a rectangle whatever that line we are going to
have parallel to that. Otherwise, parallel to this line also parallel. That is the way we have to join these
rectangles.
(Refer Slide Time: 11:56)
Once it is done we have a box, rectangular box, where these lengths have been transferred. Now,
because these are from views, this line coincides. So, we construct a line parallel to that dropping
through vertical. So, let us look at that solution.
(Refer Slide Time: 12:23)
So, those lines what we have seen the top, this one and this one coincides with each other. So, we
complete that entire rectangle. Once that is done we have this line, which is matching with this line.
Similarly, we have this length parallel to this principal axis we connect it, this one and this one once
that is done. We pick this these two lines, draw it in this way and this line coincides with this line.
(Refer Slide Time: 13:31)
Once it is done, we finish these lines remove that rectangle. So, using this way we will be in a position
to construct isometric views of given projections.
(Refer Slide Time: 13:43)
So, let us take one more example to understand these isometric views. We have given three views,
the front view, the right side view and the top view with certain dimensions these dimensions can be
1, 2, 10 and so on. So, here instead of that, we are denoting it by letters. With these lengths we have
to construct a box, so let us see.
(Refer Slide Time: 14:29)
First of all, whenever we have such kind of objects where rectangles are the dominant features we go
ahead construct a box, using principal axis. Now in the front view, we have this length A W. So, if
we are seeing from this point let us call A B, the length A B is W. So, from A B we draw a horizontal
line first, first of all, we draw a horizontal line, with respect to that 30 degrees here and with respect
to that 30 degrees.
We draw two lines, once these two lines are drawn one is W length matches with this one and there
is a B 3 length, which we can see it only from a right side view; that means, from this point to this
point the length whatever it is there that we have to draw it.
So, from B to 3 which we will see it from the top view when we are looking at the top view, the B 3
length is quite visible, in terms of 2 to 3 point. So, that length is D. So, with D length, we will, first
of all, locate point 3.
Once it is done from B, drop a perpendicular once 3 is also known to drop a perpendicular, from A
drop a perpendicular. Now from the right side view, we can see the vertical height of that so the
vertical height of this object is H. So, with H length we will connect these points and join it like a
box, always parallel to our principal axis
Here the principal axis can be taken as these edges are the principal axis. In two dimensions if we are
seeing that, it makes 120 degrees angle, in between these sides. Once the box is constructed, we can
transfer these lengths from the front view and also from the right side view.
So, the first thing what we can do is straight away, pick this right side view something like steps are
visible. So, step construction any line supposed to be parallel to this principal axis planes, we have to
do. So, this line parallel, now this line parallel with another principal axis then go ahead and draw it,
by transferring suitable lengths from this point to this point supposed to be from 3 to this point.
Similarly, from here to here whatever that length is there, we have to transfer that length here and
from this projection, we know this length. So, from here drop a perpendicular to connect it so that,
we will be in a position to join these by lines.
(Refer Slide Time: 18:43)
Similarly, we will transfer these lengths on other planes also. One of the possibility is from the frontal
view, we can see that there is something like this kind of block, which is imaginary, so we can join
along with our this one. From the top view we can see that this part is present so this one, these are
the parts of the steps which we can see it part of the steps.
(Refer Slide Time: 19:16)
Similarly, from the front view, we have those parts, from similarly front view we have these parts, in
this way we can construct our isometric drawing. So, first of all, one has to visualize the views
carefully. The way views are there on principal planes, these are the principal planes.
(Refer Slide Time: 19:55)
For example, for us draw those projections. Once these planes are available, transfer these lengths
onto this geometry, similarly from the top view when you are looking at it drop these lines. So, that
a complete isometric projection one will be in a position to get.
When we are learning about computer graphics we will see, how easy it is to construct such kind of
isometric projections and views. But the basic concepts behind these isometric drawings are first of
all identifying these principal axes, principal planes, suitably transferring these lengths from each of
these views onto these principal planes, through an intuitive approach we will join remove the lines
and get the object. Once we construct that, we have to re-verify it whether that is matching the views.
