Loading…

Flash Player 9 (or above) is needed to view presentations.
We have detected that you do not have it on your computer. To install it, go here.

Like this presentation? Why not share!

Geometricalconstruction

on

  • 11,019 views

 

Statistics

Views

Total Views
11,019
Views on SlideShare
10,827
Embed Views
192

Actions

Likes
4
Downloads
310
Comments
1

2 Embeds 192

http://lmspolisas.cidos.edu.my 189
http://kazict.wordpress.com 3

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel

11 of 1

  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
  • i want this note for reference, ask for permission..tq :)
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Geometricalconstruction Geometricalconstruction Presentation Transcript

    • Introduction In the course of engineering drawing, it is often necessary to make a certain geometrical constructions in order to complete an outline. There are no projections involved, and no dimensioning problems, the ONLY GREAT DIFFICULTY IS ACCURACY. Common geometric shapes
    • Geometrical Construction Techniques PRELIMINARY TECHNIQUES LINES GEOMETRICAL TERMS A POINT has no area, it indicates a position, it can be indicated by a dot or thus A LINE has length but no area. It may be curved or straight. A STRAIGHT LINE is the shortest distance between two points.
    • BISECTING/PERPENDICULARS/PARALLELS/DIVISION 1) BISECT A LINE 2) BISECT AN ACUTE ANGLE 3) BISECT OF A GIVEN ARC 1. With a compass opened to a 1. With centre A and radius greater distance greater than half AB, strike 1. Set an acute angle (angle less than than half AB, describe an arc. arcs from A and B. 90:), and bisect the angle. 2. Repeat with the same radius from B, 2. A line joining the points of the arcs intersecting at C and D. Join intersection of the arcs is the C to D to bisect the arc AB. bisector. 4) PERPENDICULAR AT A POINT ON A 5) PARALLEL LINE TO A LINE WITH A 6) DIVISION OF A LINE INTO EQUAL LINE GIVEN DISTANCE. PARTS AB is the given line, C is the given distance. 1. From any two points well apart on AB is the given line. 1. At point O, draw a semicircle of any AB, draw two arcs of radius equal to 1. Draw a line AC at any angle. C. 2. On line AC, make three convenient radius to touch the line at a and b. 2. Draw a line tangential to the two equal divisions. 2. With compass at a greater radius, arcs to give required line. 3. Join the last division with B and draw strike arcs from a and b. parallel lines as shown.
    • CONSTRUCTIONS OF ANGLES TERMINOLOGY NAMES OF ANGLES If two lines are pivoted . as shown in the diagram, as one line opens they form an angle. If the rotation is continued the line will cover a full circle. The unit for measuring an angle is a 7) CONSTRUCTION OF A 60° AND 30° ANGLES 8) CONSTRUCTION OF A 45° AND 90° ANGLES
    • CONSTRUCTION OF TRIANGLES TERMINOLOGY EQUILATERAL ISOSCELES RIGHT ANGLE All angles 60°. Base angles equal. One angle is 90°. A triangle is a plane figure All sides equal. All sides of different length. Opposite sides equal bounded by three straight lines. Triangles are named according to the length of their sides or the magnitude of their angles. OBTUSE ANGLE SCALENE One angle is greater than 90°. All sides of All angles different. All sides of different length. different length.
    • CONSTRUCTION OF TRIANGLES 9) TO CONSTRUCT AN EQUILATERAL TRIANGLE 10) TO CONSTRUCT AN ISOSCELES TRIANGLE, GIVEN BASE AND VERTICAL HEIGHT 1.Draw line AB. 1.Draw a line AB, equal to the length of the side. 2.Bisect AB and mark the vertical height. 2.With compass point on A and radius AB, draw an ABC is the required isosceles triangle. arc as shown above. 11) TO CONSTRUCT A RIGHT-ANGLE TRIANGLE 12) TO CONSTRUCT A TRIANGLE, GIVEN THE BASE ANGLES & THE ALTITUDE 1.Draw a line AB. Construct CD parallel to AB so that the distance between them is equal to the latitude. 1.Draw AB. From A construct angle CAB. 2.Bisect AB. Produce the bisection to cut AC at O. 2.From any point E, on CD, draw CÊF & DÊG so that they cut 3.With centre O and radius OA, draw semi-circle to AB in F & G respectively. find C. 3.Since CÊF = EFG & DÊG = EĜF (alternate angles), then Complete the triangle EFG is the required triangle.
