INTERPENETRATION OF SOLIDS
1. A square prism of base 50 mm side and height 125 mm stands on the ground with its side of base inclined at an angle of 300 to VP. It is penetrated by a cylinder of diameter 50 mm and axis 125 mm long. The axis of the cylinder is parallel to both HP and VP and bisects the axis of the prism. Draw the projection showing fully the curves of intersection.
2. Two cylinders each of 30 mm diameter and altitude 80 mm intersect each other at right angles. Their axes bisect each other and are parallel to VP. Determine the line of intersection of the two cylinders. Also, develop the lower portion of the vertical cylinder, neglecting the thickness of the metal.
3. (a) A vertical cylinder of diameter 80 mm intersects a horizontal cylinder of diameter 40 mm. The shortest distance between their axes is 40 mm. Draw the projections showing the intersection profile.
(b) A horizontal cylinder of 50 mm diameter penetrates a vertical cylinder of 75 mm diameter resting on HP. The two axes are coplanar. The axis of the horizontal cylinder is 50 mm above the HP. draw the projections showing the curves of intersection.
4. A cylindrical boiler is 2m in diameter and has a cylindrical dome 0.8m diameter and 0.6m high. The axis of the dome intersects the axis of the boiler. Draw three views of the arrangement. Also develop the surface of the dome. Take a scale of 1 cm = 0.2 m.
5. A cylinder of 60 mm diameter and 100 mm height stands on its base on the ground. It is penetrated centrally by a cylinder of 40 mm diameter and 100 mm long, whose axis is parallel to HP, but inclined at an angle of 300 to VP. Draw the projections showing the curves of intersection. Also draw the development of the penetrating cylinders.
6. A hexagonal prism of side of base 30 mm is resting on one of its bases on HP with a face parallel to VP. The prism contains a square hole of 20 mm side. The axis of the hole is parallel to VP and inclined at an angle of 300 to the HP intersecting the axis of the prism. The faces of the hole are equally inclined to VP. Draw the lines of intersection.
7. A square prism of base 50 mm side and height 125 mm stands on the ground with its side of base inclined at an angle of 300 to VP. It is penetrated by a cylinder of diameter 50 mm and axis 125 mm long. The axis of the cylinder is parallel to both HP and VP and bisects the axis of the prism. Draw the projection showing fully the curves of intersection.
8. A cylinder of 60 mm diameter stands vertically on its base. It is pierced by a horizontal square prism of 35 mm side of base such that the axes of the two solids intersect each other at right angles. A face of the prism is inclined at an angle of 600 to HP and 300 to VP. Draw the projections of the solids, showing the lines of intersection.
9. A cylinder of 60 mm diameter and axis 80 mm long is standing on its base on HP. A horizontal rectangular hole of 35 mm x 25 mm sides is cut through the cylinder. Axis of the hole is parallel to VP. The axes of both cylinder and hole intersect at right angles and bisect each other. Draw the projections and show the curves of intersection.
10. A cylinder of 60 mm diameter and axis 80 mm long is standing on its base on HP. A horizontal hexagonal hole of 25 mm side is cut through the cylinder. Axis of the hole is parallel to VP. The axes of both cylinder and hole intersect at right angles and bisect each other. A side face of the hole is inclined at an angle of 300 to the HP. Draw the projections and show the curves of intersection.
11. A square hole of 35 mm side is cut in a cylindrical shaft of 60 mm diameter and 100 mm long. The axis of the hole intersects that of the shaft at right angles. All the faces of the hole are inclined at 450 to HP. Draw the projections of the shaft when an imaginary plane containing the two axes is parallel to VP.
12. A vertical square prism of side of base 60 mm is penetrated by a horizontal triangular prism of 40 mm side. The axes are 5 mm apart. One rectangular face of the vertical prism is inclined at an angle of 600 to VP, while that of the horizontal prism is parallel to VP. Draw the projections showing the lines of intersection.
13. A vertical hexagonal prism, side of base 30 mm and 60 mm long, is completely penetrated by a horizontal square prism of 27 mm side and 90 mm length. The axis of the horizontal prism is parallel to VP and 5 mm in front of the axis of the hexagonal prism. If one rectangular face of the hexagonal prism is parallel to VP and all the faces of the square prism are equally inclined to HP, draw the projections of the prisms showing the lines of intersection.
14. (a) A right circular cylinder of 60 mm diameter penetrates another cylinder of 80 mm diameter. Their axes are at right angles to each other, but 8 mm apart. Draw the projections of the curves of intersection on a plane parallel to the axes of the cylinders.