(Refer Slide Time: 21:12)
Now, let us take another example. Here we have a block and cylinders, something like a cylinder and
there is a block, that block we can see it in the top view it is something like a rectangular block, there
is a circle. First of all, get more or less the intuitive idea, looks like a thick block though it is not
isometric view what we are drawing, just for imaginative purpose there is something like a box is
there.
And because it is having a circular kind of thing extending all the way shaft. So, there must be
something like a circular thing, supposed to come out in that way. Now this kind of intuitive way of
drawing is very helpful, once that is done we will be in a position to construct 30 degrees lines and
go ahead and in a very systematic way, we will construct this isometric views.
So, we would like to begin this one, from the front view if I would like to begin, then there is a length
of A B units. So, begin with a horizontal line, somewhere draw a 30 degrees line another 30 degrees
line, now A B length transfer it.
Now, from B drop a perpendicular, up to a unit of 10. So, call this one C than from C, D goes parallel
to our A B line, transfer C to D length, which is 50 units here. Once that is done, we can convert this
rectangle which 50 dimensions, again we have. So, here drop one more perpendicular and because it
is a sketch what we are trying to have, first of all, construct that rhombus.
Once that is done, with respect to the centre we have this circle. In the last class, we have learnt how
to transform this circle in one view into an ellipse in an isometric way. So, similarly, first of all, we
have to construct that circle into ellipse so that, we will be having this ellipse on that rectangular
block.
Once it is done, tangent to that we have to construct this vertical cylinder lines. From top view this
circle in the isometric view when we are looking at 30 degrees, again that will be a parallel ellipse
one has to construct at a height is 30.
So, once we construct this ellipse what we have to do is, we know the centre of that initial circle from
there we go ahead by 30 units up, again construct one more transform circle into this elliptical thing.
Once that is done draw join these lines because hidden line should not be visible in the case of
isometric things, we remove those hidden lines. One more thing for these isometric views, if it is
something like coming from the circle and ellipse kind of thing we show that axis. Otherwise,
anything at the backside we do not show it by hidden lines.
(Refer Slide Time: 25:47)
Now, let us look at the last example pyramid. So, first of all carefully visualize these views, the front
view and the top view.
It looks like in the top view, we can see that the object has such kind of shape. In the front view, we
have such kind of triangular shape. So, by carefully observing these views we can imagine that may
be the block the basement might look like that and because this inclination thing and because of this,
it might be something like it goes in that way where the views tell us something like a flat base is
there. So, maybe it looks like that. Because all these things are coinciding at this point. Similarly,
here it looks like this is the way the object might look like.
(Refer Slide Time: 27:33)
So, if I am removing that, perhaps the object looks like this; so, as a three-dimensional thing. Once
we have that kind of view visualization we can go ahead and systematically construct such pyramid.
(Refer Slide Time: 28:08)
So, the first step what we have to do is, as usual, a horizontal line drawn 30 degrees lines, that
coincides by bringing this box into the system. This is the rectangular box, what we would like to
change it into isometric views. So, whatever 45 units we have here 45 units there, so 45 units and
construct the basement rectangle.
Once done, transfer this small rectangle also, which is not there. So, transfer that rectangle so that we
will be in a position to identify these points. Once we have this, square into a rhombus kind of shape
we have this edge from H drop a perpendicular line.
So, you can see here the 120 degrees, 120 degrees and 120 degrees which serves as principal axis of
the system.
(Refer Slide Time: 29:41)
So, once we transfer that 50 units are the length, so that is from the base. So, base, once we have
defined, along that line up to 50 marks, point the peak. Similarly, we have to transfer this 20 units on
the rectangle, with respect to this point 20 units; that means, this is the point with respect to that 20
units first locate it.
Similarly, with respect to that point, this point is at 20 units location. So, with respect to that point,
twenty units locate it. Once done, join these by lines. This is the way we keep and typically just to
mention this axis labels, we are just leaving this 30 degrees lines as it is.
So, with that, we will conclude our isometric projections and in the next class onwards we will learn
about computer graphics. More details of this iso isometric projections, we can learn from the book
Engineering Drawing by Professor Dhananjay Jolhe.
Thank you very much.
"Nós enviaremos as instruções para resetar a sua senha para o endereço associado. Por favor, digite o seu e-mail atual."