Problem 1

Projection of Solids – ABCD is a tetrahedron of 60 mm long edges. The edge AB is in the H.P. The edge CD is inclined at an angle of 300 to the H.P. and 450 to the V.P. Draw the projections of the tetrahedron.

Tetrahedron: It is a triangular pyramid shape with all six edges of equal length, here the length is given as 60 mm and height is not given, so we need to find it. Height can be found by one of the slant edges which will show true length in elevation and a parallel line to XY (reference line) in plan. Here it is CD slant edge which is shown as c’d’ in elevation and as cd in plan.

rocedure:

Step-1 Draw a horizontal x-y reference line of some suitable length.

Step-2 To draw edge CD inclined to H.P. at 300, we need to assume that tetrahedron is resting on H.P. through one its base edges AB. Draw plan and elevation of tetrahedron resting on H.P. through one of the edge AB which will be the first stage as shown in figure above.

Step-3 To find point d in plan we need to joint corners with their opposite edge’s mid point. At a point where all joint lines will be intersected should be denoted as “d”. And all rest points of plan and elevation can be founded by general projection procedure that we have already discussed in earlier projection of solids problems.

Step-4 Now its time to draw second stage of projection in which slant edge CD is making an angle of 300 with the H.P. Draw edge c’d’ from 1st stage elevation inclined to H.P. at 300 so that perpendicular bisector of c’d’ makes 600 with H.P. In such a way we’ll get an elevation for second stage in which tetrahedron’s edge cd will be inclined to H.P. by 300.

Step-5 To find out plan of second stage we need to project all points towards plan area or towards H.P. for reference. And reference of 1st stage plan will be used to track all point of 2nd stage plan. Join a’ with a, b’ with b and similarly find all point of 2nd stage plan.

Step-6 Except ab edge all other edges will be full thick and ab will be hidden in plan as it cant be seen from top when cd is inclined to H.P. by 300. This will complete second stage as both plan and elevation drawn.

Step-7 Now to draw last stage, we need to find out locus of c as actual slant edge is making an angle of 450 with V.P. not a plan of it.

Note: If plan of that slant edge (cd) makes an angle of 450 with V.P. then we can draw second stage’s plan length of cd directly inclined to V.P. by 450 but here in current data it is given as slant edge is making an angle of 450 with V.P. so we need to follow locus procedure.

Step-8 First draw a line with true length of slant edge (T.L. = 60 mm given) inclined to V.P. by 450 , give notations as per shown in figure above. Then extend locus of c2 parallel to XY reference line upto suitable distance. Now with d as center and radius equal to plan length of edge cd (cd line in second stage plan) make an arc on locus that gives intersection point c on locus of c2.

Step-7 Now the angle of line cd with V.P. will be denoted as β as it will shows virtual angle of actual slant edge when it is inclined to V.P. by 450.

Step-8 To find out last stage elevation we need to project all point of third stage plan towards elevation or towards V.P. area. Then find all projection intersection points as per general procedure. give notations as a’, b’, c’… as shown in figure.

Step-9 Except ac edge all other edges will be full thick and ac will be hidden in elevation as it cant be seen from front when CD is inclined to V.P. by 450. This will complete third stage as both plan and elevation drawn.

Step-10 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.

Problem 2

Projection of Solids – A cone of diameter of base 60 mm and axis length equal to 100 mm rests on one of its slant generators on H.P. such that its axis is inclined at an angle of 65° with the V.P. Keep its apex near to the V.P. and draw the projections.

Procedure:

Step-1 Draw a horizontal x-y line of some suitable length.

Step-2 Draw a circle of diameter 60 mm, below the x-y line at some suitable distance, and divide this circle into 12 equal divisions, as shown into the figure. And give the notations. It is the top view of the 1st stage.

