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• ISOMETRIC PROJECTION

Contents

Introduction

Principle of Isometric Projection

Isometric Scale

Construction of Isometric Scale

Isometric View (Isometric Drawings)

Methods to draw isometric projections/isometric views

Difference between isometric projection and Isometric view

Isometric views of planes

Isometric views of solids

Triangular prism

Triangular Pyramid

Examples

Assignment

Importance of this Chapter

Isometric projection of the object helps us to visualize the three dimensions of the object in one view

It helps in conveying the real shape of the object to the viewers.

• INTRODUCTION The orthographic views we discussed are very valuable in providing us true heights, widths and depths of objects. However the formats of object representation previous chapter are two dimensional. Seeing objects in three dimensional will be more useful. A three-dimensional drawing of sketch shows the entire object in one view. The object is not scattered among top, front and side views. A three dimensional pictorial greatly enhances ones ability to visualize the object, especially if one does not understand orthographic projection. There is often a need to illustrate for a non technical person some object under discussion and the three dimensional format is probably the best way to present the object. PRINCIPLES OF ISOMETRIC PROJECTION

In isometric projection (isometric means equal measure), it is necessary to place the object such that its principal edges or axes make equal angles with the plane of projection and therefore foreshortened equally. In this position the edges of a cube would be projected equally and would make equal angles with each other 1200 .

NOTE When lines are drawn parallel to isometric axes, the lengths are foreshortened to 0.816 times the actual lengths.

• The isometric projection of solid is represented on vertical plane of projections. The solid is such that its three mutually perpendicular edges make equal inclinations with the plane of projection. When a cube is resting on one of its corner on HP, and its solid diagonal in the front view is perpendicular to VP, then the front view of the cube represents the Isometric projection of the cube. (Refer the figure).

Consider a cube resting on HP, with two of its square faces making equal inclinations with the VP. oc is the solid diagonal (Refer the figure 1 & 2).

Tilt the solid on one corner g and make the solid diagonal parallel to HP. Draw the

corresponding top view in this position, the solid diagonal oc in the top view is parallel to VP. (Refer the figure 3 & 4).

Rotate the solid diagonal oc in the top view perpendicular to VP and the project

corresponding front view which represents isometric projection of cube. The lengths of their projections are equal to the lengths of the edges multiplied by

0.816, approximately (for information refer the isometric scales). Thus the projected lengths are about 80% of the true lengths. The projections of the axes OB, OD, and OG make angles of 1200 with each other and are called the isometric axes. Any line parallel to one of these axes is called as an isometric line; a line that is not parallel to these axes is called a nonisometric line. It should be noted that the angles in the isometric projection of the cube are either 1200 or 600 and that all are projections of 900 angles. In an isometric projection of a cube, the faces of the cube and any planes parallel to them are called isometric planes.

NOTE There are three isometric planes containing any two isometric axes and planes parallel to these planes are termed Isometric planes. The planes no parallel to any of the any of the Isometric planes are termed Non-Isometric planes

• Construction of Isometric scale The isometric scales are drawn by the following two methods. Method 1:

Draw a horizontal line BD and another line BP at 450 to horizontal. From B, draw line BA inclined at 300 to BD. Mark divisions of true lengths on the line BP. From each division draw vertical lines to BA.

• The divisions obtained on the line BA gives the isometric lengths on isometric scale.

Method 2:

Draw a horizontal line AB of any length.

From A draw line making an angle of 150 with AB.

From B draw line making an angle of 450 with AB, cutting the line 150 line at C.

Mark divisions of true length on the line AB.

From each division draw parallel lines to BC.

Thus the divisions obtained on the line AC give the isometric length on isometric

scale.

• ISOMETRIC VIEW (ISOMETRIC DRAWING) The view drawn with the true scale is called isometric view, while the view drawn with the use of isometric scale is called Isometric projection.

In isometric view of any rectangular solid resting on the ground, each horizontal face will have its sides parallel to the two sloping axes; each vertical face will have its vertical sides parallel to the vertical axis and the other sides parallel to one of the slopping axes. In other words, the vertical edges are shown by vertical lines, while the horizontal edges are represented by lines, making 300 with the horizontal. These lines are very conveniently drawn with the T-square and a 300 600 set square. Refer the given figure. The procedure for drawing isometric views of planes, solids and objects of various shapes is explained in stages by means of illustrative problems. In order that he construction of the view may be clearly understood, construction have not been erased. They are, however, drawn fainter than the outlines. In an isometric view, lines for the hidden edges are generally not shown. In the solutions accompanying the problems, one or two arrows have been shown. They indicate the directions from which if the drawing is viewed, the given isometric views would be obtained.

NOTE Isometric projection are commonly used to prepare the pictorial view of smaller Objects and it is used in mechanical, production, automobile, aerospace Engineering to show the machine parts.

• METHODS TO DRAW ISOMETRIC PROJECTIONS/ISOMETRIC VIEWS Projections or drawings which are not parallel to one of the isometric axes are called Non isometric lines. An important rule is that the measurements can be made only on the drawings of isometric lines. Conversely, measurements cannot be made on the drawings of nonisometric lines. For example, the diagonals of the face of a cube are nonisometric lines; although they are equal in length, their isometric drawings will not be equal of length. There are two basic methods for drawing the isometric projections/views.

(1) Boxing method (2) Offset (or) Co-ordinate method

Boxing method When an object contains many nonisometric lines, it is drawn by the boxing method or the offset method. When the boxing method is used, the object is enclosed in a rectangular box, which is drawn around it in orthographic projection. The box is then drawn in isometric and the object located in it by its points of contact as in the given figure. It should be noted that the isometric views of lines that are parallel on the object are parallel. This knowledge can often be used to save a large amount of construction, as well as to test for accuracy might be drawn by putting the top face into isometric and drawing vertical lines equal in length to the edges downward from each other. It is not always necessary to enclose the whole object in a rectangular crate.

The pyramid would have its base enclosed in a rectangle and the apex located by erecting a vertical axis from the centre.

• Offset (or) Co-ordinate method

When an object is made up of planes at different angles, it is better to locate the ends of the edges by the offset method rather than by boxing. When the offset method is used, perpendiculars are extended from each point to an isometric reference plane. These perpendiculars, which are isometric lines, are located on the drawing by isometric coordinates, the dimensions being taken from the orthographic views. In the given figure line AB is used as a base; first to locate points on the base; then verticals from these points e, f and g.

DIFFERENCE BETWEEN ISOMETRIC PROJECTION AND ISOMETRIC VIEW

S. No Isometric Projection Isometric View

1 Isometric dimensions are considered. Isometric Length = 0.816 x True length

True dimensions are considered

2 Volume is less Volume is more. (22.5% enlarged)

Consider the following isometric projection and isometric view of a cube kept in vertical position to make the difference between them.

NOTE This method can be used for any object, however it may be complicated.

• ISOMETRIC VIEWS OF PLANES

The construction of isometric views of standard planes ( triangle , square , rectangle, quadrilateral, circle , semi- circle , arcs , hexagonal, fillets) is explained below .

Triangle

Consider the triangle as shown in the given fig.

To draw the isometric view of triangle coinciding with the right isometric plane from the point a draw a vertical line ap Then from a draw the line ab = AB.

• (isometric view ) making an angle 30 to horizontal line . Then complete the triangle abc with the help of these two lines (ap, ab).

Similarly to draw the isometric view of triangle coinciding with the left isometric plane from the point b draw a vertical line bq. Then from b draw the line

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