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Engineering Universe
  • 10/10/2024
Engineering Graphics Class Module 5 _ IIT Bombay Professor _Semester 1 and 2 _ Episode 32
Transcript
00:00you
00:30can do is, you can connect the last edge with N and connect all the points and draw.
00:43So, if this is A, our second is B. Automatically, this is C. This will be D. What will be the
00:50next one? It will be A. So, A is done. Then, B. Next, C is connected. Then, D is connected.
01:05Then, D is connected. Next, what do we do? We draw the bottom straight line. So, A, B,
01:12B, C. Then, C, D. Then, D, E. So, this is our pyramid. The only difference between these
01:17two cases is, the drawing is the same. If it were me, I would have drawn one more line.
01:23The difference is, in the case of a pyramid, the base edge is parallel. We do not need
01:29a true length line here. How do we find out if it is true length or not? That line is
01:36parallel to the X-ray line in the top view. In this case, if you look at the previous
01:43case, you will know that NC is parallel to the X-ray line. So, here the X-ray line is
01:49parallel. Since the X-ray line is parallel, it will be true length. You do not have to
01:54worry about the X-ray line being parallel. In this case, the X-ray line is not parallel
02:01to the X-ray line. It is slanted. So, there is no true length line here. So, I rotated
02:08the X-ray line and drew the X-ray line parallel to the X-ray line. I drew the X-ray line
02:13parallel to the X-ray line and drew the X-ray line parallel to the X-ray line. I drew the
02:18X-ray line parallel to the X-ray line and drew the X-ray line parallel to the X-ray line.
02:22I drew the X-ray line parallel to the X-ray line and drew the X-ray line parallel to the
02:27X-ray line. I drew the X-ray line parallel to the X-ray line and drew the X-ray line
02:32parallel to the X-ray line. I drew the X-ray line parallel to the X-ray line and drew the
02:37X-ray line parallel to the X-ray line. I drew the X-ray line parallel to the X-ray line
02:42and drew the X-ray line parallel to the X-ray line. I drew the X-ray line parallel to the
02:47X-ray line and drew the X-ray line parallel to the X-ray line. I drew the X-ray line parallel
02:52to the X-ray line and drew the X-ray line parallel to the X-ray line. I drew the X-ray
02:57line parallel to the X-ray line and drew the X-ray line parallel to the X-ray line. I
03:02drew the X-ray line parallel to the X-ray line and drew the X-ray line parallel to the
03:07X-ray line. I drew the X-ray line parallel to the X-ray line and drew the X-ray line
03:12parallel to the X-ray line. I drew the X-ray line parallel to the X-ray line and drew the
03:16X-ray line parallel to the X-ray line. I drew the X-ray line parallel to the X-ray line
03:21and drew the X-ray line parallel to the X-ray line. I drew the X-ray line parallel to the
03:26X-ray line. I drew the X-ray line parallel to the X-ray line and drew the X-ray line
03:31parallel to the X-ray line. I drew the X-ray line parallel to the X-ray line and drew
03:36the X-ray line parallel to the X-ray line. I drew the X-ray line parallel to the X-ray
03:41line and drew the X-ray line parallel to the X-ray line.
04:11xy line is not parallel to the xy line.
04:15So, if xy line is not parallel to the xy line,
04:17how do we find out this?
04:19What do we do?
04:21We have to rotate like we did earlier.
04:23What do I do here?
04:25I drew a horizontal line from n.
04:27This is the xy line.
04:29This is the same line.
04:31So, n should be parallel to the xy line.
04:33We have to incline it downwards.
04:35So, what do we do with n?
04:37We rotate it, make it parallel and find the true length.
04:39This is just a simplification.
04:41I have centered n.
04:43I am taking n-d as a compass.
04:45I take n-d as a compass.
04:47I rotate it like this.
04:49You can see the difference.
04:51When I rotated d,
04:53I saw a difference here.
04:55So, I gave it a new name.
04:57I named it d1.
04:59So, I extended d1 to the front.
05:01So, this point is d1'.
05:03Don't get confused.
05:05This is d' and this is d1'.
05:07So, I connected
05:09n' d1' line to this.
05:11n' d1' is here.
05:13This is the
05:15original true length of
05:17the sold.
05:19So, this is the second line
05:21which I drew using red pen.
05:23This is the
05:25original true length of the sold.
05:27The difference is just a simplification.
05:29But, still,
05:31n and d are not true length.
05:33The line which I drew is true length.
05:35line.
05:36Now just rotate the line.
05:37Now the rest of the lines are the same.
05:40We just have to scale the lines we drew earlier.
05:43For this we need to fix the first edge parallel to the first edge.
05:47Now just move the distance to the left.
05:49We fix the first edge.
05:50The point at the top is always the end.
05:52The point at the border is always the first edge.
05:55Now we do the rest of the things.
05:57The point at the border is always the first edge.
06:04The point at the top is always the first edge.
06:07The point at the bottom is always the first edge.
06:10The point at the bottom is always the first edge.
06:13The point at the top is always the first edge.
