Projection of Solids

Procedure

1. Draw the projections of a cube edge 70 mm, resting on one of its faces in HP and with its vertical faces equally inclined to VP.

  1. Draw the principal axis.
  2. As the axis is perpendicular to the ground that is the HP begin with the top view draw its top view keeping the sides of the base equally inclined that is at 45degree to XY line.
  3. Name all the corner points.
  4. The top corner points 1, 2, 3 and 4 exactly overlap and coincide with the corresponding points a, b, c and d.
  5. Project the front view by taking corner points on the XY line and join them. Name them as a’, b’, c’ and d’ respectively.
  6. Cut the height 70mm along each of them from XY line, name the corner points as 1’, 2’, 3’ and 4’ respectively.

2. A triangular prism, side of base 80 mm and axis 150 mm long, lies on one of its rectangular faces in HP with its axis parallel to VP. Draw its projections.

  1. As the axis of the triangular prism is parallel to both the planes so let’s begin with the side view. Draw the equilateral tringle with length of 80mm each side in profile plane (PP).
  2. Name the corner points as a’’, b’’ and c’’ along with 1’’, 2’’ and 3’’.
  3. Now let’s start drawing top view. For drawing top view, project the corner points on the YZ line.
  4. Draw the horizontal line parallel to XY line from each of these points from YZ line.
  5. Draw the top view by cutting 150mm equal to the length of the prism. You will have a rectangle with length equal to 150mm and width equal to 80mm. Name these points as a, b, c and 1, 2, 3 as shown.
  6. Project the front view horizontally from the triangle and take length of the axis as 150mm.
  7. Join the front view and the top view making lines parallel to YZ axis and perpendicular to XY axis.
  8. Label the front view with 1’, 2’, 3’ and a’, b’, c’.

3. A Hexagonal Prism having a base with 50 mm side and 125 mm long axis, has an edge of its base on the HP. Its axis is Parallel to the VP and inclined at 45° to the HP. Draw its projections.

  1. Draw the XY axis.
  2. Draw a circle with radius 50mm below the XY line.
  3. Draw the diameter of the circle perpendicular to XY lines and cut equal arcs of 50mm on the circle. and make the hexagon by the all the points.
  4. Name the points a, b, c, e, f, g and 1, 2, 3, 4, 5, 6.
  5. Draw the projection of these lines on XY lines and join them.
  6. Project the front view by cutting 125mm from each these points perpendicular to the XY lines. Join the top of the prims. Label them as 1’, 2’, 3’, 4’, 5’, 6’ and a’, b’, c’, d’, e’, f’ and label the axis is o1’ and o2’.
  7. At some distance from the top view make a line 45degree inclined to the XY line.
  8. As the axis of the hexagonal prism is 45degree inclined to the horizontal plane we need to make the front view also inclined at 45degree from the XY line.
  9. By taking equal measurement from the front view at 45degree to XY axis. Name the corner points as 1’, 2’, 3’, 4’, 5’, 6’ and a’, b’, c’, d’, e’, f’.
  10. Project the second top view by drawing vertical projector from the corner from the second front view and horizonal projector from the first top view.

4. A cone 80 mm diameter and 100 mm axis are resting on one of its generators on HP which makes 30° inclinations with VP. Draw its projections.

  1. Draw the axis XY.
  2. As the axis of the code as resting on one of its generators on HP this means it is lying on HP.
  3. Let’s us assume it standing on hp it’s top will show the true shape of its base i.e., circle.Draw a circle of 80mm diameter as top view of the cone. Divide the circle into 8 equal parts and name them as a, b, c, e, f, g, h and i.
  4. Project the front view by taking perpendicular from these corner points on the XY line and join them.
  5. Draw the axis equal to 100mm length and complete the front view by joining the vertices. Name all the points as shown.
  6. Draw the second front view by drawing the slant height o’e’ on XY line.
  7. Make an arc from e’ equal to the length on o’e’ and make an arc from o’ equal to the length of o’a’. join the intersecting point to o’ and e’ and name all the points.
  8. Project the second top view by drawing vertical projector from the corner from the second front view and horizonal projector from the first top view.
  9. Name the points n, m and p as shown in illustration.
  10. As the axis making 30degree inclination with the VP make the generator oa 30 degree inclined to the XY axis and marks the points n, p, m and e by taking arc equal to the length of on, op, om and oe from the second top view.
  11. Make arcs of equal length of og and oh from point o (in 3rd top view). Also make arc from point p equal to the length of pg and pc and join the intersecting points. Similarly draw arcs for b, d, f and h. join all the points.
  12. Project the third front view by drawing vertical projector from the corner from the third top view and horizontal projectors from the second front view and name the points.