GEOMETRICAL CONSTRUCTION

Objectives

Upon completion of this lesson, the student will be able to:- Identify and understand the techniques and method of drawing geometrical drawings: Lines and angle constructionIdentify the problems in geometrical construction and ways to solve itUnderstand the definition of scales and its uses in working drawingUnderstand different types scale and apply it in engineering drawing.

ABOBISECTING A LINE

CD OA = OBRR

DIVIDING A LINE INTO EQUAL PARTSAB1234567Example: 7 Equal parts

CONSTRUCTING A PERPENDICULAR FROM THE END OF A LINE

AB900CRRrrr

CONSTRUCTING A 600 AND 1200 ANGLE

AB

600

1200RRR

AB46C9

900400600

400A-400A-BUSING THE SCALE OF CHORD TO CONSTRUCT AN ANGLE Example : 400

BISECTING AN ANGLE

ABCDRR

DRAWING A TRIANGLE WITH THE SIDES GIVEN

ABCABCAB

CONSTRUCT A TRIANGLE WITH THE PRIMETER AND THE SIDE RATIO GIVENExample : Ratio 3: 4: 6(For this example draw the smallest ratio as it base)

AB43CDEAB = primeter of the triangle3646

AB36C

300Q

900 - 600R=MQR= APA TRIANGLE GIVEN THE BASE AB, THE RATIO OF THE TWO OTHER SIDES (e.g 5:3 and the apex angle 600)Given53MN

P

600538-33

DRAWING A CIRCLE INSIDE A TRIANGLE

ABCO* The circle touches the sides of triangleO is center of circle

DRAWING A CIRCLE OUTSIDE A TRIANGLE

ABC

O* The circle touches the edge of the triangle

O is center of circle

CONSTRUCT A TRIANGLE WITH THE BASE, HEIGHT AND VERTEX GIVEN

ABCEFGOD

BAC is the same as vertex angle

Given vertex angle

AB is the base of the triangleHeight of the triangle

Types of regular polygonsSome types of regular polygons are pentagon (five sides), hexagon (six sides), heptagon (seven sides), octagon (eight sides), nonagon (nine sides), decagon (ten sides) and dodecagon (twelve sides).

DRAWING A REGULAR HEPTAGON WITH AN INSCRIBED CIRCLE GIVEN

APQBCDEFG27R = APAB=BC=CD=EF=FG=GA=DER = PA

DRAWING A REGULAR HEPTAGON WITH THE SIDE GIVENABCDE 645

Given

60045o

BC=AB7

FGDistance 6-7 = 5-6R=7- A=CD=DE=EF=FG= given the side length

SCALESScales are drawing instrument design to help draughtmens. Two types of scales are: (i) Ordinary scales (ii) Diagonal scales

A Triangular Section Scale Rule

A Flat Section Scale Rule

Scale 1:1

Scale Rule: 1:5 and 1:25 Ratio

ORDINARY SCALES

Ordinary scales is used for easy scale that is the scale have not many small divisions. When constructing any scale, the main point to remember is the total length of the scale.The length of the scale should be a bit longer than the largest dimension of the drawings.

Equivalent Part (EP) or Substitude Part (SP)Equivalent Part shows the direct ratio between a line in the drawing and the actual size. The ratio of the top and bottom number of a part is the ratio size drawn from its actual size.Equivalent part means the actual size of an object is 4 times the size of the drawing object.

If a scale is given as 1 mm = 1 cm, so E.P is 1 mm = 1 mm = 1 1 cm 10 mm 10

If a scale is given as 1 = 1, so E.P is 1 = 1 1 12 If a scale is given as 1 cm = 1 m, so E.P i 1 cm = 1 1 m 100

The largest actual dimension is 60 cm.The scale to be used is 2 cm = 10 cm (EP = 1/5), so the scale length is 1/5 x 60 = 12 cm. A line 12 cm is drawn. 12 cm is divided into 6 equal parts with each division is equal 10 cm. The first division on 10 cm is divided into 10 division, each division is 1 cm. This division is marked cearly to show the length of each division.

Ordinary scale 2 cm = 10 cm (EP = 1/5)34 cm

Construction ordinary scale, 1 = 1, length 6, can be read up to 1 Scale length= 72 x (1/12) = 6First Division : 6 Division 1Second Division : 12Division 1

Ordinary scale 1 = 1 (E.P. 1/12) 2 3

Constructing ordinary scale, 3 cm = 1 cm, length 5 cm, can be read up to 1 mm Scale length = 5 x (3/1) cm = 15 cmFirst division : 5 Division 1 cmSecond Division : 10 Division 1 mm

Ordinary scale 3 cm = 1 cm (E.P. 3/1)01cm2 cm3 cm4 cmmm159

DIAGONAL SCALE

Numbers of division that can be made to ordinary scales have a limit. Try to divide one centimeter to 50 equal length; you will see it is hard to do it. Diagonal scale can overcome the problems of dividing it into very small parts.

Diagonal Scale 1 cm = 1 cm, can be read up to 0.01 cm (0.1 m)

Constructing a diagonal scale, 3 cm = 1 m, length 4 m, can be read in cm Scale length:400 x ( 3/100) cm = 12 cmFirst division: 4 Division 1 mSecond division:10 Division 10 cmThird Division:10 Division 1 cmcmcm3m21010901011.37 m2.05 m