Engineering Graphics Class Module 4 _ IIT Bombay Professor _Semester 1 and 2 _ Episode 25

Engineering Universe

Transcript

00:00you

00:30This is our last section of this chapter.

00:39This is question number 13.

00:42Question 13 is a star question.

00:45These two questions are 30 and 31.

00:47Same question just the values are different.

00:50Both are important.

00:5130 and 31 and also 34.

00:54The speciality of the 13th question is that we are given a square prism with a base edge of 50 mm

01:05but the speciality is that the height of the prism is not given in the question

01:09So, the problem is of a square prism without a height

01:14So, the things are as follows

01:16The cutting plane is given

01:17The height of the square prism with a base edge of 50 mm is not given

01:20Then, it is cut by a plane

01:22Perpendicular to VP and Inclined to HP, the true shape is a hexagon

01:27So, we need a hexagon

01:29The speciality of the hexagon is that it is not an irregular hexagon but an irregular hexagon

01:34Because, it is given that the opposite sides are 25 mm and the remaining 4 sides are 35 mm

01:41Opposite sides are 25 mm and the remaining 4 sides are 35 mm

01:47So, we know that if it is a regular hexagon, the 6 sides will be equal

01:52Because, it is an irregular hexagon, the opposite sides are 25 mm and the remaining 4 sides are 35 mm

02:10If you are going to do it in that way,

02:12we cannot draw the simple portion fully

02:15So, why can we draw a base shape in this simple portion?

02:18Because, it is a square prism

02:19So, we can draw a square

02:21But, I have drawn the square in an equally inclined way

02:24The reason why I have drawn it in an equally inclined way is

02:27as I have said in the interaction video of the square prism and the cube

02:31If we draw it in an equally inclined way,

02:32we can easily cut the triangle, square, pentagon, hexagon, trapezoid and many other shapes from this solid

02:40I have done an interaction video on that

02:42You will understand when you see that

02:44That is why I have drawn it in an equally inclined way

02:46In the case of a square prism, if we want to get a hexagon,

02:49we have to place the solids in an equally inclined way

02:55That is why I have drawn it in that way

02:57Now, in this portion,

02:59I have told you that the true shape is a hexagon

03:02and the opposite sides are 25 mm and the remaining 4 sides are 35 mm

03:12Now, I have asked you to find out the height of this portion

03:15We cannot draw it without knowing the height

03:17But, what we have to do is

03:18we have to draw and find out the height of this portion

03:21How to do this?

03:23There is a particular method

03:24If you want to know the method to solve this problem,

03:28you can learn it by heart

03:30To know how to solve this problem,

03:33I have drawn two solids in a square prism

03:37You already know that

03:39If you want to get a hexagon,

03:41I have told you in the previous introduction video

03:43how to cut a hexagon

03:46To get a hexagon,

03:49Do you remember how to get a hexagon?

03:52To get a hexagon,

03:54we have to cut this line at the top and this line at the bottom

04:03If you cut those two lines and draw like this,

04:05you will get a hexagon

04:06If it is a regular hexagon,

04:08you have to cut this line at the top and this line at the bottom

04:15If you draw like this,

04:16you will get a regular hexagon

04:17Because,

04:18you will get two points if you cut this line

04:20and two points if you cut the middle line

04:22and two points if you cut this line

04:23I have told you that in the previous introduction video

04:25We don't have to draw the midpoint of this line

04:28Because, the true shape of our question is

04:31an irregular hexagon

04:32So, we have to cut this line at the top and this line at the bottom

04:38But, we don't have to cut the midpoint

04:40We can cut it any way we want

04:42But, what do we get when we cut it?

04:43Two sides should be 25mm

04:45and the other four sides should be 35mm

04:47to get a hexagon

04:49So, what I am going to do is

04:51I am going to draw an irregular hexagon

04:56I am going to draw an irregular hexagon

04:59I drew an irregular hexagon

05:02So, these two sides should be of opposite size

05:05That is 25mm

05:08and the remaining sides should be 35mm

05:10This is 35mm, this is 35mm, this is 35mm

05:13This is how we are going to get a hexagon

05:15So, this is how we are going to fix any edge

05:17If you draw a line in the middle

05:19Now, it is equal to half

05:21If you draw a line in the middle

05:23and if you take the edge like this

05:26We will not get any perpendicular V1 and V2 distances

05:29Is it clear?