(b) A vertical pipe, 60 mm diameter has a horizontal branch of 40 mm diameter on one side. The axis of the horizontal pipe is 6 mm from the axis of the main pipe and parallel to VP. Draw the projections of the pipe showing the curves of intersection.
15. A vertical pipe of 64 mm diameter is welded to another pipe of diameter 32 mm. The axis of the second pipe is inclined at 600 to HP, parallel to VP. Draw the projections showing the curves of intersection.
16. A vertical square prism, base 50 mm side, has a face inclined at 300 to the VP. It has a hole of 65 mm diameter drilled through it. The center line of the hole is parallel to both the HP and the VP and is 5 mm away from the axis of the prism. Draw the projections of the prism and show the curves of intersection.
17. A vertical cylinder of 60 mm diameter is penetrated by a square prism of 35 mm side. The axis of the prism is inclined at an angle of 300 to the ground, but parallel to the VP. The faces of the prism are equally inclined to the VP and the axis of the prism is 10mm in front of the axis of the cylinder. Draw the projections of the solids showing the curves of interpenetration.
18. A right circular cone of base 50 mm and altitude 80 mm standing on HP with its axis vertical is penetrated by a cylinder of diameter 20 mm such that the axes intersect at an angle of 600 at a height of 35 mm from the base and the plane containing the axes is parallel to VP. Draw the curves of intersection.
19. A hexagonal prism, having base with a 40 mm side and a 100 mm long axis, is resting on its base on the H.P. with a side of the base parallel to the V.P. It is penetrated by a square prism having base with a 35 mm side and a 100 mm long axis such that the axes of both the prism intersect each other at right angles. The faces of the square prism is equally inclined to the H.P. Draw the projections of the combination and show the lines of intersection.
20. A pentagonal prism, having base with a 45 mm side and a 100 mm long axis, is resting on its base on the H.P. with a side of the base parallel to the V.P. It is penetrated by a square prism having base with a 35 mm side and a 100 mm long axis, such that the axes of both the prism bisect each other at right angles. The faces of the square prim are equally inclined to the H.P. Draw the projections of the combination and show the lines of intersection.
21. A square prism, having base with a 50 mm side, is resting on its base on H.P. with the faces equally inclined to the V.P. It is completely penetrated by a horizontal cylinder with a 50 mm base diameter such that their axes of bisect each other at right angles. Assuming suitable lengths of both the solids, draw their projections and show the curves of intersection.
22. A square prism, having base with a 60 mm side and a 100 mm long axis, is resting on its base on H.P. with the faces equally inclined to the V.P. It is completely penetrated by a hexagonal prism having base with a 30 mm side and a 100 mm long axis having a face parallel to H.P. The axes of the prisms bisect each other at right angles. Draw their projections and show the curves of intersection.
23. A cylinder of 60mm diameter, having its axis vertical is penetrated by another cylinder of 40mm diameter. The axis of the penetrating cylinder is parallel to V.P and bisects the axis of the vertical cylinder making an angle of 600 with it. Draw the projections showing the curves of intersection.
24. A cylindrical boiler is 2m in diameter and has a cylindrical dome 0.8m diameter and 0.6m high. The axis of the dome intersects the axis of the boiler. Draw three views of the arrangement. Also develop the surface of the dome. Take a scale of 1 cm = 0.2 m.
25. A cylinder of 60 mm diameter and 100 mm height, stands on its base on the ground. It is penetrated centrally by a cylinder of 40 mm diameter and 100 mm long, whose axis is parallel to HP, but inclined at an angle of 300 to VP. Draw the projections showing the curves of intersection. Also draw the development of the penetrating cylinders.
26. A square prism of base 50 mm side and height 125 mm stands on the ground with its side of base inclined at an angle of 300 to VP. It is penetrated by a cylinder of diameter 50 mm and axis 125 mm long. The axis of the cylinder is parallel to both HP and VP and bisects the axis of the prism. Draw the projection showing fully the curves of intersection.
27. A cylinder of 60 mm diameter stands vertically on its base. It is pierced by a horizontal square prism of 35 mm side of base such that the axes of the two solids intersect each other at right angles. A face of the prism is inclined at an angle of 600 to HP and 300 to VP. Draw the projections of the solids, showing the lines of intersection.
28. A vertical square prism, base 50 mm side has its faces equally inclined to the V.P. It is completely penetrated by another square prism of base 30 mm side, the axis of which is parallel to both the planes and is 6 mm away from the axis of the vertical prism. The faces of the horizontal prism also are equally inclined to the V.P. Draw the projections of the solids showing lines of intersection.
