Theories of Projections

Theory of Projections  

Projection theory

In engineering, 3-dimensonal objects and structures are represented graphically on a 2-dimensional media. The act of obtaining the image of an object is termed “projection”.  The image obtained by projection is known as a “view”.  A simple projection system is shown in figure 1.

All projection theory are based on two variables:

·                  Line of sight

·                  Plane of projection.

Plane of Projection

A plane of projection (i.e, an image or picture plane) is an imaginary flat plane upon which the image created by the line of sight is projected.  The image is produced by connecting the points where the lines of sight pierce the projection plane. In effect, 3-D object is transformed into a 2-D representation, also called projections. The paper or computer screen on which a drawing is created is a plane of projection.

Projection Methods

Projection methods are very important techniques in engineering drawing.

Two projection methods used are:

·        Perspective and

·        Parallel 

the observer is assumed to be stationed at finite distance from the object. The height of the buildings appears to be reducing as we move away from the observer.  In perspective projection, all lines of sight start at a single point and is schematically shown in figure. 

In parallel projection, all lines of sight are parallel and is schematically represented in figure. 4. The observer is assumed to be stationed at infinite distance from the object.

Parallel vs Perspective Projection

Scaling In engineering Drawing

Scales

There is a wide variation in sizes for engineering objects. Some are very large (eg. Aero planes, rockets, etc) Some are vey small ( wrist watch, MEMs components)
There is a need to reduce or enlarge while drawing the objects on paper. Some objects can be drawn to their actual size. The proportion by which the drawing of aan object is enlarged or reduced is called the scale of the drawing.

Definition
A scale is defined as the ratio of the linear dimensions of the object as  represented in a drawing to the actual dimensions of the same.

·        Drawings drawn with the same size as the objects are called full sized drawing.

·        It is not convenient, always, to draw drawings of the object to its actual size. e.g. Buildings,

·        Heavy machines, Bridges, Watches, Electronic devices etc.

·        Hence scales are used to prepare drawing at

o   Full size

o   Reduced size 

o   Enlarged size

BIS Recommended Scales are shown in table 1.

Intermediate scales can be used in exceptional cases where recommended scales can not be applied for functional reasons.

Types of Scale :-
Engineers Scale :  The relation between the dimension on the drawing and the actual dimension of the object is mentioned numerically  (like 10 mm = 15 m).

Graphical Scale:  Scale is drawn on the drawing itself. This takes care of the shrinkage of the engineer’s scale when the drawing becomes old.

Types of Graphical Scale :-

·        Plain Scale

·        Diagonal Scale

·        Vernier Scale

·        Comparative scale

·        Scale of chords

Representative fraction (R.F.) :-

When a 1 cm long line in a drawing represents 1 meter length of the object

Length of scale  = RF x Maximum distance to be represented

Plain scale :-

·        A plain scale is  used to indicate the distance in a unit and its nest subdivision.

·        A plain scale consists of a line divided into suitable number of equal units. The first unit is subdivided into smaller parts.

·        The zero should be placed at the end of the 1st main unit.

·        From the zero mark, the units should be numbered to the right and the sub-divisions to the left.

·        The units and the subdivisions should be labeled clearly.

·        The R.F. should be mentioned below the scale.

Lines and Dimensions

Lines 
Lines is one important aspect of technical drawing.  Lines are always used to construct meaningful drawings. Various types of lines are used to construct drawing, each line used in some specific sense.  Lines are drawn following standard conventions mentioned in BIS (SP46:2003). A line may be curved, straight, continuous, segmented. It may be drawn as thin or thick. A few basic types of lines widely used in drawings are shown in Table 1.  

Table 1. Types of letters used in engineering drawing.

Line Strokes 
Line strokes refer to the directions of drawing straight and curved lines. The standards for lines is  given in  BIS : SP-46,  2003 
Vertical and inclined lines are drawn from top to bottom, horizontal lines are drawn from left to right. Curved lines are drawn from left to right or top to bottom. The direction of strokes are illustrated in figure 1.

Conventions used in lines

·       1. International systems of units (SI) – which is based on the meter.

·       2. Millimeter (mm) - The common SI unit of measure on engineering drawing.

·    3. Individual identification of linear units is not required if all dimensions on a drawing are in the same unit (mm).

·       4. The drawing should contain a note: ALL DIMENSIONS ARE IN MM. (Bottom left corner outside the title box)

5.Typical figures showing various lines used in the construction of engineering drawing is shown in figure 2.

Geometric Construction

Drawing consists of construction of primitive geometric forms viz.  points, lines and planes that serve a the building blocks for more complicated geometric shapes and defining the position of object in space.

The use of lines for obtaining the drawing of planes is shown in figure 1.

Figure 1 illustrates various planes generally encountered

Solids are obtained by combination of planes. Plane surfaces of  simple solids are shown in figure 2.

Figure 2 surfaces of few simples solids .  

In addition curved surfaces also exists. Figure 3 shows some of  solids having curved surfaces.

Figure 3. Solids having curved surfaces.

Engineering Drawing Layout and Lettering

Layout of a drawing sheet 
Every drawing sheet is to follow a particular layout.  As a standard practice sufficient margins are to be provided on all sides of the drawing sheet.  The drawing sheet should have drawing space and title page.  A typical layout of a drawing sheet is shown in the figure below:

• Borders – A minimum of 10 mm space left all around in between  the trimmed edges of the sheet.
• Filing margin – Minimum 20 mm space left on the left hand side with border included. This provided for taking perforations .
• Grid reference system – This is provided on all sizes of industrial drawing sheets for easy location of drawing within the frame.  The length and the width of the frames are divided into even number of divisions and labeled using numerals or capital letters.  Number of divisions for a particular sheet depends on complexity of the drawing. The grids along the horizontal edges  are labeled in numerals where as grids  along vertical edges are labeled using capital letters. The length of each grids can be between 25 mm and 75 mm.  Numbering and lettering start from the corner of the sheet opposite to the title box and are repeated on the opposite sides. they are written upright. Repetition of letters or numbers like AA, BB, etc., if they exceed that of the alphabets. For first year engineering students grid references need not be followed.
• Title box – An important feature on every drawing sheet.  This  is located at the bottom right hand corner of every sheet and provides the technical and administrative details of the drawing.  The title box is divided into two zones
• a.    Identification zone : In this zone the details like the identification number or part number, Title of the drawing, legal owner of the drawing, etc. are to be mentioned.
• b.    Additional information zone : Here indicative items lime symbols indicting the system of projection,  scale used, etc., the technical items lime method of surface texture, tolerances, etc., and other administrative items are  to be mentioned.

Layout of the title box recommended for Engineering Drawing Course
The title box shown in figure 2  can be used for  the engineering Drawing Course.