Transcript for:
Isometric Drawings in Engineering and Architecture

[Music] so [Music] [Applause] [Music] good morning welcome to this online course on engineering or architectural graphics part 2 and i am your course instructor professor of lokita agriwal from department of architecture and planning iit roorkee in this course we are going to learn about isometric drawings isometric projection so if you are familiar and if you search the available courses on nptel you would find that we have already completed part one of this course which was totally focused on orthographic projections and we already completed the entire range of discussion related to orthographic projection in this particular course we are going to be talking about isometric projection now if whether you have gone through my course or not or if you just know about orthographic projection you would say that why at all do we need to have another projection system isometric projection when we have this orthographic projection with us which is quite a robust projection system so we have all the possibilities of dimensioning of communicating our idea our creativity through those two dimensional drawings which is what we saw when we were doing orthographic projection so what we were doing in orthographic projection was that we were taking these parallel projectors and we were taking different views of the same object and we were relating these views so what we see from the top was a top view what we see from the front was a front view and what we see from the side was a side view there was also an oblique plane and we could also have oblique projections and things like that and together when we read all these two dimensional drawings ah simultaneously we will get this entire representation of 2d drawings which are representing a 3d object or whatever idea you have in your mind this is what was called orthographic projection so here what we are doing is we are taking a set of these drawings so one two three or more depending upon how complex the object is and how many drawings we need to represent it fully with different types of lines these nomenclature all put together yet there are certain limitations with orthographic projection which is what we will just see so if you take this example which is what we are seeing here so we have a front view we have a top view and we have a side view now it will take us little time to understand what the set of drawing is going to communicate to us what this actual object is so we will read it we will connect the dimensions we will connect the drawings and then arrive at what this 3d is so there is certain limitation of course there are several advantages of orthographic projection which is why it is used worldwide it is the language of engineers and architects when we conceive something when we conceive certain idea whether it be building a furniture or machinery or you know omega structure anything we communicate with the help of orthographic projection the reason being that it is very easy to convey the technical and dimensional information there is no ambiguity there is very less possibility of miscommunication and that is why we prefer to use orthographic projection then we also can very conveniently communicate the accurate measurement so when we have this orthographic projection which means that we have projectors which are perpendicular or parallel to a face of the object we will surely be getting the exact measurement and as we know that in orthographic projection if we have measured a dimension once we do not need to repeat it that's where the clarity of dimensioning is in orthographic projection which is why it is such a popular system of projection then we can actually arrive rather derive the hidden details and all the connecting parts but for that we need to have a bigger set of these drawings representing the same object or same you know design and it is much easier to scale down or up with the help of this orthographic projection for all these benefits that we derive out of orthographic projection orthographic projection remains the most common the most popular projection system in engineering and architecture however as i say there are certain challenges and the biggest challenge is that orthographic projection does not provide us with a with a realistic view with with a 3d view which is much easier for anybody to perceive and understand and that is why in addition to orthographic projection we often supplement this set of information in 2d which is orthographic projection with something which is in 3d of which one example or one type is isometric projections so this is the isometric view of the same object which is represented by these two dimensional drawings we can derive at this in fact this isometric projection this isometric drawing has been derived out of these three drawings which are given here but it is much easier it's very easy to perceive that oh this is the this is the object we are talking about when we look at these drawings it's not very easy it's not very direct that you would understand that ok this is the object in question but with the 3d it is like that now the problem often with 3d so artists sketch they can make a sketch of the entire city or they can make a sketch of the entire building but the problem with 3d sketches is that you cannot read dimensions out of that there may be an artistic rendering of say i am i am an architect and i am also a wonderful architect i might be conveying my idea in the form of a sketch but can we construct a building out of this representation of my idea most often we will not be able to do that because there are