Geometrical construction

It is important to understand the following terms before proceeding to the construction of lines and angles.

A point is defined as something which has a position and an extremely small magnitude so that it is barely visible. A point can be made on paper by a well sharpened pencil or a needle. A point is used to indicate position only, and in technical drawing it is usually represented by a cross or a dot.

A line has position and length, but has virtually no thickness. A line may either be straight or curve. A straight is defined as the shortest distance between two points. Two lines are said to be parallel if they are always the same distance apart and cannot meet, however far they may be produced (extended) in either direction.

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Types and Uses of Lines

Lines are represented in drawings in various ways;

Thick continuous lines are used for visible outlines and edges. The thickness of this kind of line is about 0.7mm. However, you do not have to measure the thickness of lines each time you draw. If you draw with a well-sharpened HB or 2Hpencil and apply a moderate pressure, you will produce a thick line.

Thin continuous lines are used as dimension lines, projection lines, construction lines, and outlines of adjacent parts and resolved sections. They are also used as hatching lines. Thin lines are usually drawn with well-sharpened 3H, 4H or harder pencils with moderate pressure and resolved sections. They are also used as hatching lines.

Thick long chain lines are used for cutting planes and viewing planes. They are also used ac centre lines, path lines and indicating movement, or extreme positions of movable parts, and for pitch circles. Like thick long-chain lines, thin long-chain lines, with thick ends may be used to indicate cutting planes.

Thick continuous wavy or irregular lines are used for short break lines and boundary lines.

Thin ruled lines with short zig-zags are used for long break lines.

Thin continuous wavy lines are used for limits or partial views or for sections when the line is not an axis.

Arrowheads are used at the ends of dimension lines. They are also used to indicate viewing planes and to indicate labeled parts. Arrowheads should be sharp, filled-in, and should be about 3mm long.

Construction of Lines and Angles

Important guides to good construction;

1. In technical drawing, all horizontal lines are drawn with the T-square and all vertical lines are drawn with a triangle (or a set-square) placed on the T-square.
2. When drawing a line with the triangle, ensure that its edge rests firmly on the edge of the T-square.

iii. Always ensure that the edge of the stock or head of the T-square slides firmly on the left hand side edge (the square of the drawing board. The T-square should never be used to draw a line in any other position.

1. Use well pointed pencils and take utmost care to draw lines through the required points, otherwise the result will not be satisfactory.
2. In using dividers and compasses, avoid pressing the points deeply into the drawing paper, as this will cause in accuracy. Remember that a point has position only and should have no magnitude.
3. In joining two points, adopt the following procedure: with the pencil point firmly placed on one point, slide the triangle up to meet it. Then swing the lower portion of the triangles until the lines up the other point on a straight-line with the first point. Check the second point for alignment by putting the pencil on point. Then draw the line joining the two points.

vii. There is no alternative to constant practice if you intend to draw accurately, neatly and fast.

Bisection of Lines

To bisect a given line;

1. Draw the given line AB
2. With centre A and any radius greater than half AB, draw the arcs above and below the line.

iii. With centre B, draw arcs of the same radius to cut the previous ones.

1. The line is drawn through the intersections of the arcs.

Division of Lines

(A) To divide a straight-line into a number of equal parts;

Suppose it is required to divide a straight-line 70mm long into 5 equal parts –

1. Draw AB 70mm long.
2. Draw AC at any convenient acute angle and set off from A, five equal divisions on this line using either a pair of dividers or a scale and pencil.

iii. Join point 5 to B using at 60⁰ triangle. Through the other points draw lines parallel to 5B by sliding the triangle on any straight edge, such as a T-square. The line AB is divided into five equal parts by the line 1 – 1, 2 – 2, 3 – 3, and -4.

Division of Lines in a Given Line Proportion

Suppose it is required to divide a straight-line 9cm into four parts in the proportion of 2:3:7:4:

1. Draw AB9cm long
2. Draw line AC at a convenient angle and set off on it from A 2 + 3 + 7 + 4 = 16.

iii. Join point 16 to B. Through the point 12 = 2 + 3 + 7, 5 = 2 + 3, and 2 = 0 + 2 draw lines parallel to 16B. The parallel lines divide AB in the required proportion.

ASSESSMENT

1. What is the definition of a point?
2. What are the steps in bisecting a line?
3. Mention 5 guides in making good construction.
4. List 5 types of lines.