 Hello, I am Mr. D.J. Doshi, Assistant Professor, Department of Mechanical Engineering, Valshan Institute of Technology, Solapur. Today, we will be learning about projection of solids. At the end of this session, students will be able to draw the projections of solids as per given conditions. Now, this is the given problem. Draw the plan and elevation of a cube of solid diagonal 80 mm length when the solid diagonal is perpendicular to the VP and the corner of the cube is in HP. Initially, we will first discuss about what is plan, what is elevation. Now, plan is a top view, elevation is a point view. So, this word we have not yet come across. So, plan is the top view and elevation is the front view. Now, later on cube we know of which all the faces are square, cube is a all the faces are square where there are 4 plus 2, 6 faces and what is solid diagonal. Solid diagonal is a diagonal drawn across as a diagonal joining the line opposite corners of different faces that is base and face and the corners opposite to each other will be joined. So, it will be called as a solid diagonal. Now, here the length of the solid diagonal is given as 80 mm. So, how will you calculate then the base edges? So, for that the formula is length of solid diagonal is root 3 into base side. So, this is the formula you have to remember if you are attempting the problem related to solid diagonal. So, solid diagonal is equal to root 3 into base edge length then the problem becomes simple. Now, we want the solid diagonal to be perpendicular to VP and the corner of the cube is in HP. So, here from this we will understand that its top view will be a square and the front view will be a rectangle. Now, while drawing the square we have to draw in such a way that the solid diagonal must be parallel to the HP when we will go for second stage. So, that is 1 3 will be the solid diagonal which will be parallel to HP in second stage. So, here you have to draw the top view in such a way that the base edges will be making angle equal angle or 45 degree angle with VP. So, we have drawn a square as a top view here. So, base 3 4 is making 45 degree and 1 4 is making 45 degree. So, we have to draw a square in such a way that all the base edges will be making 45 degree with VP. So, project it upwards that is project 1 upwards, project 2 and 4 upwards and project 3 upwards. You will get a top view of the same height again that is which we have calculated that that is 80 is equal to root 3 into base edge. So, base edge will be equal to 80 divided by root 3. So, that length we have calculated. Now, see sometimes we will name the top face as A, B, C, D and the base as 1, 2, 3, 4, but here we have given the names as 1, 2, 3, 4 both. So, 1, 2, 3 is a base, 1, 2, 3, 4 is a base and 1, 2, 3, 4 is a top surface. Now, we have drawn the projections 1, 1 dash will be equal to the length we have calculated base edge. Similarly, 3, 3 dash will be of same length 2, 2 dash and 2, 4 dash will be of the same length. So, a completed rectangle which will be a front view of a cube. Now, what is solid diagonal as I told you it is a diagonal joining the corners which are opposite or diagonally opposite to each other on different faces. So, this is the base and this is the top face of which 1 is on the base and 3 is on the top face which will if we join this 1, 3 it will be a solid diagonal. So, I have joined the solid diagonal as 1, 3 and completed the front view. So, now of course, 1, 3 will be a thin line as it is a construction line. Now, what is first second stage that is solid diagonal is perpendicular to V p. So, to make it perpendicular to V p we will rotate the front view in such a way that the 1, 3 or 1 dash, 3 dash will be parallel to H p and perpendicular to V p. So, now here we will rotate in such a way that of course, another condition is the corner must be on H p. So, the corner is on H p. So, 3 dash will remain on H p and we will rotate in such a way that the solid diagonal will be parallel to H p and perpendicular to V p. So, now the difficult part here is construction of the front view or rotation of the front view to get the 1 dash, 3 dash parallel. So, for that what we have done 1, 3 is a solid diagonal we have drawn a perpendicular from 3 dash to the solid diagonal. So, here we will take a point on x y line that is 3 dash draw a line perpendicular to it of the same length that is 3 dash and this length and draw a horizontal line or a perpendicular line to it such a way that this distance will be equal to this distance here and this distance will be equal to this here and join the edges and complete the view such that the solid diagonal is parallel to H p. Now, project it upwards, project it downwards, 1 project it downwards and accordingly we will project 1, 2, 3, 4 of the base and 1, 2, 3, 4 of the top face downwards. Now, here when we join the points 1, 2, 3, 4 as a base and 1, 2, 3, 4 as a top face if you observe now the observer is from here observing from here. So, this will be totally visible. So, the top face will be totally visible to the observer. So, we will join 1, 2, 3, 4 as a dark line. Now, when you observe from here this 1, 2 and 1, 4 will be also visible. So, 1, 4 and 1, 2 is joined with a dark line join 4, 4 dash 1, 1, 1, 1 and 2, 2. Now, as the point 3 is away from the observer the lines related to 3 will be dotted lines. Now, what are the lines related to 3? It is 3, 4, 3, 2 and 3, 3. So, while drawing we have to draw these lines 3, 4, 3, 3 and 3, 2 as dotted lines. Now, why these are the lines dotted lines? You think over it as we have observed it from the top the point is away from the observer is 3. So, lines related to 3 will be dotted. Now, next part so this is related to HP that is the corner is resting on HP and of course this is made parallel to HP. Now, our next step is the solid icon is perpendicular to VP. Pause the video and think it that how we can make the solid diagonal perpendicular to VP. Yes, now see what is the solid diagonal? 1 dash, 3 dash. So, here it is 3 and here it is 1 ok. So, this one and this 3 if you join this is called as a solid diagonal or top view of a solid diagonal. Now, we have to make it perpendicular to VP. Now, as this 1 dash, 3 dash is parallel to HP of course this here 1, 3 will be the true length line. So, there is no necessity to think of whether the true solid diagonal is true or not. So, it is of course true length line. So, we will make it perpendicular. So, now here we will rotate this top view of the second stage such that 1, 3 will be perpendicular to VP. So, we have rotated it such that 1, 3 is perpendicular to you, redraw this case same again. So, take a point 1 here draw a 1, 3 perpendicular to it draw the required angles and all these things we have to copy it here accordingly we will make the line. Now, here also 3, 4 and 3 to are dotted. So, here I have drawn 3, 4 this one and 3, 2 and 3, 3 as a dotted line. Now, I will project 2, 2 dash here 2, 2, 4, 4, 3, 3 and 1, 1 above projected horizontal. So, 1 dash and projector from 1 we will get 1 dash of the top face, 2 dash and 2 from here. So, you will get 2 dash of the top face, 4 dash and 4 from here you will get 4 dash for the top face and remaining is 3. So, 3 is also projected from here of course, that will be on the same line 3, 3 and 1, 1 are on the same line. So, 3 dash you will get here. So, I will join 1, 2, 3, 4. Now, as we are observing from this side the lines which are related to 1 will be dotted. See because you are observing from here 1 is away from the observer. So, 1, 2 and 1, 4 and 1, 1 will be dotted lines. So, now this is the bottom face. So, we have projected it upwards we project it horizontally. You will get again 1, 2, 3, 4 or 1 dash 2 dash 3 dash 4 dash join accordingly. Now, this face related to this will be a dark line. Again as I told you as this point 1 is away from the observer. So, this one and this one will be the dotted line. So, 1 dash, 1 dash then 2 dash, 4 dash and 2 dash, 2 dash will be the dotted lines. So, join this with the dotted lines and other thing will be joined as the dark line. So, this is the final view of the cube. So, this is the A TMM whose solid diagonal is perpendicular to V p and whose corner of the base is resting on H p. So, this for this referral book engineering drawing by Mr. P H Jane. Thank you. Thank you.