no dimensions attached with it there is no other information majorly we talking about the dimensions of course other details like what the material is going to be how those minor details of joinery and things going to come up but other than that if even if it is like a 3d thing for example a furniture we know it this furniture is going to be manufactured in wood ok the material is clear but still with the help of just sketch can we really make it can we really manufacture it no we would need dimensions that is where isometric projection comes handy because this is the projection system where it allows us enables us to view a certain idea in the form of a three dimensional picture three dimensional object plus it has the possibility to add dimensions to add measurement on top of that that is why isometric projection and we also have exonometric projection but isometric projection is very common its popular is used in engineering and architectural drawing so what we're doing going to do in this course is learn how to draw this isometric projection and as a prerequisite i expect that all those students who are going to learn this course learn the contents of this course are familiar with orthographic projection that is something that you have to know you have to know how to read two dimensional drawings which have to be converted into this isometric drawing so we will start with this isometric projections so what is an isometric projection it is a type of pictorial projection in which all the three dimensions of an object are shown in one single view and if required their actual sizes can also be measured directly from it so as i said as i just explained it is not just a pictorial representation there is a possibility of measuring dimensions directly from the object which is drawn in isometric projection this is one example of this isometric projection so this is a block maybe some machine block now we can very clearly see that how this machine block is we can look at the slanting line slanting surfaces we can see these horizontal vertical all these combination of surfaces and in addition to that we also have these dimensions which are associated this is an isometric projection now how do we really derive this isometric projection is what we would have to see first now assume that we have a cube so this is the cube now if i place this cube and just assume that there is a vertical plane so you are familiar with what a vertical plane is what a horizontal plane is and what a side plane is so assuming that between the camera and mean there is a vertical plane okay transparent vertical plane and beneath this block we have a horizontal plane which is flat now i have kept this cube in a rotated manner which is where its base is flat it is resting on h b horizontal plane but its one of its edges is parallel to vp and it is perpendicular to hp so it is kept rotated at 45 degrees now what we have to see here is that there is a body diagonal of this cube which is going to be made perpendicular to vp what a body diagonal is that if i connect this point in the bottom to this point on top this is a body diagonal one of the body diagonals now if i have to make this body diagonal parallel to h p and perpendicular to vp what do we do so the first step which is what you can also see on your screen so the first thing that we will draw in orthographic projections which is what you have already seen is this cube kept in simple position so what we have here this is 45 degrees so what we see here so we have this a b c d on top which is a b c and d on top and e f g and h in the bottom e f g and h in the bottom and this cube is kept such that it is making an angle of 45 degree one of its surfaces is making this angle 45 degree rather all of them would be making this angle 45 degree and this is the body diagonal which is connecting e to c so this is in elevation you can see it very clearly in plan it will still appear to be a straight line which is parallel to vb so this is this body diagonal ec so now what we have to do is we have to make this ec perpendicular to vp and parallel to hp of course it will come out like that so the second step of this is that i rotate this cube on this point on this vertex by certain angles such that this body diagonal is now parallel to hb as well as vp so what we did here is that we are rotating it about say g here g is the point in the bottom so we rotate it like this so we will first be seeing this rotation happening in the elevation because very simply we will be seeing this rotation this angle in vp and that is what we do all the time that when we have a double rotation coming we first do it in one of the planes and then bring it down to the other plane or vice versa here seeing it in elevation is easier so we'll be doing it there so what we have done whatever this angle was if we rotate this particular image this particular image by this say x degrees we will get this e c coming to be parallel to h p and v p both so what we have done here is about this point we rotated it like this now you must be seeing it from the front from that side and this is what we are seeing here in the in the bottom in the plan so we first rotate this entire rectangle its exactly the same its just that this angle which was here has been so this is the same angle x degrees so we get this this is how so this is the line which is parallel to h p and v p and we just move this picture this rectangle and all the associated lines like like this ok so this is what we have got now we project it back so we take the projectors just as we always do in orthographic projection we bring it down all the points