29. Two equal prisms whose ends are equilateral triangles of 40 mm side and axes 100 mm long, intersect at right angles. One face of each prism is on the ground. The axis of one of the prisms makes 300 with the V.P. Draw three views of the solids.
30. A square prism of base 50 mm side and height 125 mm stands on the ground with a side of the base inclined at 300 to the V.P. It is penetrated by a cylinder, 50mm diameter and 125 mm long, whose axis is parallel to both the H.P. and the V.P. and bisects the axis of the prism. Draw the projections showing fully the curves of intersection.
31. A cylinder of 75 mm diameter and 125 mm height, stands on its base on the ground. It is penetrated centrally by a cylinder, 50 mm diameter and 125 mm long, whose axis is parallel to the H.P. but inclined at 300 to the V.P. Draw the projections showing curves of intersection. Draw also the development of the surface penetrated cylinder.
32. A right circular cylinder of 75 mm diameter penetrates another of 100 mm diameter, their axes being at right angles to each other but 10 mm apart. Draw the projections of the curves of intersection on a plane parallel to the axes of the cylinders.
33. Two circular pipes of 75 mm and 50 mm diameters (inside) meet at 300. The axes of both the pipes are in one plane and the 75mm pipe is vertical. The thickness of the pipes is 6 mm in both cases. Draw the projections showing curves of intersection.
34. A square hole of 35 mm side is cut in a cylindrical shaft 75 mm diameter and 125 mm long. The axis of the hole intersects that of the shaft at right angles. All faces of the hole are inclined at 450 to the H.P. Draw three views of the shaft when the plane of the two axes is parallel to the V.P.
35. Two equal triangular prisms whose axes intersect each other at right angles, have side of base 40 mm and altitude 100 mm. The vertical prism has one edge of its base perpendicular to VP. The horizontal prism has one of its rectangular faces vertical, making an angle of 300 with V.P.
Draw the projections showing the lines of intersection.
36. A hexagonal prism of side of base 30 mm is resting on one of its bases on HP with a face parallel to VP. The prism contains a square hole of 20 mm side. The axis of the hole is parallel to VP and inclined at an angle of 300 to the HP intersecting the axis of the prism. The faces of the hole are equally inclined to VP. Draw the lines of intersection
37. A square pipe of 60 mm side is connected to another square pipe of side 45 mm. The axis of bigger pipe is vertical and the axis of the smaller pipe intersects the axis of the bigger pipe at an angle of 450. All the faces of both the pipes are equally inclined to VP. Draw the projections showing the lines of intersection.
38. Two cylinders each of 30 mm diameter and altitude 80 mm intersect each other at right angles. Their axes bisect each other and are parallel to VP. Determine the line of intersection of the two cylinders. Also, develop the lower portion of the vertical cylinder, neglecting the thickness of the metal.
39. (a) A vertical cylinder of diameter 80 mm intersects a horizontal cylinder of diameter 40 mm. The shortest distance between their axes is 40 mm. Draw the projections showing the intersection profile.
(b) A horizontal cylinder of 50 mm diameter penetrates a vertical cylinder of 75 mm diameter resting on HP. The two axes are coplanar. The axis of the horizontal cylinder is 50 mm above the HP. Draw the projections showing the curves of intersection.
40. A cylinder of 60 mm diameter and axis 80 mm long is standing on its base on HP. A horizontal rectangular hole of 35 mm x 25 mm sides is cut through the cylinder. Axis of the hole is parallel to VP. The axes of both cylinder and hole intersect at right angles and bisect each other. Draw the projections and show the curves of intersection.
41. A cylinder of 60 mm diameter and axis 80 mm long is standing on its base on HP. A horizontal hexagonal hole of 25 mm side is cut through the cylinder. Axis of the hole is parallel to VP. The axes of both cylinder and hole intersect at right angles and bisect each other. A side face of the hole is inclined at an angle of 300 to the HP. Draw the projections and show the curves of intersection.
42. A cylindrical pipe of 36 mm diameter has a similar branch of the same size. The axis of the branch intersects the axis of the main pipe at an angle of 600. Draw the projections, when the two axes lie in a plane parallel to the VP and the axis of the main pipe is vertical. Also, develop the surfaces of the two pipes assuming suitable lengths.
43. A square hole of 35 mm side is cut in a cylindrical shaft of 60 mm diameter and 100 mm long. The axis of the hole intersects that of the shaft at right angles. All the faces of the hole are inclined at 450 to HP. Draw the projections of the shaft when an imaginary plane containing the two axes is parallel to VP.
