MACHANICAL DRAWING

 

    DRAWING LINES

    STRAIGHT LINE

a.         Hold the pencil naturally.

b.         Spot the beginning and endpoints.

c.         Swing the pencil back and forth between the points, barely touching the paper until the direction is clearly established.

d.         Draw the line firmly with a free and easy wrist-and-arm motion

Horizontal line

Vertical line

Nearly vertical inclined line

Nearly horizontal inclined line

    To bisect a line

 

    1.  Draw AB of any length, say 77 mm long.

    2.  Set the compass to about 2/3

    3.  AB.

    4.  With the compass centered at B, draw two arcs C and D.

    5.  With the compass centered at a, draw two arcs E and F inter setting arcs C and D at G and H.

    6.  Join GH with a straight line.

    7.  J is the center of AB is said to be bisected at J. 

    To divide a line into equal parts

 

    Line AB is to be divided into seven equal parts.

    1.  Draw AB of any length, say 95 mm long.

    2.  Draw AC at any angle to AB-about 300is a good angle for this purpose.

    3.  Set compass to about 1/7 of AB.

    4.  with the compass mark off seven equal spaces along AC.

    5.  Join AC

    6.  Draw lines from points 1 to 6 along AC parallel to B7 using a ruler and set square (As shown.)

    7.  AB is now divided into seven equal parts.

 

To divide a line into twelve equal parts

 

    In construction developments for sheet metal work it is necessary to know how to divide a line into  twelve equal parts. The procedure is the same as for dividing a line into any number of equal parts.

 

    1.  Draw AB 127 mm long.

    2.  Draw AC at an angle to AB.

    3.  Set a compass to about 11/2 of AB.

    4.  With the compass mark off twelve equal spaces along AC.

    5.  Join the twelfth point Don AC to B.

    6.  Draw lines from the other eleven points on AC parallel to BD.

    7.  AB is now divided into twelve equal parts.

    8.  Join the twelfth point Don AC to B.

    9.  Draw lines from the other eleven points on AC parallel to BD.

    10.AB is now divided into twelve equal parts. 

    SMALL CIRCLE

    Method1: Starting with a square

 

 

1. Lightly sketch the square and mark the mid-points.

 

2. Draw light diagonal sand mark the estimated radius.

 

            3. Draw the circle through the eight points

    Step 1

Step 2     

Step 3

Method2: Starting with the centerline

 

1. Lightly draw a center line.

 

            2. Add light radial line sand mark the estimated radius.

 

3. Sketch the full circle.

Step 1

Step 2

Step 3

    ARC

 

 

    Method1: Starting with a square

    Method2: Starting with the center line

    PROJECTIONS

 

    ORTHOGRAPHIC  PROJECTION

 

We have discussed both the role of the design model in the design process and the importance of the representation of the form or shape in this role.

 

Now we will consider in detail the methods designers use to represent  the form of their designs.

Back in the 18th century a French mathematician and engineer, Gaspard Monge (1746-1818), was involved with the design of military armory.  He developed a system, using two planes of projection at right angles to each other, for graphical description of solid objects.

This system, which was, and still is, called Descriptive Geometry, provided a method of graphically describing objects accurately and unambiguously. It relied on the perpendicular projection of geometry from perpendicular planes.

 Monge's Descriptive Geometry forms the basis of what is now called Orthographic Projection.

 

Orthographic projection is the graphical method used in modern engineering drawing. In order to interpret and communicate with engineering drawings a designer must have a sound understanding of its use and a clear vision of how the various projections are created.

 

There are two predominant orthographic projections used today.  They are based on Monge's original right-angle planes and are shown fully in Figure 3.1b. They define four separate spaces, or quadrants.  Each of these quadrants could contain the object to be represented. Traditionally however, only two are commonly used, the first and the third.

Projections created with the object placed in the first quadrant are said to be in First Angle projection, and likewise, projections created with the object placed in the third quadrant are said to be in Third Angle projection.

 

a.                  First  Angle Projection.