Step-3 From the center of the circle in top view, draw a perpendicular vertical projector of the length equal to 100mm from x-y line, and give the notations as shown into the figure. And from the notations of the circle in top view, draw perpendicular vertical projectors up to the x-y line. From these end points draw slant lines connecting to the apex point “ o’ ” in the front view, and give the notations as shown into the figure. It is the front view of the 1st stage

Step-4 Now copy the front view of the 1st stage as the front view of the 2nd stage with the same dimensions, such that the line o’- a’, should be parallel to the x-y line & resting on it, and the remaining drawing should be drawn accordingly as shown into the figure. It is the front view of the 2nd stage.

Step-5 From the notations of the front view of the 2nd stage draw vertical projectors into down ward direction and from the top view of the 1st stage draw projectors into horizontal direction as shown into the figure, which will intersect with each other at respective points.

Step-6 From these respective points of intersections, draw a medium dark smooth curve passing through the points a to h in sequence as shown into the figure. And connect the extreme two points i.e., h & c, with straight lines with the apex o as shown in the figure. And give the notations. It is the top view of the 2nd stage.

Step-7 Copy the top view of the 2nd stage as the top view of the 3rd stage at an angle 60° with the x-y line such that the apex of the cone should be near to the x-y line, as show into the figure with the same dimensions. And give all the notations on it. It is the top view of the 3rd stage.

Step-8 From the front view of the 2nd stage, draw horizontal projectors, and from the top view of the 3rd stage draw vertical projectors in upward direction, which will intersect with the previously drawn projectors at respective points.

Step-9 From these respective points of intersections, draw a medium dark smooth curve passing through the points a’ to h’ in sequence as shown into the figure. And connect the extreme two points i.e., d’&a’, with straight lines with the apex o’ as shown in the figure. It is the front view of the 3rd stage.

Step-10 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.

Problem 3

Projection of Solids – A pentagonal prism of side of base equal to 40 mm and axis height 110 mm rests on one of its corner of its base on H.P. such that the axis is inclined at an angle of 40° with H.P. and 60°

with the V.P. Draw its projection.

Procedure:

Step-1 Draw a horizontal x-y line of some suitable length.

Step-2 Draw a pentagon of side of length 40 mm, below the x-y line at some suitable distance such that one side of the pentagon should be perpendicular with the x-y line, as shown into the figure. And give the notations. It is the top view of the 1st stage.

Step-3 From the notations of the pentagon in top view, draw perpendicular vertical projectors of the length equal to 110 mm from x-y line, and connect all the points in sequence with straight lines and give the notations as shown into the figure. It is the front view of the 1st stage.

Step-4 Now copy the front view of the 1st stage as the front view of the 2nd stage with the same dimensions, such that the center line of the pentagonal prism should be inclined at an angle 40° with the x-y line, and the corner of the prism that is d’ should touch with the x-y line, as shown into the figure. And give the notations. It is the front view of the 2nd stage.

Step-5 From the notations of the front view of the 2nd stage draw vertical projectors into down ward direction and from the top view of the 1st stage draw projectors into horizontal direction as shown into the figure, which will intersect with each other at respective points.

Step-6 From these respective points of intersections, draw straight lines between all the points in sequence as shown into the figure. It is the shape like a pentagonal prism. But be careful that some of these lines are dotted lines because of hidden. And give the notations. It is the top view of the 2nd stage.

Step-7 Copy the top view of the 2nd stage as the top view of the 3rd stage, at an angle 60° with the x-y line such that the center line should be inclined at the angle 60°, as show into the figure with the same dimensions and the top end of the pentagonal prism should be near to the x-y line as shown in the figure. And give all the notations on it. It is the top view of the 3rd stage.

Step-8 From the front view of the 2nd stage, draw horizontal projectors, and from the top view of the 3rd stage draw vertical projectors in upward direction, which will intersect with the previously drawn projectors at respective points.

Step-9 From these respective points of intersections, draw straight lines between all the points in sequence as shown into the figure, It is the shape like a pentagonal prism, as shown into the figure. But be careful that some of these lines are dotted lines because of hidden. It is the front view of the 3rd stage.

Step-10 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.

