 Hello, I am Mr. D. J. Doshi, working as assistant professor, Department of Mechanical Engineering, Walsh University of Technology, Solop. At the end of this session, students will be able to draw the projections of solids as per given conditions. So, we will solve simple problem, first problem, pentagonal prism, side-off base of the TMM, axis 60 mm, rests on one of its corner of the base on HP and axis makes an angle of 40 degree with HP, draws projections when the side-off base opposite to the corner is in HP, remains parallel to HP and perpendicular to Vp. So, before going for second stage, we will draw a first stage as it is given that axis is making 40 degree with HP, so we will be rotating or inclining the solid such that the axis is making 40 degree. So, prior to that, we will consider that axis is perpendicular to HP and parallel to Vp. So, now as it is resting on HP, its top view, when we observe from the top, its top view will be a pentagon and front view will be a rectangle. So, while drawing a pentagon, you have to take care that whether the corner will be towards right hand side or towards left hand side. So, in this case, as one of its side is parallel, we will be drawing the corner towards your right hand side such that the line drawn from the corner and perpendicular to the base side will be parallel to XY line. So, pentagon, while drawing pentagon, you have to take care or while drawing top view, you have to take care that corner of the pentagon is towards your right hand side. So, draw a pentagon 1, 2, 3, 4, 5. Now, front view, for drawing front view, we will project one upwards. Axis height is given as 60 mm, so we will complete 60 mm height line that is 1 dash 1 dash, again 2 and 3, projector through 2, draw a projector through 2, complete it as 2 dash 2 dash, 3 as 3 dash, 3 dash, 3 dash, 4 as 4 dash, 4 dash and 5 dash will be on the same line. So, we will complete a rectangle such that it will have a height that is axis height as 60 mm and base will be equal to the pentagonal top view. So, this is completion of a first view. Now, second stage is such that angle is making 40 degree with HP, axis is making 40 degree with HP. So, we will draw axis making 40 degree or else another shortcut is that when axis is making 40 degree, the base will be making 50 degree with XY or with HP. So, better take a point resting point on HP or on XY line from there draw a base that is line through base at 50 degree and then draw the axis or draw an axis such a way that you will be drawing the prism front view that is a rectangle we will be copying from the first stage in such a way that the base is making 50 degree or axis is making 40 degree and complete the second stage front view that is redrawing the same view when axis is making 40 degree with HP. So, complete the rectangle now project it downwards. Now, if when you are observing from the top that is from here this total view will be visible. So, draw vertical projects from 1, 2, 3, 4 and 5. So, when you are drawing a projectors from 1 to 2, similar projectors you will draw horizontally from 1 and 2, you will get the intersection point 1 here, 2 here for the bottom phase, 1 here and 2 here for the top phase. Similarly, you will draw the projectors from 3 and 5, so draw vertical projectors from 3 dash 5 dash and draw horizontal projectors from this 3 and 5. So, you will get here 3 and 5, similarly you will get 3 and 5, this will be representing the top phase, this points will be representing the bottom phase. Similarly, project 4 which is resting on HP downwards draw horizontal projectors through 4, now which lines are to be dotted lines, so when observer is from this side, observer is observing from this side, the point away from the observer is 0.4, so the lines related to 0.4 will be dotted line. So, if you observe there are 3 lines through 0.4 that is 4, 4 dash, 4, 5 and 4, 3, so those lines will be joining other dotted lines, so this is 3, 4 and 4, 5 and this is 4, 4 dash. So, these 3 lines are dotted lines because those are not visible from this side and complete the projections, so this is about 2 stage problem. Now, we will switch over to another problem which is a pyramid, so a square pyramid of 40 mm edge of base and 60 mm axis length is resting on one of its triangular phase on HP, draw the projections of the pyramid when edge of base contained by the triangle is perpendicular to VP. Now, here as it is resting on base edge, you have to draw as square base as a top U and a triangle as a front U because it is resting on HP. So, its top U will be a square, front U will be a triangle and in case