05:31Now, suppose I take the edge like this

05:33For example, if I take the edge like this

05:36If I take the edge like this

05:38We will not know the value of this edge

05:40The perpendicular distance of this edge is

05:42This is our distance

05:43This point and this point are our distances

05:45So, we will not know the distance between these two distances

05:49So, we will know

05:51This is 25mm, this is 25mm

05:53and the remaining four sides should be 35mm

05:55So, I am going to take a hexagon in this

05:58Or, I am going to fix the edge in the middle

06:03Is it clear?

06:04So, that means

06:05If I draw a rough true shape in the problem

06:09I am going to take the edge

06:11Or, in this problem, I can take the edge

06:13Now, I am going to draw a rough hexagon

06:28This is an irregular hexagon

06:30I am fixing these two opposite sides

06:33Opposite sides are 25mm

06:35This is 25mm

06:36This is 25mm

06:37I am fixing

06:38The remaining four sides are 35mm

06:40So, I am going to take the edge in this

06:42Like this

06:43We can make the hexagon equal half

06:45If I take the line in the middle as an edge

06:47We will not know the value of that

06:49But, when we fix the vertical distances perpendicular to that

06:53The first vertical distance is

06:55This is our vertical distance

06:57V1

06:58That is equal to 25

07:00The next vertical distance is

07:02V2

07:04We don't know the value of that

07:06The next vertical distance is

07:08V3

07:09We will get the value of that

07:10V3 is equal to 25

07:12So, we have V1 and V3

07:14We will get two vertical distances

07:16If we fix the edge horizontally

07:20We will get the vertical distance

07:22So, I am going to solve the problem in that way

07:24So, if I fix it like that

07:26In the same way, I have fixed the vertical distance and horizontal distance

07:29So, now we have to know

07:31Where do we normally fix the vertical distance?

07:33This is where we are going to fix the vertical distance

07:35Now, I know V1 is equal to 25

07:37So, what did I do?

07:38I fixed V1 at the point where 25 comes

07:42I got 25

07:43So, we will get these two points

07:45Usually, we project these two points straight up

07:49We have to start from where it comes

07:51So, we got the starting point

07:54Now, we just have to cut this line down

07:56But, we cannot cut it anywhere

07:58Next, I am going to fix V2

08:00So, V2 is equal to 25

08:02I fixed V2 at 25

08:04So, if we fix V2 at 25, we can project it down

08:06So, we will get this point

08:08What can we do?

08:10We can draw a section plane like this

08:12So, what do we get?

08:14We have V1 and V2

08:16The remaining four sides

08:18We can draw a vertical line with a chance of 35

08:22But, there is a problem

08:24This is a rough sketch

08:26I have already drawn the height here

08:28But, there is no height

08:30So, we know one thing

08:32If there was a height

08:34The distance from this point to this point

08:36was h

08:38This is the actual h

08:40If we know the value of h

08:42We can solve the problem

08:44I have not drawn the height here

08:46Is it clear?

08:48I am not drawing the height

08:51I have not drawn the horizontal line

08:53We don't know where it will extend

08:55So, I have not drawn this

08:57The center axis line was also extended

08:59I don't know how high it will extend

09:01The center line was also extended

09:03We don't know where this will extend

09:05But, we can know one thing

09:07What was the vertical distance?

09:09It was 25

09:11So, I have fixed the first vertical distance as 25

09:13So, I have fixed the first vertical distance as 25

09:15Then, I have drawn the 25 line

09:17I drew the line of 25 straight up.

09:20Because I don't know how far it will go.

09:21I drew it straight up because there was a height here.

09:25If there is no height, what can we do?

09:27We can just draw it straight up.

09:30So I don't know how far it will go.

09:31Next I fixed V2.

09:3425

09:35No, V3. 25.

09:37But we can extend that.

09:39Because we can extend that to the base.

09:40The base is already there.

09:42So I got that.

09:43So I got this point.

09:45I don't know the point on top.

09:47If you look at this side, you will know.

09:48I got this point.

09:49I don't know the point on top.

09:50There is this line.

09:52What can we do to get the point on top?

09:54From here, if we know H,

09:57if we draw an arc from H to the composite,

09:59we will get this top point.

