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:
Firstly intersection of two prisms
Secondly intersection of two cylinders
Thirdly intersection of two cones
Fourthly intersection of a prism and a cylinder
Fifthly intersection of a prism and a cone
Sixthly intersection of a prism and a sphere
Seventhly intersection of a pyramid and a cylinder
Eighthly intersection of a pyramid and a cone
Ninth intersection of a pyramid and a sphere
Tenth intersection of a cone and a cylinder
Eleventh intersection of a cone and a sphere
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
(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