Examples On Sections And Developing Of Solid | Application Of Projections Of Solid.
Examples On Sections And Developing Of Solid
Engineering Application Of Projections Of Solid.
1 ] A pentagonal prism, 30 mm base side & 50 mm axis is standing on hp on its base whose one side is perpendicular to VP. it is cut by a section plane 45º inclined to hp, through midpoint if axis draw FV, sec.TV & sec. side view. also draw the true shape of section and Development surface of remaining solid.
Solution steps:
For section views:
Draw three views of standing prism. Locate sec. plane in FV as described. Project points where edges are getting cut on TV & SV as shown in the illustration. Join those points in sequence and show section lines in it.
Make the remaining part of the solid dark.
For True shape:
Draw x1 y1 || to sec. plane Draw projectors on it from cut points. Mark distance of points of sectioned part from TV, on above projectors from x1 y1, and join in sequence. Draw section lines in it. It is required true shape.
For Development:
Draw the development of the entire solid. Name from cut-open edge I.e. A in sequence as shown. Mark the cut points on respective edges. Join them in sequence in st. lines. make existing parts dev. dark.
2 ] A cone, 50 mm base diameter and 70 mm axis is standing on its base on HP. It cut by a section plane 45º inclined to Hp through base end of end generator. Drae projections, sectional views, the true shape of section and development of surface of remaining solid.
Solution steps:
for sectional view:
Draw three views of a standing cone. Locate sec. plane in FV as described. Project point where the generator is getting cut on TV & SV as shown in the illustration. Join those points in sequence and show section lines in it. Mke remaining part of solid dark.
For True shape:
Draw x1 y1 || to sec. plane Draw projectors on it from cut points. Mark distance of points of sectioned part from TV, on above projectors from x1 y1, and join in sequence. Draw section lines in it. It is required true shape.
For Development:
Draw the development of the entire solid. Name from cut-open edge I.e. A in sequence as shown. Mark the cut points on respective edges. Join them in sequence in curvature. Make existing parts dev. dark.
3 ] A cone 40 mm diameter and 50 mm axis is resting on one generator on HP(lying on HP) which is || to VP. Drae its projections. It is cut by a horizontal section plane through its base center. Draw sectional TV, development of the surface of the remaining part of the cone.
4 ] A hexagonal prism. 30 mm base side & 55 mm axis is lying on HP on its react. face with axis || to VP. It is cut by a section plane normal to HP and 30º inclined to VP bisecting axis. Draw sec. Views, true shape & development.
Use similar steps for a sec. views & true shape.
NOTE:- for development always cut open object from an edge in the boundary of the view in which sec. appears as a line. Here it is TV and in boundary, these are c1 edge. Hence it is opened from c and named C, D, E, F, A, B, C.
5 ] A solid composed of a half-cone and half-hexagonal pyramid is shown in the figure. It is cut by a section plane 45 inclined to HP, passing through mid-point of axis. Draw F.V, sectional T.V., the true shape of section and development of remaining part of the solid. (Take the radius of cone and each side of hexagon 30 mm long and axis 70 mm)
NOTE: FV & TV 8f two solids sandwiched section lines style in both: Development of half cone & half pyramid:
6 ] Draw a semicircle of 100 mm diameter and inscribe init the largest circle. If the semicircle is a development of a cone and the inscribed circle is some curve on it, then draw the projections of cone showing that curve.
Solution steps:
Draw semicircle of given diameter, divide it into 8 parts, and inscribe in it the largest circle as shown. Name intersecting points 1, 2, 3, etc. Semicircle being dev. of a cone its radius is the slant height of the cone. ( L) Then using the above formula find R of a base of the cone. Using this data draw FV & TV of cone and from 8 generator and name. Take o-1 distance from dev., mark on TL i.e o' a' on FV & bring on o' b' and name 1' similarly locate all points on FV. then project all on TV on a respective generator and join by a smooth curve.
7 ] Draw a semicircle of 100 mm diameter and inscribe in it the largest rhombus. If the semicircle is the development of a cone and rhombus is some curve on it, then draw the projections of cone showing that curve.
Solution steps:
Similar to the previous problem.
8 ] A half cone of 50 mm base diameter, 70 mm axis, is standing on its half base on HP with its flat face parallel and nearer to VP. An inextensible string is wound around its surface from one point of base circle and brought back to the same point. If the string is of shortest length, find it and show it on the projections of the cone.
Concept:
A string wound from a point up to the same point, of shortest length must appear st. line on Its development.
Solution steps:
Hence draw development, Name it as usual and join A to A This is the shortest length of that string. Further steps are as usual. On dev. name the point of intersections of this line with Different generators. Bring those on FV & TV and join by smooth curves. Draw 4' a' part of string dotted As it is on the backside of the cone.
9 ] A particle that is initially on the base circle of a cone, standing on HP, moves upwards and reaches an apex in one complete turn around the cone. Draw its path on projections of a cone as well as on its development. Take base circle diameter 50 mm and axis 70 mm long.
Its a construction of curve Helix of one turn on cone:
Draw FV & TV & dev. as usual on all from generators & name.
Construction of curve Helix:
Show 8 generators on both views Divide axis also in the same parts. Draw axis also in the same parts. Draw horizontal lines from those points on both end generators. 1' is a point where first horizontal line & gen. b' o' intersect. 2' is a point where second Ariz. Line & gen. c' o' intersect. In this way locate all points on FV. Project all on TV. Join in curvature.
For Development:
Then taking each points true Distance from reps. generator from apex, Mark on development & join.