06:16The point at the bottom is always the first edge.
06:19The point at the bottom is always the first edge.
06:22The point at the top is always the first edge.
06:25The point at the bottom is always the first edge.
06:28The point at the bottom is always the first edge.
06:31The point at the bottom is always the first edge.
06:34The point at the bottom is always the first edge.
06:37The point at the bottom is always the first edge.
06:40The point at the bottom is always the first edge.
06:43The point at the bottom is always the first edge.
06:46The point at the bottom is always the first edge.
06:49The point at the bottom is always the first edge.
06:52Connect NC.
06:55Connect D.
06:58Connect E.
07:03If you keep doing this, you will never get a curve.
07:06It will look like a sector.
07:08You should always get a curve.
07:10The base should always be straight.
07:12This is a curve.
07:14Each edge should be very dark.
07:17Draw A to B and make it dark.
07:20Connect B to C.
07:22Connect C to D.
07:25Connect D to E.
07:28Connect E to A.
07:30This is the development of a pyramid.
07:32The base should always be straight.
07:34Otherwise, it will look like a cone.
07:37Keep this in mind.
07:39Check if there is a true length or not.
07:44Now we need the last fold.
07:47The last fold is the cone.
07:50This is how we draw the development of a cone.
07:54What should we do when we draw a cone?
07:56We should draw the paper in the same way as we did for the pyramid.
08:03When we draw a cone, we should draw it in the same way as we did for the pyramid.
08:11There is no problem in drawing a cone.
08:13We can draw it by learning an equation.
08:16When we draw a cone, there is no need to check if there is a true length or not.
08:22We can draw it in the same way as we did for the pyramid.
08:25This is the fourth question.
08:27We can draw it in the same way as we did for the pyramid.
08:30We have 8 generators.
08:35That is why we drew cross lines.
08:37This is parallel to the X-axis.
08:39What is this NE?
08:41It is a true length.
08:42There is no problem.
08:43We can fix the first edge.
08:45I drew a horizontal line here.
08:47I fixed the first edge parallel to the NE.
08:52But the problem here is capital N.
08:55Now we have to draw an arc.
08:57But the problem is, how far will this arc go?
09:00First I drew an arc parallel to NE.
09:10But we don't know how far this arc will go.
09:14In the case of the pyramid, we could have drawn 4 base edges here.
09:21But the problem here is,
09:23This is a circle.
09:25The circumference of the circle is the circumference of the cylinder.
09:30If you calculate the circumference, you can't measure it in a curve.
09:36If you calculate 2Ï€r,
09:392Ï€r is the length that has to come here.
09:41The length that has to come through this curve is 2Ï€r.
09:46But 2Ï€r was lengthwise when it was a cylinder.
09:49We could measure it and mark it.
09:51But we can't mark 2Ï€r in a curve.
09:54So, when we develop the cone,
09:57We know that there is a sector here.
10:00We have to find the angle inside this sector.
10:03It will be a sector like this.
10:05We have to find a sector like this.
10:08This is N and this is A.
10:11We don't know where this point is.
10:13We don't know this length.
10:14That's our problem.
10:15If we want to know the point from N to A,
10:19We can find out the angle inside this.
10:22We can close this with that angle.
10:26We will get the length correctly.
10:28There is an equation to find that angle.
10:30We have to know it.
10:31We will do it in the case of cone.
10:33As I said in the cylinder case, 2Ï€r equation,
10:36In the case of cone, the internal angle,
10:38The angle that comes inside the sector of development,
10:41is small r by capital R into 360.
10:46Small r is the radius of the cylinder.
10:50The radius of the cylinder is 25.
10:54This is our small r.
10:56What is capital R?
10:58Small r is 25.
11:00This is our small r.
11:02Capital R is the length of the first fixed edge.
11:09This is capital R.
11:11This is not given in the question.
11:13We will get it only if we measure it.
11:15What do we do in the case of scale?
11:17We have to measure the length of this.
11:19When I measure this, I get 75.
11:22So, capital R is 75.
11:24Small r is 25.
11:26So, 25 is given.
11:28I measured capital R as 75.
11:30I will do it into 360.
11:34So, 1 by 3 into 360.
11:36What is the equality?
11:37It is 120 degrees.
11:40What is the internal angle?
11:42It should be 120.
11:44In all problems, you can use this equation,
11:46small r by capital R into 360,
11:48and find the angle.
11:50Small r is the radius of the cone given in the question.
11:55Capital R is the slanted edge we drew in the front view.
11:59The length of the true length line is capital R.
12:01You will get it only if you draw it and measure it.
12:04So, angle is 120.
12:06What do we do now?
12:08Mark it using a protractor.
12:13We got the angle as 120.
12:16So, take a protractor.
12:18This is the internal angle, 120.
12:20We have fixed the fill line as NA.
12:22So, put a protractor.
12:24Put a protractor in the NA line.
12:26Then measure 120.
12:29120.
12:31After measuring 120,
12:33we can connect a line and draw.
12:35This is the end.
12:41This is the last edge.
12:47This is the internal angle, 120.