and this is what we get so this is a b c d this is the top square which we are seeing this is e f g h and what we had as a as a diagonal we had e c so this is e and this is c now you can see this e c is parallel to h p and v p which is what we are seeing here also now what do we have to do we have to rotate this in such a manner that now this e c is perpendicular to v p and remains parallel to h p if any line is parallel to hp where would you be seeing it you would actually be seeing it in the vp and if it is perpendicular to vp you will be seeing it in the hp so we further rotate it rotate this entire thing so we rotate this entire thing in by say 90 degrees so that this ec becomes perpendicular and what we get as as a result is this particular object you can draw it and you can verify so what we will actually be getting is this these two angles coming to be 30 degrees each each of this one being 60 degrees okay and this is the same square abcd which is now become a rhombus so it has shrunk and the same is with this bottom one same as with these vertical squares which have now which are now appearing as rhombuses this is the isometric projection which we are seeing now if we have to derive the dimension of this square further so i am just taking so this is this image which is here i am just taking it here okay so what we had we had this a b c d these four points this is the top square and we also have this e f g and h which is the bottom square so what and these angles i told you this is 30 and this is 60 you can draw and you can verify now what we have is this is the resultant one which is actually the isometric projection now what we will do about this diagonal bd we can make the original square so we can actually make it like this which is going to be the actual square but we will just have it have it like this the actual dimension of the square so this is the true length right so this is the true length and this is the isometric length so this dp is the true length this d a is the isometric length and this d o rather db is the diagonal the diagonal of the square which is in question this abcd now if we look at this triangle ado so we know that this entire angle is 45 half of 90 and here this one is 30 so this is 30 the remaining one becomes 15. so if you apply trigonometry here you will find out so you can go through this entire calculation d a by d o d p by d o cos 30 cos 45 and eventually what we have to do is we have to arrive at d a by d p which is 0.815 approximately 9 by 11 parts so the isometric length is reduced slightly reduced from the true length by a factor of zero point eight one five or nine by eleven times so this is the what you get out of here this particular is the isometric scale now why are we doing this is because isometric projections are capable of giving us measurements and dimensions so we can do that we may not want to do that if we have a supporting orthographic projection with us but we may want to do that if we want to just represent everything within this isometric projection and it is very much possible so if you look at this scale so i have again this part this part i have taken it to be here do not go by the nomenclature but so we have this isometric length this is the true length this is this diagonal so we know this is 30 this is 45 and we know how what connection is this now all i am doing here is when you are drawing this isometric scale that we will take this true length which is a b and at 15 degrees we have this isometric length which is ac so we know this is what this is 15 degrees this is 45 degrees and once we draw this isometric scale if we are drawing this isometric scale so you will simply take a line whatever unit you are using you could be using centimeters or whatever so we make this we connect it it's simple using set square so you just set your set square to 45 degrees and here 15 degrees and wherever it intersects at every at every division we will draw these parallel lines so these are 45 so whatever diminishing has to happen will happen here and we would know that if the actual dimension the true length is this whatever and we will get the corresponding isometric length this will be used all the time when we have the intention of measuring the dimensions on isometric projections this is the scale that we are going to use this is your isometric scale so when we are talking about isometric projections we have to talk about we have to first make this isometric scale however all the time you would not be requiring this isometric scale and i will tell you where why you would not be needing this isometric scale okay now before we go about discussing why and where you will not need this isometric scale let us understand about these lines some fundamentals about the isometric projection so there are certain rules of isometric projection which you have to keep in mind and we will pract as we will practice along you will practice along with me these will become formed in your minds related to isometric projection so first things the lines that are parallel on the object are parallel in the isometric projection i can show you this example if we go back to this let us take this one so if you look at this assume the original cube so this was parallel to this was parallel to this and this was parallel to this so there were four edges which were parallel to each other which may be parallel to one of the reference planes us look at the other one this is parallel to this is parallel to this and parallel to this you will see all of them parallel in isometric projection also so if there is a set of lines which is parallel in the object they will