General Principles of Design, Drawing & Importance of Safety Short Notes Part 3

Projections of Planes

Solid

A solid is a 3-D object having length, breadth and thickness and bounded by surfaces which may be either plane or curved, or combination of the two.
Solids are classified under two main headings

Polyhedron
Solids of revolution

A regular polyhedron is solid bounded only by plane surfaces (faces). Its faces are formed by regular polygons of same size and all dihedral angles are equal to one another. when faces of a polyhedron are not formed by equal identical faces, they may be classified into prisms and pyramids.

Five regular polyhedral are shown in figure below

Prism

Prisms are polyhedron formed by two equal parallel regular polygon, end faces connected by side faces which are either rectangles or parallelograms.

Different types of prisms are shown in figure below

Various types of prisms generally encountered in engineering applications

Some definitions regarding prisms

Base and lateral faces. When the prism is placed vertically on one of its end faces, the end face on which the prism rests is called the base. The vertical side faces are the lateral faces, as shown in Figure.

Base edge/Shorter edge: These are the sides of the end faces, as shown in figure.

Axis – it is the imaginary line connecting the end faces is called axis and is shown in figure.

Longer edge/lateral edges: These are the edges connecting the respective corners of the two end faces. The longer edge of a square prism is illustrated in figure.

Right prism: A prism whose axis is perpendicular to its end face is called as a right prism. Prisms are named according to the shape of their end faces, i.e, if end faces are triangular, prism is called a triangular prism.
Oblique prism: It is the prism in which the axis is inclined to its base.
Pyramids: Pyramid is a polyhedron formed by a plane surface as its base and a number of triangles as its side faces, all meeting at a point, called vertex or apex.
Axis – the imaginary line connecting the apex and the center of the base.
Inclined/slant faces – inclined triangular side faces.
Inclined/slant/longer edges – the edges which connect the apex and the base corners.
Right pyramid – when the axis of the pyramid is perpendicular to its base.
Oblique pyramid – when the axis of the pyramid is inclined to its base.

Solids of revolution

when some of the plane figures are revolved about one of their sides – solids of revolution is generated some of the solids of revolution are:

Cylinder: when a rectangle is revolved about one of its sides, the other parallel side generates a cylinder.
Cone: when a right triangle is revolved about one of its sides, the hypotenuse of the right triangle generates a cone.
Oblique cylinder: when a parallelogram is revolved about one of its sides, the other parallel side generates a cylinder.
Sphere: when a semi-circle is revolved about one of its diameter, a sphere is generated..
Truncated and frustums of solids – when prisms, pyramids, cylinders are cut by cutting planes, the lower portion of the solids (without their top portions) are called, either truncated or frustum of these solids. Some examples are shown in the figure.

Methods of drawing the projections of solids
These are two methods for drawing the projections of solids:

Change of position method.
Auxiliary plane method (Change of reference-line method)

Problem 1.
A cube of 30 mm sides is held on one of its corners on HP such that the bottom square face containing that corner is inclined at 30⁰ to HP. Two of its adjacent base edges containing the corner on which it rests are equally inclined to VP. Draw the top and front views of the cube.

Solution:
The procedure of obtaining the projections is shown in figure 6. InStep-1, the projections of the cube is drawn in the simple position. The cube is assumed to lie with one of its faces completely on HP such that two vertical faces make equal inclinations with VP. Draw a square abcd to represent the top view of the cube such that two of its sides make equal inclinations with the XY line, i.e., with VP. Let (a₁), (b₁), (c₁) and (d₁) be the four corners of the bottom face of the cube which coincide in the top view with the corners a, b, c and d of the top face. Project the front view of the cube. The bottom face a₁’b₁’c₁’(d₁’) in the front view coincide with the XY line. Now the cube is tilted on the bottom right corner c₁’ (step-2) such that the bottom face a₁’b₁’c₁’(d₁’) is inclined at 30⁰ to HP. Reproduce the front view with face a₁’b₁’c₁’(d₁’) inclined at 30⁰ to the XY line.
Draw the vertical projectors through all the corners in the reproduced front view and horizontal projectors through the corners of the first top view. These projectors intersect each other to give the corresponding corners in the top view

Section Views

Introduction

Sectional views are an important aspect of design and documentation since it is used to improve clarity and reveal interior features of parts.
Sectional drawings are multi-view technical drawings that contain special views of a part or parts, that reveal interior features. A primary reason for creating a section view is the elimination of hidden lines, so that a drawing can be more easily understood or visualized.
Traditional section views are based on the use of an imaginary cutting plane that cuts through the object to reveal interior features.

This imaginary cutting plane is controlled by the designer and are generally represented by any of the following:

(a) Full section view, where the section plane go completely through the object. Example shown in figure 1.
(b) Half section view, where the section plane go half-way through the object. Example shown in figure 2.
(c) Offset section, where the sectional plane bent through the features that are not aligned. Example shown in figure 3.
(d) Broken-out section where the section go through part of the object . Example shown in figure 4.