of pyramid you have to take care that the generators are visible directly, so you can join O 1, O 2, O 3 and O 4. Now, what next step is given is triangular phase is on HP, now here these are the triangular phases 1, 2, 3 and 4, so you are tilting this triangular front U such that O 3, 4 which is a triangular phase that is this one O 3, 4 which is represented by this line will be resting on XY line. So, O 3, 4 will be resting on XY line that is triangular phase is resting on HP, then redraw this triangle here, project it downwards, now here again when you are observing from top 1, 2, 3, 4 will be totally dark, so 1, 2, 3, 4 will be visible, so it is dark. Now, point 3, 4 is away from the observer that is observer is here, so 3, 4 is away from the observer, so lines O 3 and O 4 will be dotted lines, other lines will be dark line. Now, accordingly you have to complete the view, now it is regarding to square prism which is resting on VP. So, when it is resting on VP, its top U will be visible as a rectangle, whereas front U will be visible as a square, because it is nailed on VP. So, when you observe it from the top, it will be visible as a rectangle and when you observe as a front U, it will be a rectangle. Now, what is given here, its corner is on VP, so you will be drawing the square in such a way that the corner is towards your right hand side. So, draw a square in such a way that the corner is towards your right hand side, project it downwards according to the axis length, draw this length and complete the top U of the square prism and this is a square of 40 by 40 by 40, this is drawn in such a way that this diagonal will be parallel to x y line and it will be when it is rotated, it will be resting on one of its corner. So, now, this is first stage, what is second stage, it is given that axis is making 30 degree with sorry, resting with VP. So, now, redraw this, so initially you will draw axis, which is nothing but a generator again. So, this generator you will draw at 30 degree or if you draw a 60 degree here, that is base is making 60 degree, it will be same. So, draw a 60 degree angle with the base, redraw this sketch here, so that this rectangle is drawn in such a way that axis is making 30 degree with VP or base is making 60 degree with VP, bottom base will be making 60 degree. So, this is redrawn, project it upwards. Now, the problem is related to when you will observing this for a front view, you will come to know that 0.3 is away from the observer. So, when you will observe from here the lines related to this 3 will not be visible. So, 3 3, 3 2, 3 4 and again 3 2 and 3 4 will not be visible. So, if you observe here this 3 dash 4 dash 3 dash 2 dash and 3 dash 3 dash are drawn as dotted line. When you observe from here, this total rectangle which is converted to rhombus will be visible, but base regarding base edge or base face, this point related lines will not be visible. So, you will be drawing these lines that is 3 dash 3 dash 4 dash and 3 dash 2 dash as a dotted line and complete the related. So, this is also called as two stage problem. Fourth problem is related to square pyramid. Now, it is resting on base. So, it is resting on VP and it is resting on base when it is tilted. So, you will be drawing the square as a front view, but in this case the side of the base or base edge will be towards right hand side because it is not resting on corner. So, you draw a square in such a way that the side of the base will be towards your right hand side. Again join O 1 O 2 O 3 O 4 projected downwards 60 degree mm is the length of the axis. So, join this and now again axis is making 30 degree. So, you will draw a 30 degree line. So, this angle is 30 degree. So, this angle also will be 60 degree. So, redraw it projected upwards. Horizontal projections and vertical projections are necessary to complete the projections. Now, in this case again if you observe 3 4 is resting on VP and the observer will not be able to observe the lines related to O and joining this point O 3 and O 4. So, while drawing take care that the lines which are here will not be visible. So, those lines will drawn as dotted line. So, complete the rectangle as the total rectangle will be visible and O 3 O 4 you will be completing accordingly. So, visibility is important part. So, the lines related to 3 4 will not be visible. So, accordingly I have drawn these lines as dotted lines and complete the projections. So, now as we have already studied now square pyramid square prism and so on. You can try it for the pentagonal and hexagonal parts as well as cylinder and cone accordingly. Thank you.