ENGINEERING DRAWING (CHAPTER-5)

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📘 ENGINEERING DRAWING

Chapter 5 – Geometrical Constructions

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5.1 Introduction

Geometrical constructions form the foundation of engineering drawing.
They help in constructing angles, polygons, tangents, perpendiculars, bisectors, and divisions with accuracy using only compass, straightedge (scale), and set squares.

These constructions are widely applied in mechanical drawings, civil plans, gear tooth profiles, cams, and machine parts.

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5.2 Basic Constructions

(A) Bisecting a Line Segment

Steps:

1. Draw a line AB.

2. With A as center and radius > ½ AB, draw arcs above and below AB.

3. With B as center and same radius, draw arcs to cut previous arcs.

4. Join intersection points → perpendicular bisector of AB.

👉 This gives both the midpoint and right angle bisector.

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(B) Bisecting an Angle

Steps:

1. Draw ∠ABC.

2. With B as center, draw an arc cutting BA and BC at D and E.

3. With D and E as centers, draw arcs intersecting at F.

4. Join BF → bisector of ∠ABC.

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(C) Dividing a Line into Equal Parts

Steps:

1. Draw line AB to be divided.

2. Draw an inclined line AX.

3. Mark required number of equal parts on AX (say 6).

4. Join last point on AX to B.

5. Draw lines parallel to this through other points (using set-square).

6. These divide AB into 6 equal parts.

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(D) Drawing Perpendicular to a Line

1. From a point on line.

2. From a point outside line.
   (Both use arcs and compass methods).

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5.3 Construction of Regular Polygons

(A) Regular Hexagon (given side)

Steps:

1. Draw a circle of radius equal to given side.

2. Mark 6 equal divisions on circumference using compass.

3. Join consecutive points → regular hexagon.

👉 Application: Hexagonal bolts, nuts, and machine parts.

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(B) Regular Pentagon (given side)

1. Draw circle of required radius.

2. Use special geometric methods (like intersecting arcs) to mark 5 equal divisions.

3. Join points → regular pentagon.

👉 Application: Gaskets, architectural patterns.

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(C) Regular Polygon (general method)

• Can be inscribed in a circle by dividing circumference into equal arcs.

• Or constructed on a given side using compass.

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5.4 Construction of Tangents

(A) Tangent to Circle from a Point Outside

Steps:

1. Draw circle with center O.

2. Mark external point P.

3. Join OP.

4. Bisect OP → let M be midpoint.

5. Draw circle with center M, radius MO.

6. It cuts main circle at A and B.

7. Join PA and PB → tangents.

👉 Used in gear tooth, cams, pulley systems.

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5.5 Construction of Special Angles

(A) 30°, 45°, 60°, 90°

• Can be drawn using set squares.

(B) 75°, 105°, 120° etc.

• Obtained by addition/subtraction of standard angles.

(C) Any given angle (without protractor)

• By constructing arc and dividing appropriately.

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5.6 Locus of Points

• Definition: Locus is the path traced by a point moving under certain conditions.

• Examples:

  1. Perpendicular bisector locus – set of points equidistant from two points.

  2. Angle bisector locus – set of points equidistant from two lines.

  3. Circle locus – set of points equidistant from a fixed point.

👉 Locus is used in cam design, gear motion, and mechanical linkages.

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5.7 Practical Applications of Geometrical Constructions

• Designing polygons → nuts, bolts, gear profiles.

• Drawing tangents → cams, pulleys, belt drives.

• Bisectors and perpendiculars → locating holes, slots, joints.

• Locus → path of moving parts in mechanisms.

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5.8 Summary of Chapter

• Basic constructions: bisecting lines, angles, dividing lines, perpendiculars.

• Polygons: constructed by inscribing in circle or on given side.

• Tangents: drawn using circle and arcs.

• Special angles: constructed with set squares and compass.

• Locus of points: important for motion studies in machines.

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