Design, Drawing & Importance of Safety: Projection of Planes and Solids

By Vijay Pratap Singh|Updated : May 22nd, 2021

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Projection of plane: 

Plane are the surfaces which is having only two dimensions i.e. length and breadth whereas its thickness is very low which can be neglected.

Planes may be divided into two main types:

(1) Perpendicular planes: These planes can be divided into the following sub-types:

(i) Perpendicular to both the reference planes.

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(ii) Perpendicular to one plane and parallel to the other.

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(iii) Perpendicular to one plane and inclined to the other.
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(2) Oblique planes: Planes which are inclined to both the reference planes are called oblique planes.

Traces of planes:

A plane, extended if necessary, will meet the reference planes in lines, unless it is parallel to any one of them, these lines are called the traces of the plane.

The line in which the plane meets the H.P. is called the Horizontal trace.

The line in which it meets the VP is called its Vertical trace.

 

Conclusions of Traces:
(i) When a plane is perpendicular to both the reference planes, its traces lie on a straight line perpendicular to xy.

(ii) When a plane is parallel to a reference plane, it has no trace on that plane. Its trace on the other reference plane, to which it is perpendicular, is parallel to xy.

(iii) When a plane is perpendicular to one of the reference planes, its trace upon the other plane is perpendicular to xy (except when it is parallel to the other plane).

(iv) When a plane is inclined to the HP and perpendicular to the VP, its inclination is shown by the angle which its VT makes with xy. When it is inclined to the VP and perpendicular to the HP, its inclination is shown by the angle which its HT makes with xy.

(v) When a plane has two traces, they, produced if necessary, intersect in xy (except when both are parallel to xy as in case of some oblique planes).

 

(3) Projections:

(a) When a plane is perpendicular to a reference plane, its projection on that plane is a straight line.

(b) When a plane is parallel to a reference plane, its projection on that plane shows its true shape and size.

Its projection on the plane to which it is inclined, is smaller than the plane itself.

i.e. inclination with the horizontal plane will be visible in Vertical Plane and Vice versa.

 

Projection of Solids:

A solid has three dimensions, viz. length, breadth and thickness.To represent a solid, at least two orthographic views are necessary.  

Solids may be divided into two main groups:

(1) Polyhedra: A polyhedron is defined as a solid bounded by planes called faces.

When all the faces are equal and regular, the polyhedron is said to be regular.

There are seven regular polyhedra which are shown below:

 (i) Tetrahedron: It has four equal faces, each an equilateral triangle.

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(ii) Cube or hexahedron: It has six faces, all equal squares.

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(iii) Octahedron: It has eight equal equilateral triangles as faces.

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(iv) Dodecahedron: It has twelve equal and regular pentagons as faces.

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(v) Icosahedron: It has twenty faces, all equal equilateral triangles.
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(vi) Prism: This is a polyhedron having two equal and similar faces called its ends or bases, parallel to each other and joined by other faces which are parallelograms.
   

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(vii) Pyramid: This is a polyhedron having a plane figure as a base and a number of triangular faces meeting at a point called the vertex or apex.

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Projection of Solids:

(a). Solid whose axis is perpendicular to One reference plane

(i) Axis perpendicular to the H.P.:
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(ii) Axis perpendicular to the V.P.:

Front view will be a hexagon of size equal to the base of the prism.

Top view will be a rectangle of size equal to dimeter of the cylinder from which hexagon is made.

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(iii) Axis parallel to both the HP and the VP:

When axis of solid is parallel to both HP & VP then it must be perpendicular to Profile plane so its cross section will be visible in Side view.

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Projections of Spheres:

The projection of a sphere in any position on any plane is always a circle whose diameter is equal to the diameter of the sphere.

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This circle represents the contour of the sphere.

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