10:01Right?

10:02So what I am doing is,

10:02if we know the value of H from this point,

10:04I am repeating, if we know the value of H,

10:08from this point,

10:09take H as the composite.

10:11Then this red line,

10:12if I take H and cut it to the line where 25 was fixed earlier,

10:16I am drawing H.

10:17So this is the value of H.

10:18If we know H,

10:20if we cut it,

10:21what will that be?

10:22The top point of this solid.

10:25Because we can fix it there.

10:26So what can we do?

10:27We can close this solid there.

10:28This is this much.

10:29So we can determine the height of the solid.

10:33So this is the height of the solid.

10:36The height of the solid is H.

10:37Is it clear?

10:38So even if we have the value of H,

10:40we can find the height of the solid.

10:43So in the problem that we fixed here,

10:46in this problem,

10:46the value of H that we took,

10:49the value from here to here,

10:51we don't actually know the value of H.

10:52What we know is V1 and V3 only, 25.

10:57So if we can find the value of H,

10:59even if we draw a true shape,

11:02we can complete this solid.

11:07We can complete it.

11:08So for that,

11:09to find the value of H,

11:12what we are going to do is,

11:13we are actually going to draw a true shape.

11:15So in the actual case,

11:16how do we draw a true shape?

11:19So to draw that,

11:20if you look here,

11:22I have already drawn the axis in the middle of this square.

11:26You can see how I am going to draw a real true shape.

11:31So I extended this axis line horizontally.

11:36Then there is the bottom corner of this.

11:38I am going to extend the bottom corner line horizontally.

11:49So I extended the bottom corner line horizontally.

11:54So this is the bottom corner line.

11:56Then the top line.

11:58I extended the axis line in the middle,

12:01this line and this line.

12:03These are the three extremes of this solid.

12:04These are the three extremes in the middle.

12:06So I extended those three lines first.

12:09Now we know where to fix the vertical distance.

12:12The first vertical distance V1.

12:14I am going to scale it perpendicularly.

12:16How much should it be?

12:18How much should it be?

12:19It is 25.

12:20So 25.

12:23Let's see where it should be.

12:33So V1 is 25.

12:35I am going to fix it.

12:381, 2, 25.

12:45So I fixed V1 at 25.

12:49So this is the distance V1.

12:51I fixed 25.

12:54Similarly, we can fix V3 at the other side.

12:57It will be at the same height as V3.

12:59So there is no problem.

12:59If you fix V1 and draw a horizontal line, what will you get?

13:03If you mark here, you can fix it quickly.

13:06If you scale it, you can fix it quickly.

13:11So if I measure it from here, how much is it?

13:15Around 25.

13:18There is a dimensional error.

13:201, 2, 25.

13:28Okay, keep it correct when you draw.

13:30So V1, V3, 25.

13:32So these distances are 25.

13:34I fixed both of them at 25.

13:36Next, I am going to extend the projector lines that I fixed at 25.

13:43So when you first fix it, you have to take the correct dimension to get the correct height.

13:47I have not done it so accurately.

13:50You can do it accurately.

14:06Okay, I am going to project those lines at 25.

14:16These are the projector lines at 25.

14:19Next is this.

14:22This is the first line I drew.

14:2425 will be a little less.

14:26So I drew the projector line at 25.

14:28So it is the same.

14:29Here also 25.

14:30So here I am taking 25.

14:31I am taking V3 at 25.

14:32I projected those two lines.

14:35This is the middle line.

14:37This is the line projected at the top.

14:39This is the line projected at the bottom.

14:41When we fixed V1, V3, we got two points.

14:45So these are the lines projected at those points.

14:48So we projected the points and drew them.

14:51Now we are going to fix it.

14:53Here we are going to draw the real true shape.

14:56We already know that this is 25.

14:59I fixed the first base edge at 25.

15:04This is the first base edge of our hexagon.

15:07I fixed it at 25.

15:09Now we are going to take the compass to get the next 4, 35.

15:13We already know that we have to get this when we cut this.

15:16So these are the two extreme lines.

15:18So how much do we take in the compass?

15:2035 is the remaining 4 sides.

15:22I am measuring 35.

15:24I am measuring 35.

15:26From this line which we got 25,

15:29we are going to the extreme end which we drew at the top.

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