 

Consider the first quadrant in Figure 3.1b. The resultant drawing of the cone   would be obtained by flattening the two perpendicular projection planes, 

For this example, you could say that the right hand side image is the plan or top elevation and the image to the left is the side elevation.

 

Whether you view the objects from the left or the right, the order in which the drawing views are arranged puts the image that you see after the object, object first then the image.   This is always true for First Angle projection.

 

Put another way:

                        Viewing from the left: The drawn image on the right is your view of the drawn object on the left. Viewing from the right: The drawn image on the left is your view of the drawn object on the right.

 

This can get confusing, particularly when also considering other drawings created using other projections.  You may develop your own way of recognizing First Angle projection. The author uses:

 

The OBJECT is FIRST for FIRST Angle projection. or...EYE > OBJECT > IMAGE or...You look through the object and place the image

 Third angle projection.

 

Consider the third quadrant in Figure 3.1b. The resultant drawing of the cone would be obtained by flattening the two perpendicular projection planes, 

For this example of the cone, you would say that the left hand image is the plan or top elevation and the image to the right is the side elevation.

 

            Whether you view the objects from the left or the right, the order in which the drawing views are arranged puts the image that you see before the object, image first then the object. This is always true for Third Angle projection.

 

Put another way:

                    Viewing from the left: The drawn image on the left is your view of the drawn object on the right.

                    Viewing from the right: The drawn image on the right is your view of the drawn object on the left.

 

            Again, you may develop your own way of recognizing Third Angle projection. Perhaps:    EYE > IMAGE> OBJECT

CREATING  OR ETHNOGRAPHIC  PROJECTION   DRAWINGS

This is an introduction into how to create and interpret multi-view orthographic projection drawings.

First Angle Projection

The component:

Your drawing will, for this example consist of four views:

 

•       Front                                 F

•       Left                                   L

•       Right                                 R

•       Plan (Top)                         P

 

           The usual practice is to orient the component in a position that

it is most likely to be found in.

Your aim is to create, from the front view, an orthographic projection drawing as shown below in Figure 3.2a. Note how the views are constructed in line with each other, allowing the features to be 'projected' between the views.

A completed First angle projection drawing

Third angle projection

 

The construction method used is the same. The difference between first and third angle projection when creating or reading really lies with the positions of the views. For the same component, an orthographic projection drawing with the same front, side and plan views 

Third angle projection.

    Observe how, in third angle, the views give the image then the object. In other words, what you see     then what you are looking at.

 

In first angle you are given the object then the image, or what you are looking at, then what you see.

TO DIVIDE A CIRCLE INTO SIX EQUAL PARTS.

1.  Draw a circle of, say radius 40 mm. Its center is O.

2.  Without altering the compass, and starting at any point on the circumference of the circle, step off arcs around the circle.

3.  This is carried out carefully; it will be found that the sixth are crosses the circle at the point where the compass was first centered.

4.  Try this with circles of various radii. It will be found that the radius can always be stepped off exactly six times around its circle.

Note: - From this construction, it can be seen that the angle AOB must be 60°. This is because the circle contains 360° and AOB is 1/6 of the circle. 

TO DRAW A REGULAR HEXAGON OF A GIVEN SIDE LENGTH.

 

1.  Take the side length as 30 mm. Draw a circle of radii us 30mm.

2.  Draw a horizontal line across the circle through its center O.

3.  Without altering the compass, mark off arcs Band F (centered at A) and C and E (centered at D).

4.  Join AB, BC, CD, DE, EF and FA to complete the regular hexagon. 

TO DRAW A REGULAR OCTAGON OF GIVEN SIDE LENGTH.

 

1.  Take the side length as 25 mm. Draw AB 25 mm long.

2.  With the aid of a 45° set square draw angles of 135° to AB at Mandate.

3.  Set a compass to 25 mm and mark off arcs from A and from B to give Hand C.

4.  At C and at H draw verticals with the set square.

5.  Mark off and G with the compass from C and H.

6.  Continue in this manner to complete the regular octagon.

Note: - The smaller drawing shows how a regular octagon can be drawn within a given square.