12:50We got the last point.
12:52This is the last point.
12:54We got the curve.
12:56Now, we have to darken the curve.
12:58In the case of cone, it is dark.
13:01Now, we need to generate 8 divisions.
13:05In the case of cylinder, we need to divide it into 8 lines.
13:09In the case of cone, we need to divide it into 8 lines.
13:12So, we need to divide it into 8 lines.
13:14If we divide it into 8 lines here,
13:16we will not get it correctly if we take a compass in this small distance.
13:20What do we do now?
13:22The internal angle is 120.
13:24So, 120 by 8.
13:26If we do it first,
13:28it will be the division of one section.
13:31It is the division of one section.
13:34So, 120 by 8.
13:38We will get 15.
13:40So, 120 by 8.
13:42If we do 120 by 8, it will be 15.
13:44It is the angle of one division.
13:46If we take 8 lines, it is the angle of one division.
13:48If we do it in parallel,
13:50we will get 8 divisions.
13:52If we mark the 15 degrees of the first division,
13:54it will be easier.
13:56I am keeping the tractor in the same scale.
13:59Let's mark 15 degrees.
14:0210, 15 degrees.
14:04So, we mark 15 degrees.
14:06If we draw a line,
14:08it will be the first division.
14:11If we do it,
14:13it will be 15 degrees.
14:15I have taken this angle as 15 degrees.
14:17I drew this line to show you.
14:19It should be dark.
14:21Our curve should be dark.
14:25So, N, B.
14:27It is the first division.
14:28We have divided it into 8.
14:30We have got the first division.
14:32We do not have to take the remaining 15 degrees.
14:34What we have to do is,
14:36we have to take this from the compass
14:38and mark it.
14:40120 is equal to 8.
14:42So, we get C,
14:44D,
14:46E,
14:48F,
14:50G,
14:52H,
14:54and A.
14:57Now, connect all these.
14:59As I said earlier,
15:01you have to draw very lightly.
15:03Otherwise,
15:05it will look like the edges of a pyramid.
15:07Actually,
15:09there are no edges.
15:11We are drawing the generator.
15:13So, we have to draw the divisions
15:15in the case of the cone and cylinder.
15:17Similarly,
15:19in the case of the cone,
15:21we do not draw the bottom portion.
15:23We do not draw the straight lines.
15:25It should be curved and dark.
15:27It should be curved.
15:29This is the development of a cone.
15:31These 4 are the base divisions.
15:33In the case of a cone,
15:35do not forget this equation.
15:37These are the cases of 4 developments.
15:39You have to follow these cases
15:41when you solve each problem.
15:43We have studied these 4.
15:45Now, let us see how to develop
15:47the basic 4 solutions.
15:49After knowing these developments,
15:51we can develop the sectional solutions.
15:53If we take this simple portion,
15:55we have to cut this portion
15:57and use the remaining portion
15:59to draw the section.
16:01If we cut this portion,
16:03we can use the remaining portion
16:05to draw the section.
16:07There is nothing to draw.
16:09It is very easy.
16:11We have to know the basic developments.
16:13What we do is,
16:15we draw the development
16:17of the full solution first
16:19and then we do the section.
16:21If we want to know the development
16:23of the full solution,
16:25we have to know how to develop
16:27these 4 basic solutions.
16:29In the case of a cone,
16:31we have to know how to
16:33divide it into equal parts.
16:45In the case of a prism,
16:47we have to keep the book
16:49in the middle.
16:51How can we develop this?
16:53We have to take 4 base edges
16:55and 5 base edges.
16:57The first edge and the last edge
16:59will have the same naming.
17:03In the case of a pyramid,
17:05we have to keep the book
17:07in the middle.
17:09In the case of a pyramid,
17:11we have to keep the book
17:13in the middle.
17:15In the case of a pyramid,
17:17we have to keep the book
17:19in the middle.
17:21In the case of a pyramid,
17:23we have to keep the book
17:25in the middle.
17:27In the case of a pyramid,
17:29we have to keep the book
17:31in the middle.
17:33In the case of a pyramid,
17:35we have to keep the book
17:37in the middle.
17:39In the case of a pyramid,
17:41we have to keep the book
17:43in the middle.
17:45In the case of a pyramid,
17:47we have to keep the book
17:49in the middle.
17:51In the case of a pyramid,
17:53we have to keep the book
17:55in the middle.
17:57In the case of a pyramid,
17:59we have to keep the book
18:01in the middle.
18:03In the case of a pyramid,
18:05we have to keep the book
18:07in the middle.
18:09In the case of a pyramid,
18:11we have to keep the book
18:13in the middle.
18:15In the case of a pyramid,
18:17we have to keep the book
18:19in the middle.
18:21In the case of a pyramid,
18:23we have to keep the book
18:25in the middle.
18:27In the case of a pyramid,
18:29we have to keep the book
18:31in the middle.
18:33In the case of a pyramid,
18:35we have to keep the book
18:37in the middle.
18:39In the case of a pyramid,
18:41we have to keep the book
18:43in the middle.

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