# Projections of Lines

The literal definition of projections of lines is somewhat complicated but

Projection of Lines:  Projection of intersecting lines When the lines are intersecting, the point of intersection lies on both the lines and hence these lines have no shortest distance between them.

### INTRODUCTION TO PROJECTION

Projecting the image of an object to the plane of projection is known as projection. The object may be a point, line, plane, solid, machine component or a building. Consider the following illustration to project the image of an object onto a plane. In engineering drawing practice, two principal planes are used to get the projection of an object as shown in figure.

#### Q) How do you find a projection of a line?

“Consider line AB and point P. Construct a perpendicular PQ from P on AB that meets AB at Q. This point Q is known as the projection of P on the line AB.” This is the simplest explanation of projections of lines.

#### Q) A point C is 20mm below HP and 30 mm behind VP. Draw its projection.

To draw the projections Draw the reference line XY. Mark a point c’ at a distance of 20 mm below XY. Through this point draw a perpendicular line to XY and mark the top view c at a distance of 30 mm above XY.

### PROJECTION OF STRAIGHT LINES

A straight line is the shortest route to join any two given points. It is a one-dimensional object having only length (l). The projection of the straight line is obtained by joining the top and front views of the respective end points of the line. The actual length of the straight line is known as true length (TL).

Example:

Explain the true length concept with an example.

#### Solution

“Hold a pencil in your hand and open a note-book in such a way that some pages are on the table and some pages are held perpendicular to the table top. Consider these as two planes HP and VP. Put one end of the pencil on the HP and let it make some angle with HP. Make the pencil parallel to VP (imagine the pencil to be a line). Under the condition if the line is projected on HP and VP, its projections will be as shown in the following figure.”

#### EXAMPLE

A line AB 70 mm long has its end A 15 mm above HP and 25 mm in front of VP. Its top view (plan) has a length of 40 mm. Draw its projections and find the inclination of the line with HP.

#### SOLUTION

“The projections of the line are drawn with reference to the XY lien as follows: 1. Mark the projections of end A by considering it as a point. Its front view a’ is 15 mm above XY and top view a is 25 mm below XY. 2. The top view of the line ab is drawn parallel to XY to the given length of 40 mm. 3. Draw a vertical line (projector) from b. 4. Using true length 70 mm as radius and a’ as Centre, mark a point in the vertical line to get b’. 5. The inclination of a’b’ with XY is measured to get” .

#### Q) What are the four methods of projection?

There are four main types of projection methods used in mechanical drawing in order to convey information such as geometry, dimensions, tolerances, material and finish.

1. #### Orthographic Projection

However, it is not a realistic view of the object, because it requires multiple views to get all of the information in order to “see” the design. An orthographic projection can also include a section view, which is when a portion of the object is cross sectioned along the specified plane

Orthographic projection shows a 3D object in two dimensions so that you can see three views: the front view, side view and top view. It is usually positioned relative to the rules of first-angle or third-angle projection. The difference between the two is the view. However the view of the object isn’t realistic. This is due to the fact that it requires multiple views to see the object thoroughly. But more accurate measurements can be obtained because all views have the same scale. It may include a section view, which happens when the portion of the object is cross sectioned along the plane, and the information about that section is displayed. It’s used to show internal specifications.

1. #### Axonometric Projection

Axonometric is another type of orthographic projection. It is seen as complex due to the fact that only one image is drawn on the paper’s plane. These are further divided into 3 types of classifications. The most common is isometric, where the angles between the three axes are equal. The second is diametric. Only two of the angles between the axes are equal in this type. Trimetric is the third type. It can have three axes with different angles between them. It is the most common type. Axonometric projection is good for rectangular or square objects rather than objects with curved lines.

1. #### Oblique Projection

Oblique projection only requires only one image so that makes it a simple type. Since it’s not complex they can be drawn with traditional tools.  It depicts a 2D image of a 3D object. . The object is drawn from the front view, and then the other areas are added in relation to it. It can be divided into two types based on the scaling of the object: cavalier projection, which uses a 1:1 scale, and cabinet projection, which uses a 2:1 scale. It uses parallel lines to produce the source of the object in the image.

1. #### Perspective Projection

Of the four methods, perspective projection is not based on parallel lines. It is an approximate representation of the object as it would be seen by the eye in respect to depth perception. The projection lines emerge from a single point, showing the closer part larger than the more distant part. The object can feel more realistic with this projection, but it does require a good imagination.      