    • THE CIRCLE PARTS OF A CIRCLE 13) TO FIND THE CENTRE OF A 14) TO FIND THE CENTRE OF 15) TO FIND THE CENTRE OF GIVEN ARC CIRCLES (METHOD 1) CIRCLES (METHOD 2) 1. Draw two horizontal lines facing one 1. Draw a horizontal line across the another across the circle at a place circle at a place approx. halfway from approximately halfway from the top the top to the centre of the circle. to the centre of the circle. These lines 2. Draw perpendicular lines downward 1. Draw two chords, AC and BD. pass through the circle form points A, from A and B. Where these lines cross 2. Bisect AC and BD as shown. The B, C and D. the circle forms C & D. bisectors will intersect at E. 2. Bisect these two lines. Where these two 3. Draw a line from C to B and from A to 3. The centre of the arc is point E. bisect lines intersect, thus the centre D. Where these lines cross is the exact of the given circle. centre of the given circle.
    • QUADRILATERALS TERMINOLOGY The quadrilateral is a plane figure bounded by four straight sides SQUARE RECTANGLE RHOMBUS PARALLELOGRAM TRAPEZIUM Opposite sides Two parallel All four sides equal. Opposite sides of All four sides equal. equal. sides. All angles 90:. equal. Opposite angles Opposite angles Two pairs of All angle 90:. equal. equal. angles equal. 16) TO CONSTRUCT A SQUARE 17) TO CONSTRUCT A 18) TO CONSTRUCT A RHOMBUS PARALLELOGRAM 1.Draw AD equal to the length of one of 1.Draw the side AB. From B erect the sides. From A construct the known a perpendicular. Mark off the angle. Mark off AB equal length to length of side BC. other known side. 1.Draw the diagonal AC. 2.With centres A & C draw arcs, 2.With compass pt. at B draw an arc 2.From A and C draw intersecting radius equal to the length of the equal radius to AD. With compass pt. at arcs, equal in length to the sides, to side of the square, to intersect at D draw an arc equal in radius to AB. meet at B and D. D. ABCD is the required parallelogram. ABCD is the required rhombus. ABCD is the required square.
    • REGULAR POLYGONS TERMINOLOGY A polygon is a plane figure bounded by more than four straight sides. Regular polygons are named according to the number of their sides. PENTAGON :5 sides HEPTAGON :7 sides NONAGON :9 sides UNDECAGON :11 sides HEXAGON :6 sides OCTAGON :8 sides DECAGON :10 sides DODECAGON :12 sides The regular polygons drawn on this page are the figures most frequently used in geometrical drawing. Particularly the hexagon and the octagon which can be constructed by using 60⁰ or 45⁰ set-square. REGULAR PENTAGON REGULAR HEXAGON REGULAR OCTAGON Five sides equal. Six sides equal. Eight sides equal. Five angles equal. Six angles equal. Eight angles are equal. IRREGULAR PENTAGON RE-ENTRANT HEXAGON IRREGULAR HEPTAGON One interior angle greater than Five sides unequal. 180:. Seven sides unequal. Five angles unequal. Six sides & six angles unequal. Seven angles unequal.
    • 19) TO CONSTRUCT A 20) TO CONSTRUCT A HEXAGON, 21) TO CONSTRUCT AN HEXAGON, GIVEN THE GIVEN THE DISTANCE ACROSS THE OCTAGON, GIVEN THE DISTANCE DISTANCE ACROSS THE FLATS (A/F) ACROSS CORNERS (A/C) CORNERS (A/C) 1.Draw a vertical and horizontal 1.Draw vertical and horizontal centre 1.Draw vertical and horizontal centre lines and a circle with a lines and a circle with a diameter equal centre lines and a circle with a to the given distance. diameter equal to the given diameter equal to the given distance. distance. Use a 60: set-square and tee-square as shown to give the six sides. 2.With a 45: set-square, draw 2.Step off the radius around the points on the circumference 45: circle to give six equally spaced apart. points, and join the points to give the required hexagon. Connect these eight points by straight lines to give the required octagon.
