Projections of Solids

Unit No:05Projections of Solids

Yash B. ParikhM.Tech. (CIM)

Assistant ProfessorDepartment of Mechanical Engineering

Symbiosis Institute of Technology

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What are Solids?

Any object having definite width (length), depth and height is called a Solid.

The study of the projections of a solid is very important in mechanical-design problems.

The knowledge of which is essential in 3D modeling and animation.

Wide applications in the construction industry.

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Shapes of Solids

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Solids & their Types

Basic solids are those which have predefined shapes. There are two categories of solids. Theses are :

# Polyhedra

# Solids of revolution

Polyhedra : Polyhedra are bounded by plane surfaces. They are sub-divided into three types :

i. Regular Polyhedra

ii. Prisms

iii. Pyramids

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Solids & their Types

Solids of revolution : They are formed by revolution of plane figures, like

rectangles, triangles or semicircles about a fixed line.

They have curved outer faces.

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Polyhedra

i. Regular Polyhedra :

In a regular polyhedron, all the faces are similar, equal and regular.

The angles formed between the faces are also equal.

Since all the edges are of same length, a regular polyhedron is expressed by length of any edge.

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Polyhedra

Tetrahedron : A regular polyhedron having four equal equilateral

triangular faces.

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Polyhedra

Cube : (hexahedron) A regular polyhedron having six equal square faces.

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Polyhedra

Octahedron : A regular polyhedron having eight equal equilateral

triangular faces.

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Polyhedra

Dodecahedron : A regular polyhedron having twelve equal

pentagonal faces.


Polyhedra

Icosahedron : A regular polyhedron having twenty equal

equilateral triangular faces.


Prisms

In a prism, there are two equal and similar end faces, parallel to each other, joined together by other rectangular faces.

In some cases, the faces joining the end faces may be parallelogram instead of rectangles.

The faces joining the end faces are called side faces or lateral faces or simply faces.


Prisms

The imaginary line joining the centres of the end faces is called the axis of the prism.

A prism is called a right-angled prism if its axis is perpendicular to the end faces.

If the axis is inclined to the end faces, the prism is called an oblique prism.


Prisms

A right regular prism is the right-angled prism whose all lateral faces are equal rectangles.

Types of Prisms :

Triangular, Square, Rectangular, Pentagonal & Hexagonal

Prisms


Pyramids

In a pyramid, there is a polygonal face for the base.

It is connected at the edges to a number of triangular faces equal to the no of sides of the base.


Pyramids

All these adjacent triangular faces are joined to each other at a point called an apex of the pyramid.

The imaginary line joining the centre of the base to the apex is called the axis of the pyramid.


Pyramids

Types of Pyramids:

Triangular, Square, Rectangular, Pentagonal & Hexagonal

Pyramids


Solids of Revolution

Three most common solids of revolution are :

1. Cylinder

2. Cone

3. Sphere



Cylinder :

Solid generated by revolving a rectangle about one of its sides, keeping that side fixed.

A cylinder is specified by the radius (or dia) of the base and length of the axis.

Cone :

Solid generated by revolving a right-angled triangle about one of its perpendicular sides, keeping that side fixed.

A cone is specified by the radius (or dia) of the base and length of the axis (height).



Sphere :

Solid generated by revolving a semicircle about its

diameter, keeping it fixed.

A sphere is specified by its radius ( or dia).


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