MEMB113

1. MEMB113 04 Geometrical construction

2. Contents • Overview • Basic geometrical constructions • Bisect lines, angles, etc. • Draw circles, hexagon, pentagon, etc. • Draw arc tangents, etc.

3. Basic Geometrical construction • To develop the skill of • Division of lines and angles • Construction of tangents • Blending of radii • Accuracy is important, inaccuracy causes the constructions unusable

4. Example

5. Bisect a straight line Bisecting a straight line • To divide a line into two equal parts

6. Drawing a perpendicular line from a point in a line • AB is the line, and C is the point on it • With center C and any radius, describe equal arcs to cut AB at E and F • From E and F describe equal arcs to intersect at D • Join C and D to give the required perpendicular

7. Bisecting an angle • ABC is the given angle • From B describe an arc to cut AB and BC at E and D respectively • With centers E and D, draw equal arcs to intersect at F • Join BF, the required bisector of the angle

8. Drawing a line parallel to a given line at a given distance from it • AB is the given line, and c is the given distance • From any two points well apart of AB, draw two arcs of radius equal to c • Draw a line tangential to the two arcs to give the required line

9. Constructing hexagon To construct a regular hexagon on a given line • AB is the given line • From A and B, and with radius AB, draw two equal arcs to intersect at O • With radius OA or OB and center O draw a circle • From A or B, using the same radius, step off arcs around the circle at C, D, E and F • Join these points to complete the hexagon

10. Constructing hexagon Constructing a hexagon, given the distance ‘across flats’

11. Constructing pentagon Constructing a pentagon, given the diameter/radius of the circumscribe circle

12. Constructing pentagon To construct a regular pentagon on a given line • AB is the given line • Bisect AB at C, erect a perpendicular at B, and mark off BD equal to AB • With C as center and radius CD, describe an arc to intersect AB produced at E • From A and B, and with radius AE, describe arcs to intersect at F • With radius AB and centers A, B and F describe arcs to intersect at G and H • Join FG, GA, FH and HB to complete the pentagon

13. Draw tangent from a point to a circle • draw straight line from centre point A of the circle to the given point B • find the midpoint O of the line AB • set the compass to the radius AO • draw a circle or arc intersecting the circle A • the crossing point is the tangent point

14. Drawing a tangent to two given circles • A and B are the centers of two given circles of radii r and R respectively • With center B and radius R-r, describe a circle • Bisect AB at X, and draw a semicircle on AB to cut circle R-r at C • Join BC, and produce it to cut the larger circle at D • Draw AE parallel to BD • Join ED to give the required tangent

15. Drawing an arc tangential to two straight lines • AB and CB are the given lines, and c is the radius of the required arc • Draw two lines parallel to the given lines at a distance c from them to intersect at D • With centers D and radius c, draw an arc, which will be tangential to both given lines • Erect perpendiculars at D to intersect AB and BC at E and F respectively. These are the points of tangency of the lines with the arc

16. Drawing an arc tangential to two arcs (externally) • A and B are the centers of the given arcs of radii a and b respectively; c is the external arc radius • From centers A and B, describe two arcs of radii a + c and b+c respectively to intersect at C • With center C and radius c, describe an arc which will be tangential to the given arcs • E and F are the points of tangency of the three arcs

17. Drawing an arc tangential to two arcs (internally) • A and B are the centers of the given arcs of radii a and b respectively; c is the required tangential arc radius • From centers A and B, describe two arcs of radii c-a and c-b respectively to intersect at C • With center C and radius c, describe an arc which will be tangential to the given arcs • E and F are the points of tangency of the three arcs

18. Drawing an arc tangential to a line and another arc • A is the center of the given arc of radius a. BC is the given line, and b is the radius of the required arc • From A, describe an arc with radius a+b • Draw a line parallel to BC and distant b, from it to intersect the arc a+b at D • From D, describe an arc of radius b, which will be tangential to the given line BC and the given arc a • E and F are the points of tangency

19. Drawing an arc tangential to two arcs and enclosing one of them • A and B as centers of two arcs of radius a and b respectively. Line c is the radius of the required arc • With A and B as centers, describe arcs of radii a+c and c-b respectively to intersect at C • With center C and radius c, describe the required arc • Join AC to intersect the curve at E, and produce CE to intersect the curve at F. Then E and F are the points of tangency of the three arcs

20. End of chapter [04] References: Engineering Drawing, A.W. Boundy, McGraw-Hill, 2000 Fundamentals of Graphics Communication 3rd Edition, Gary Bertoline & Eric Weibe, McGraw-Hill