 Hello, I am Mr. D. J. Doshi, Assistant Professor, Department of Mechanical Engineering, Valgen Institute of Technology, Solapur. Today we will be studying 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, if you read this problem, a cone with 40 mm diameter and 60 mm height rests on HP such that the base is inclined at 30 degrees to horizontal and top view of the axis is inclined at 44 degree to vertical plane, draw its projections if the apex of the cone is away from the observer when viewed from front. Now, this is a three stage problem, so initially we will study about a cone with 40 mm diameter and 60 mm height resting on HP. So, when the cone is resting on HP means its top view will be a circle of diameter 40 and the front view will be an isocidal triangle of height 60 mm and base 40 mm. So, draw a circle as a top view with radius 40 mm sorry with diameter 40 mm and project it upwards. So, project it upwards to get the triangle, so center will be projected up at a height of 60 mm, you will get the apex of the cone join those with the diameter projected upwards and you will get the triangle isocidal triangle of height 60 mm and base 40 mm and top view will be a circle. Now, for the convenience of drawing the second stage, we will divide the circle into 12 parts. So, we will divide the circle into 12 parts in such a way that each angle will be 30 degree, of course these are all construction lines. So, we will divide the circle into 12 parts, project those points upwards. So, if you observe from top 1, 2, 3, 4 clockwise direction we have given the numbering till 12. So, it is 1, 2, 12, 1, 2, 3, 4, 2, 12 and then project upwards, so 10 and 4 will be on the base and accordingly the numbers will be given that is 1, 2, 3, 4, 5, 6 and so on. So, the top view of the circle will be a line resting on HP with 1 dash, 2 dash, 3 dash, 4 dash and accordingly projected points. Join those points with thin lines with the apex, why the thin lines should be there? Because these are all generator lines, so only slant lines both sides slant lines and base will be dark, other lines will be the generator lines, so those will be thin lines. So, now first stage, so for first stage as the triangle is resting on HP or the cone is resting on HP, we will incline the triangle or a cone front view such that, what is the inclination? The inclination of the base is at 30 degrees, so we will incline the cone or the triangle in clockwise direction such that base will be making 30 degree. Now, if you observe this angle is 30 degree, so this angle will be 30 degree, redraw this triangle or the cone front view of the cone and again name in the same fashion. So, apex will be O dash O here and from here 1 dash, 2 dash, 3 dash, 4 dash, 5 dash and so on till 12 dash and again 1 dash, this is the center line or the height line what is called as. So, it will be drawn as a center line and the base is making 30 degrees. Now, project upwards from the front view projected downwards O dash will be projected downwards O will be projected horizontally you will get O which is again the apex when observed as a front view for first stage. So, this is the front view, now when we will observe the front view from the top it will be get a top view. So, it is O and project 1 dash to 12 dash, so all the 12 points will be projected downwards and 1 by 1 suppose now 1 is projected horizontally, 1 dash will be projected vertically we will get 0.1, then 2 dash will be projected downwards, 2 dash will be projected horizontally we will get 2 and so on we will get the 12 points. Now, the question arises which of part will be drawn as a dotted line or which is the part away from the observer. So, when you are observing from for the top view the point 4 or 4 dash is away from the observer which must not be or may not be visible. So, the line related to 4 dash will be dotted line. So, when we will get the point 1, 2, 3, 4 so on we will join the part or we will join the with a thick line this part that is which is visible part that is from here 1 dash to 10 dash and so on. So, this part will be a dark line then join those points with O, so O 1 and O 7 and later on the remaining part will be drawn as a dotted line because it is not visible when we are observing in the first stage top. So, now we have a first stage solved this is first stage this is second stage. So, here the first stage is the front view and top. Second stage is the base inclined at 30 degree to H P and accordingly we are projected downwards. Now the main part which is not studied up till now is droids projection if the apex of the cone is away from the observer when viewed from front. So, this is the second stage top view now for the front view next for front view we will be observing from this side. So, here the apex must be away from the observer means this apex will go away from the observer. So, this if it is rotated in anticlockwise direction this will be away from the observer if the apex is drawn towards this side this will be towards the observer. So, redraw this top view in such a way that the top view of the axis. So, here the top view of the axis is making 45 degree to H P. So, draw an angle angular line at 45 degree now as it is given clearly that top view of the axis is inclined at 45 degree there is no necessity to draw a true length locus and all these things only we will be drawing the top view on the line which is making 45 degree. So, mark point O here from their O O dash is the top view length that is this length O dash is this length then O dash will be drawn here then draw perpendicular lines 1 2 3 4 and 5 on these respective distances. So, these are the distances on which you will be drawing perpendicular lines here on the same distances and mark the points 1 2 3 4 till 12. So, again we will be redrawing this sketch of which the top view of the axis is making 45 degree with V P. So, here the V P angle is drawn on this top view length is marked again perpendicular to this lines will be drawn which are construction lines and respective distances will be marked on this. So, this total elliptical part will be redrawn here apex is already there. So, join the apex with this redrawn sketch or ellipse this part will be dotted because this is already dotted in here then we have to project it upwards. So, here project 1 upwards project 1 dash here horizontal you will get point 1 dash again 2 dash to 2 will be projected of course 2 dash will be projected horizontally and so on we will go on plotting all the 12 points here. Now, if you observe here when you are observing from this side the base of the cone is nearer to the observer is nearer to the other and apex is away from the observer. So, this part will be totally visible. So, here if you observe the when we join the points 1 to 12 or 1 dash to 12 dash the ellipse you are getting will be dark ellipse you are getting will be the dark ellipse because the base is towards the observer and this apex when we are joining as the external lines or the peripheral lines are never drawn dotted from O dash will draw it tangent to the ellipse here and tangent to the ellipse here and this will be drawn O dash will be vertically projected upwards O dash will be projected horizontally will get O dash. So, O dash O 1 dash O dash O dash will be the center line and other generator lines of course will be drawn as thin lines. So, here specifically it is given as O is or the apex is away from the observer. So, we have drawn accordingly and projected upwards and one more thing here if you think of why we are drawn the top view line or the line making angle with the HP as a two length line of the axis because think over it because here it is specifically given that top view of the axis is making 45 degree. So, the top view of the axis will be at 45 degree and we have constructed this projected upwards draw the generators you will get the final view that is third stage view when the apex is away from the observer making for top view of the axis is making 45 degree with VP and base of the cone is making 30 degree with HP. So, for this I have used engineering graphics by Mahalakshmi publication house. Thank you.