1.  Draw the diagonals of the square.

2.  Draw arcs of radius AO, BO, CO and DO to give the side lengths of the regular octagon.

  Complete the octagon.

TO DIVIDE A CIRCLE INTO TWELVE EQUAL PARTS

 

1.  Draw a circle of, say, 70 mm diameter (set compass to 35 mm).

2.  Draw horizontal and vertical lines through 0, the center of the circle.

3.  Do not alter the setting of the compass.

4.  With the compass centered at the ends of each of the lines drawn across at the circle draw arcs across its circumference. 11From 1 draw arcs 3 and 11; from 4 draw arcs 2 and 6; from 7 draw arcs 5 and 9; from 10 draw arcs 8 and 12.

5.  The circle is now divided into twelve equal parts.

 

   TO DIVIDE A CIRCLE INTO TWELVE EQUAL PARTS - ANOTHER METHOD.

 

1.  Draw a circle, of say, 60 mm diameter (radius 30 mm)

2.  Draw horizontal and vertical lines through its center O.

3.  With the aid of a 30° , 60° set square draw lines at 30° and 60° through 0 across the circumference of the circle .

4.  The circle is now divided into twelve equal parts. 

DEVELOPMENT OF RIGHT SQUARE PYRAMID

The pyramid is of a square base of sides 40 mm long and of height 55 mm.

To develop the pattern for the sides of the pyramid:

1.  Draw a front view and plan.

2.  Find the true length of edge. AB. With a compass centered at A and set to radius AB, draw arc BC to meet a horizontal line. Through the apex A of the pyramid. Project from C on to the ground line of the front view. The line b is the true length of edge AB.

3.  Draw an arc of radius b.

4.  Set a compass to a - the side length of the square base.

5.  Mark off along the arc of radius b four arcs of radius a.

6.  Complete the required development as shown. 

DEVELOPMENT OF RIGHT CONE- METHOD 1

The cone is of base diameter 56 mm and height 80 mm.

1.  Draw front view and plan of cone.

2.  Divide the circle of the plan into twelve equal parts.

3.  Join the points 1 - 12 on the circle to its center.

4.  Project points 1 - 12 to the base of the front view.

5.  Join these points to A, the apex of the cone.

6.  A 7 (or AI) is the true length of anyone of the lines from A to the equally spaced points on the base.

7.  Draw an arc of radius. L.

8.  Step off, with a compass, twelve spaces along the arc, each of length a, taken from a in the plan.

9.  Complete the development as shown.

 

 

   DEVELOPMENT OF RIGHT CONE- METHOD 2

The cone is of diameter 54 mm and height 75mrn.

1.  Draw front view and plan.

2.  Measure the length L. In this example L 79 mm.

  Calculate the angle for the sector of radius L which forms \ the development. Use the 

Development of Frustum of right square pyramid.

The pyramid is of a square base of sides 34 mm and height 55 mm cut horizontally 18 mm above the base.

To develop a pattern for the sides of the frustum:

1.Draw front view and plan.

2.Find the true length of the edge CD to give length d.

3.Project top line EF on to line d to give true length e.

4.Draw an arc of radius d and step off four base side lengths c along the arc.

5.From the same center as for arc d draw an arc of radius e.

            6.Complete the development as shown

Development of truncated right square pyramid.

The base is of 34 mm sides, height 60 mm truncated at 30° to horizontal. Line 2 - 3 is 8 mm above base.

 

To develop a pattern for the sides of the truncated pyramid:

1.Draw front view and plan.

2.Find true length of one edge to give length f.

3.From edges 2- 3 and 1 - 4 in the front view project on to

Line fro gives the two true lengths g and h.

4.Draw an arc of radius f and step off four base side lengths along the arc.

5.From the same centre as for arc f draw arcs of radius g and h to give points 1,2,2,4 and 1 on the development.

6.Complete the development as shown. 

The development of the surfaces of right cones.

When developing patterns for right cones it is imagined that the cone is placed on a flat surface and rolled around its apex. This is shown in a pictorial drawing.

Two methods may be used for the developments of right cones. The first method is that most commonly employed when devel­oping patterns for sheet metal working.