    • 22) TO CONSTRUCT AN 23) TO CONSTRUCT AN OCTAGON, GIVEN THE DISTANCE OCTAGON, GIVEN THE ACROSS THE FLATS (A/F DISTANCE ACROSS CORNERS (A/C) 1.Draw vertical and horizontal centre lines and a circle with a diameter equal to the given distance. 2.With a 45: set-square, draw points on the circumference 45: 1.vertical and horizontal centre lines and a circle with apart. a diameter equal to the given distance. 3.Connect these eight points by straight lines to give the 2.Use a 45: set-square and tee-square as shown in required octagon. construction of hexagon A/F to give the eight sides. 24) TO INSCRIBE ANY REGULAR POLYGON WITHIN A CIRCLE. e.g. PENTAGON
    • TANGENTS TO CIRCLES TERMINOLOGY If a disc stands on its edge on a flat surface it will touch the surface at one point. This point is known as the point of tangency as shown in the diagram and the straight line which represents the flat plane is known as a tangent. A line drawn from the point of tangency to the centre of the disc is called normal, and the tangent makes an angle of 90° with the normal.
    • 25) EXTERNAL TANGENT TO TWO CIRCLES OF 26) INTERNAL TANGENT TO TWO CIRCLES OF DIFFERENT Ø (CROSS BELT) DIFFERENT Ø (OPEN BELT) 1. Join the centres of circles a and b. Bisect ab to obtain the 1. Join the centres of circles a and b. Bisect ab to obtain the centre c of the semicircle. centre c of the semicircle. 2. From the outside of the larger circle, subtract the radius 2. From the outside of the larger circle, add the radius r of the r of the smaller circle. Draw the arc of radius ad. Draw smaller circle. Draw the arc of radius ad. Draw normal Na. normal Na. 3. Normal Nb is drawn parallel to normal Na. Draw the 3. Normal Nb is drawn parallel to normal Na. Draw the tangent. tangent.
    • JOINING OF CIRCLES 27) OUTSIDE RADIUS 28) INSIDE RADIUS Two circles of radii a and b are tangential to arc of radius R. Two circles of radii a and b are tangential to arc of radius R. 1. From the centre of circle radius a, describe an arc of R + a. 1. From the centre of circle radius a, describe an arc of R - a. 2. From the centre of circle radius b, describe an arc of R + 2. From the centre of circle radius b, describe an arc of R - b. b. 3. At the intersection of the two arcs, draw arc radius R. 3. At the intersection of the two arcs, draw arc radius R.
    • THE ELLIPSE TERMINOLOGY 29) CONCENTRIC/AUXILIARY CIRCLE METHOD 1.Draw two circles around the major and minor axis. 2.Divide into twelve equal parts using 30: - 60: set-square. 3.Draw horizontal lines from the minor circle and vertical lines from the major circle. 4.The intersection points between horizontal and vertical lines are points of an ellipse.
    • AN INVOLUTE TERMINOLOGY There are several definitions for the involutes, none being particularly easy to follow. An involute is the path of a point on a string as the string unwinds from a line, polygon, or circle. And it is also the locus of a point, initially on a base circle, which moves so that its straight line distance, along a tangent to the circle, to the tangential point of contact, is equal to the distance along the arc of the circle from the initial point to the instant point of tangency. The involute is best visualized as the path traced out by the end of a piece of cotton when cotton is unrolled from its reel. 30) TO DRAW AN INVOLUTE OF A CIRCLE Let the diameter of the circle is given 1. Divide the circle into 12 equal parts. 2. Draw tangents at each of the twelve circumferential divisions point, setting off along each tangent the length of the corresponding circular arc. 3. Draw the required curve through the points set off and can be determined by setting off equal distances 0-1, 1-2, 2-3, and so on, along the circumference. NOTE: The involutes of a circle are used in the construction of involutes gear teeth. In this system, the involutes form the face and a part of the flank of the teeth of gear wheels; the outlines of the teeth of racks are straight lines.