Problem4

Projection of Solids – A cylinder diameter of base 50 mm and height 70 mm is resting on the H.P. on a point of its periphery of the base. The axis of the cylinder is inclined to H.P. by 300 and the axis is inclined at 450 to the V.P. Draw the projections. Keep top end of the cylinder near to observer.

Step-1 Draw a horizontal x-y line of some suitable length.

Step-2 Draw a circle of diameter 50 mm, below the x-y line at some suitable distance, and divide this circle into 12 equal divisions, as shown into the figure. And give the notations. It is the top view of the 1st stage.

Step-3 From the notations of the circle in top view, draw perpendicular vertical projectors of the length equal to 70 mm from x-y line, and give the notations as shown into the figure. Its shape is a rectangle. It is the front view of the 1st stage.

Step-4 Now copy the front view of the 1st stage as the front view of the 2nd stage with the same dimensions, such that the center line of the rectangle should be inclined at an angle 30° with the x-y line, and the corner of the rectangle that is point a’ should touch with the x-y line, as shown into the figure. And give the notations. It is the front view of the 2nd stage.

Step-5 From the notations of the front view of the 2nd stage draw vertical projectors into down ward direction and from the top view of the 1st stage draw projectors into horizontal direction as shown into the figure, which will intersect with each other at respective points.

Step-6 Now connects these all the points with either straight lines or curves in sequence, depending on the shape of the solid cylinder, as shown into the figure. It is the shape like a cylinder. But be careful that some of these lines or curves are dotted because of hidden. And give the notations. It is the top view of the 2nd stage.

Step-7 Copy the top view of the 2nd stage as the top view of the 3rd stage, at an angle 45° with the x-y line such that the center line should be inclined at the angle 45°, as show into the figure with the same dimensions. And give all the notations on it. It is the top view of the 3rd stage.

Step-8 From the front view of the 2nd stage, draw horizontal projectors, and from the top view of the 3rd stage draw vertical projectors in upward direction, which will intersect with the previously drawn projectors at respective points.

Step-9 Now connects these all the points with either straight lines or curves in sequence, depending on the shape of the solid cylinder, as shown into the figure. It is the shape like a cylinder. But be careful that some of these lines or curves are dotted because of hidden. And give the notations. It is the front view of the 3rd stage.

Step-10 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.

Problem 1

Projection of Planes – A circular plate of diameter 80 mm is resting on a point of its periphery on H.P. such that it makes an angle of 40° to the H.P. And the diameter passing through the point of its resting on H.P. makes an angle of 60° with V.P. Draw the projections of it.

Step-1 Draw a horizontal x-y line of some suitable length.

Step-2 Draw a circle of radius 40 mm below the x-y line at some suitable distance. It is the plan of the 1st stage.

Step-3 Divide the circle into 8 equal divisions, and give the notations.

Step-4 From the notations given on the circle, draw vertical projectors up to the x-y line, through these projectors, draw a horizontal medium dark line on the line x-y & give the notations. It is the front view of the 1st stage.

Step-5 Copy the front view of the 1st stage at an angle 40° with x-y line such that the point a’ should be on the x-y line. And give the notations on it. This is front view of the 2nd stage.

Step-6 From the front view of the 2nd stage draw downward projectors and from the top view of the 1st stage draw horizontal projectors in right hand side direction as shown in the figure which will intersect with each other at respective points. Then give the notations on it and connects these all the points in sequence by a medium dark smooth free hand curve. It is top view of the 2nd stage.

Step-7 Copy the top view of the 2nd stage at an angle 60° with the x-y line such that the line c-g should make the angle, as show into the figure with the same dimensions. And give all the notations on it. It is the top view of the 3rd stage.

Step-8 From the front view of the 2nd stage, draw horizontal projectors, and from the top view of the 3rd stage draw vertical projectors in upward direction, which will intersect with the previously drawn projectors at respective points.

Step-9 From these respective points of intersections, draw a smooth medium dark free hand curve, and give the notations. It is the front view of the 3rd stage.

