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PROJECTIONS INTERSECTION OF SURFACES CLASS NOTES

 

 

 

PROJECTIONS INTERSECTION

OF SURFACES CLASS NOTES

 

Most objects in reality are formed by more

than one object. Two or more objects are

joined by principle of intersection of solids.

Intersection means that one solid is

entering another solid. It is easy to connect

any object of plane surfaces to a plane

wall. But it is very difficult for an object of

curved surfaces. For example a pipe is to

be connected at right angles to another

pipe. In the ordinary way it is almost

impossible. Here the role of intersection of

solids comes into existence. A pipe is

inserted into another pipe. One of

pipe is cut as per curves of intersection.

Only then the second pipe is inserted.

Fig. Intersection of a Cone with a Cylinder

Lines of Intersection

Between plane objects, there will be lines of intersection. Lines of intersection are common to both the surfaces. Between two curved surfaces, there will be curves of penetration.

Consider the following cases:

  1. Firstly intersection of two prisms
  2. Secondly intersection of two cylinders
  3. Thirdly intersection of two cones
  4. Fourthly intersection of a prism and a cylinder
  5. Fifthly intersection of a prism and a cone
  6. Sixthly intersection of a prism and a sphere
  7. Seventhly intersection of a pyramid and a cylinder
  8. Eighthly intersection of a pyramid and a cone
  9. Ninth intersection of a pyramid and a sphere
  10. Tenth intersection of a cone  and a cylinder
  11. Eleventh intersection of a cone and a sphere
  12. Twelfth intersection of a sphere and a cylinder
 

METHODS TO FIND THE LINES OF INTERSECTION

(a) Line Method

                 Number of lines are drawn on the LATERAL surface of one of the solids in the vicinity of intersection. Points of intersection of these lines with the surface of the other solid are then located and marked. Joining of these points will give the required line or curve of intersection.

(b) Cutting plane method

      In this, the two surfaces of the solids are supposed to be cut by a number of parallel cutting planes. These cutting planes can be vertical, or horizontal or inclined but must be parallel to each other. From these one can easily locate the curves of intersection.

Second method is more common because of its easiness.
PRACTICAL APPLICATIONS OF INTERSECTION
Practical applications of intersection of surfaces or interpenetration of solids
(i) Manufacture of tables
(ii) Installation of air conditioning ducts
(iii) In the construction of boilers
(iv) Chimneys
(v) Connecting pipe to a cylinder
(vi) Making a tee joint in a pipe line
(vii) Arm of a person going into the main body.

https://www.mesubjects.net/wp-admin/post.php?post=13384&action=edit       MCQ Intersection of surfaces

https://www.mesubjects.net/wp-admin/post.php?post=7286&action=edit         Section of solids

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