appear as parallel in isometric projection also same as with these vertical ones one two three and four you get all these twelve edges which so four four four which were parallel to each other are also seen as parallel in this isometric projection okay so that's the first rule parallel lines in the object remain parallel in isometric projection the second one vertical lines on the object appear vertical in the isometric projection i just showed you that i will go back to the same object so these were perpendicular so these were vertical lines the vertical lines will appear as vertical in the isometric projection so if an object is there which is kept perpendicular you will see these perpendicular lines these vertical lines appearing as vertical lines in the isometric projection that is the rule number two the third horizontal lines on the object are drawn at an angle of 30 degree with the horizontal in isometric projection and the ones which are on the up the other axis they will appear at minus 30 say so just anti-clockwise which is again something that you are seeing here so say this was x so things which are parallel to x will be seen at 30 degree and the the ones which are perpendicular but in the same plane will be seen making another angle 30 degree but from the reverse direction this is what we will see so parallel lines perpendicular lines and the lines which are parallel to axis these three are the most basic fundamentals which we have to keep in mind don't worry we will be practicing a lot of example of all different types of objects and 2d objects 3d objects kept in different positions and we will be seeing how these rules are applied and how do we make these isometric projections the fourth one is about the true length and isometric length which is what we know that it is shortened to approximately 82 percent which is what we will be seeing every time we are going to make an isometric projection okay now there is a slight difference between isometric drawing and isometric projection isometric drawing and isometric projection are very ah they are actually similar the only difference being the scale that we are using now in isometric projection what we are doing is we are using isometric scale to draw to measure the length that we have used so suppose we have the same object i am taking the same object here suppose this is say 2 units and this one here is four units the height being one unit okay and this is say one just i am just assuming again one and this total height being say five units ok suppose this is the object now what we would do in isometric drawing so usually what happens is we already have the dimensions coming through the orthographic projections so the dimensions are going to be measured in 2d drawings orthographic projection but just for the sake of clarity for understanding better visuals we will be drawing an isometric drawing here where we are not measuring yet we can measure out of it and it is very simple that we will just take the true length that's our isometric drawing okay so we will you be using the true lengths here in isometric drawing while in isometric projection we will be first drawing this isometric scale which we just saw at 15 degrees and 45 degrees and we will be using those diminished lengths those shortened lens as per this isometric scale and this is what we will be using now when we are drawing using isometric drawing versus isometric projection the isometric drawings will be slightly enlarged okay the isometric projection drawing will look very realistic so if you measure it you will actually be getting at the real dimensions but in isometric drawing we are just using directly true lengths and measuring the same which is fairly possible we are just not reducing these lengths okay for all practical purposes you would see when ah we practice in the profession that we use isometric drawing because it's quick it's faster every time if i have to say draw two units of true length and if i get to convert it to isometric scale so i will be multiplying two by zero point eight one five and i arrive at certain ah dimension which is say not possible to measure by scale so we will just be using the ah the graphical scale of isometric scale and then measuring and using so it becomes little t tedious so to avoid that and to make our work faster we use these direct true length dimensions on isometric projections and then it is called isometric drawing it does not remain isometric projection that is very common thats very practical and we use this isometric drawing in addition to the orthographic projections ok so these two are put together read together and the final drawing the understanding of the concept and idea through this means is communicated so if we look at some little examples it will become clear of course we will be dealing with these examples in detail from the next lecture onwards but i will just give you a glimpse of how this isometric drawing will be done so let us take this very simple cuboid so we have this cuboid which the dimension of which is given here we can assume any scale we can reduce of course we will have to take the scale so 30 centimeter by 60 centimeter by 90 centimeter now if you look at this depending upon how it has been kept we will be drawing this isometric drawing here so what we have is we have this one rectangle here another one which is here and this third one so what we simply ah suppose i assume that this edge is actually parallel to x axis so i say 60 assuming this is equal to 20 units each 60 on this one 30 on the other side so one and a half 30 on the other side now i am not drawing the one at the