Step-10 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.

Problem 2

Projection of Planes – An isosceles triangle plate ABC having its base 50 mm and altitude 90 mm resting on H.P. on its base. The isosceles triangle is inclined at an angle 40° to the H.P. And the altitude in the top view is inclined at the angle 60° to the V.P. Draw the projections.

Procedure:

Step-1 Draw a horizontal x-y line of some suitable length.

Step-2 Draw an isosceles triangle of length of base equal to 50 mm and altitude equal to 90 mm such that the base should be perpendicular with the x-y line, below the x-y line at some suitable distance as shown into the figure. And give the notations. It is the top view of the 1st stage.

Step-3 From the notations of the isosceles triangle, draw vertical projectors up to the x-y line, from these points of intersections, draw a medium dark horizontal line, and give the notations as shown into the figure. It is the front view of the 1st stage.

Step-4 Copy the front view of the 1st stage at an angle 40° with the x-y line, such that the point a’-b’ should touch on the x-y line, and give the notations as given into the 1st stage front view. It is the front view of the 2nd stage.

Step-5 From the notations of the front view of the 2nd stage draw vertical projectors into down ward direction and from the top view of the 1st stage draw projectors into horizontal direction as shown into the figure, which will intersect with each other in respective points.

Step-6 Connect these respective points of intersection in sequence with medium dark straight lines as shown in the figure. And give the notations. It is the top view of the 2nd stage.

Step-7 Copy the top view of the 2nd stage at an angle 60° with the x-y line such that the altitude in the top view of the 2nd stage should be inclined, as show into the figure with the same dimensions. And give all the notations on it. It is the top view of the 3rd stage.

Step-8 From the front view of the 2nd stage, draw horizontal projectors, and from the top view of the 3rd stage draw vertical projectors in upward direction, which will intersect with the previously drawn projectors at respective points.

Step-9 Connect these respective points of intersection in sequence with medium dark straight lines as shown in the figure. And give the notations. It is the front view of the 3rd stage.

Step-10 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.

Problem 3

Projection of Planes – A semi- circular thin plate of 60 mm diameter rest on the H.P. on its diameter which is inclined at 45˚ to the V.P. and the surface is inclined at 30˚ to the H.P. Draw the projection of the plate.

Procedure:

Step-1 Draw a horizontal x-y line of some suitable length.

Step-2 Draw a semi-circle of radius 30 mm, below the x-y line at some suitable distance as shown into the figure. And give the notations. It is the top view of the 1st

Step-3 From the notations of the semi-circle, draw vertical projectors up to the x-y line, from these points of intersections, draw a medium dark horizontal line, and give the notations as shown into the figure. It is the front view of the 1st stage.

Step-4 Copy the front view of the 1st stage at an angle 30° with the x-y line, such that the point a’ should touch with the x-y line, and give the notations as given into the 1st stage front view. It is the front view of

the 2nd stage.

Step-5 From the notations of the front view of the 2nd stage draw vertical projectors into down ward direction and from the top view of the 1st stage draw projectors into horizontal direction as shown into the figure, which will intersect with each other in respective points.

Step-6 From these respective points of intersections, draw a smooth medium dark curve passing through the points a to g in sequence, and a straight line between the point a & g. It is in the shape like a semi-circle. And give the notations. It is the top view of the 2nd stage.

Step-7 Copy the top view of the 2nd stage at an angle 45° with the x-y line as show into the figure with the same dimensions. And give all the notations on it. It is the top view of the 3rd stage.

Step-8 From the front view of the 2nd stage, draw horizontal projectors, and from the top view of the 3rd stage draw vertical projectors in upward direction, which will intersect with the previously drawn projectors at respective points.

Step-9 From these respective points of intersections, , draw a smooth medium dark curve passing through the points a’ to g’ in sequence, and a straight line between the point a’ & g’ as shown into the figure. It is the front view of the 3rd stage.

Step-10 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.