Upload
yash-parikh
View
23
Download
3
Tags:
Embed Size (px)
Citation preview
Unit No:05Projections of Solids
Yash B. ParikhM.Tech. (CIM)
Assistant ProfessorDepartment of Mechanical Engineering
Symbiosis Institute of Technology
Prof. Yash Parikh 2
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.
Prof. Yash Parikh 3
Shapes of Solids
Prof. Yash Parikh 4
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
Prof. Yash Parikh 5
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.
Prof. Yash Parikh 6
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.
Prof. Yash Parikh 7
Polyhedra
Tetrahedron : A regular polyhedron having four equal equilateral
triangular faces.
Prof. Yash Parikh 8
Polyhedra
Cube : (hexahedron) A regular polyhedron having six equal square faces.
Prof. Yash Parikh 9
Polyhedra
Octahedron : A regular polyhedron having eight equal equilateral
triangular faces.
Prof. Yash Parikh 10
Polyhedra
Dodecahedron : A regular polyhedron having twelve equal
pentagonal faces.
Prof. Yash Parikh 11
Polyhedra
Icosahedron : A regular polyhedron having twenty equal
equilateral triangular faces.
Prof. Yash Parikh 12
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.
Prof. Yash Parikh 13
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.
Prof. Yash Parikh 14
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
Prof. Yash Parikh 15
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.
Prof. Yash Parikh 16
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.
Prof. Yash Parikh 17
Pyramids
Types of Pyramids:
Triangular, Square, Rectangular, Pentagonal & Hexagonal
Pyramids
Prof. Yash Parikh 18
Solids of Revolution
Three most common solids of revolution are :
1. Cylinder
2. Cone
3. Sphere
Prof. Yash Parikh 19
Solids of Revolution
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).
Prof. Yash Parikh 20
Solids of Revolution
Sphere :
Solid generated by revolving a semicircle about its
diameter, keeping it fixed.
A sphere is specified by its radius ( or dia).
Prof. Yash Parikh 21
Thank You