back because this is going to be a hidden line and 90. so this is 80 and 1090. so this is the one which is perpendicular so this is parallel to x parallel to y and this is z so ok actually we are looking at this point as being the origin so we make it like this 60 30 90 approximately and then i mark the points on the top okay so we again have this like this okay and this is the object that we get in isometric drawing so the scale may vary i am using this grid as the scale you may have a certain separate scale which you may use just as we did for orthographic projections you can assume your scale and you can draw now for the hidden ones we will just take these dotted lines ok this is the same concept as we did as we used when we did orthographic projections so the hidden lines and we very clearly know that this is the object that we are talking about suppose it was kept in a different position we might also be seeing something like this right so we may also see the same object being seen like this right and then we will have these hidden lines coming so just as orthographic projection the type of lines that you use here in isometric that becomes important because you will be seeing some things in the front and some things will actually be hidden so we have to clarify we have to make it very clear what is seen in the front and what is actually going behind you can look at certain other examples now so ok so one more thing which you have to understand here is the difference between isometric lines and non-isometric lines so all the lines edges in 3d objects and in 2d the planar surfaces the lines which are parallel to either of the three axis ok these are isometric lines okay so these edges which are parallel to x these edges which are parallel to say y this is the simplest example but we will go on to the other one and this is parallel to this z so these are isometric lines we may also have non-isometric lines so for example look at this particular drawing so this is the ortho given now if i have to convert this ortho into an isometric drawing ah we will start so this one is front elevation now we just assuming that this front elevation is parallel to vb so let us let us look at this and this is 60. so i will start from the the top drawing so this is approximately i am just approximately taking these dimensions you will have to measure it every time you draw okay so suppose i have this now i do not know how this slant line is going to come or what its dimension is but i surely know the dimension of the other lines right so which is what i will continue to make so this is how they have made it this is easy so we did that now if you look at it from the top this is what we are seeing so we can arrive at this one this line right similarly you can arrive at the lines in the in this part of the object right now we know that in between these there is something which is connecting this point to this point and this point to this point and we will just draw these points now you can see the principles the basic fundamentals of isometric projection being reflected very clearly so the lines which were parallel remain parallel right and even if we were to draw the hidden one we will actually be seeing this right these hidden lines this is parallel this is parallel this is parallel they may be at any different level but they remain parallel if they are parallel in the object they remain parallel here these are all isometric lines the vertical ones so this is z right these are all parallel now what about the slant lines they were not parallel to any of the axis yet since they were parallel they are actually seen parallel here so you can see these non-isometric lines right these two lines and if your drawing is correct if your projections are taken correctly you will get these to be parallel which is what we have got here ok so any lines which are parallel in the object are seen parallel the ones which are parallel to the axis will actually be seen parallel to the axis the ones which are not which are these non isometric lines can be derived out of the other dimensions in case we do not have any reference for these we will have to create reference ok so we will actually have to create reference for example suppose this one was just becoming something like this ok so what we would have had we would have had another line here now how do you arrive at this one we have no reference so what we would do we would actually go back to the orthographic projection we would create a reference so this is the reference what is the height what is the distance and accordingly we will actually measure this arrive at this point join this say join this and we will accordingly arrive at any other point which is not easily derivable through the major axis which we are following so that is all for the lecture today i hope with this you are clear with the fundamentals of isometric projection from tomorrow onwards from the next lecture onwards we will actually be starting to look at the examples the simple examples to start with i will not start with the projection of lines in isometric projection we will directly start with planes because you have already i am assuming that you have already understood how orthographic projection works so we will directly be starting with planar objects ok so we will be starting with quadrilaterals and polygons first we will not be taking the curves and gradually we will move on and we will graduate to the level of 3d objects in various different positions so thank you very much for joining this lecture with me today see you again for the next lecture bye [Music] [Applause] [Music] [Music] you