1. ENGINEERING CURVES
By:
Muhammad Zahid

2. ENGINEERING CURVES
While designing Objects various types of curves are used. Curves which are commonly used in engineering drawing are: 1. conic section. 2. cycloidal curves. 3. involute. 4. evolutes. 5. spirals 6. helix

3. CONIC CURVES
Section formed by the intersection of a right circular cone by a plane in different positions relative to the axis of the cone are called conics . e.g. Parabola, hyperbola and ellipse.

4. CONIC CURVES
CONIC
Conic is defined as the locus of a point moving in a plane such that the ratio of its distance from a fixed point and a fixed straight line is always constant. This ratio is called Eccentricity.
Fixed point  is called Focus
Fixed line is called Directrix

5. CONIC CURVES
The eccentricity is always < 1 for   Ellipse = 1   for Parabola > 1   for Hyperbola  

6. CONIC CURVES
when e=1/2, the curve is an  Ellipse, when e=1, it is a parabola and when e=2, it is a hyperbola.  Figure below shows the ellipse, parabola and hyperbola.

7. CONIC CURVES
ELLIPSE:- Construction of Ellipse:- An ellipse can be defined as where a & b are the length of major and minor axes of the ellipse.

8. CONIC CURVES
ELLIPSE:-

9. CONIC CURVES ELLIPSE:- draw any vertical line AB as directrix.
at any point C on this line draw a perpendicular line to the AB.
Mark a focus F on the axis such that CF=80mm
Divide CF into 7 equal parts (sum of numerator and denominator of eccentricity) and mark the forth point from C as vertex V. so
AT point V draw a perpendicular VB equal to length VF.

10. CONIC CURVES ELLIPSE:- draw a line joining C and B.
Though point F draw a line at 45° which meets the line CB at point D.
Through D, drop a perpendicular DV’ on CC’.
Bisect the line VV’ and mark O on the intersection point.
Mark any point on the axis between VF and draw perpendicular line to meet CD at point 1’.
With F as a centre and radius = 1–1’, cut two arcs on the perpendicular through 1 to locate P1 and P1’.

11. CONIC CURVES ELLIPSE:-
P1 and P1’ are the points on the ellipse because the distance of P1 from AB is equal to C1. So
P1-F=1-1’ and
Similarly, with F as centre and radii = 2–2’, 3–3’, etc., cut arcs on the corresponding perpendiculars to locate P2 and P2’, P3 and P3’, etc. Also, cut similar arcs on the perpendicular through O to locate V1 and V1’.

12. PARABOLA
Parabola(Applications) There are a large number of applications for parabolic shapes. Some of these are in searchlight mirrors, telescopic mirrors, a beam of uniform strength in design applications, the trajectory of the weightless flight, etc.

13. PARABOLA Constructing a Parabola
draw any vertical line AB as directrix.
at any point C on this line draw a perpendicular line to the AB.
Mark a focus F on the axis such that CF=60mm
Bisect CF into equal parts and mark the mid point from C as vertex V. so
AT point V draw a perpendicular VB equal to length VF.
draw a line joining C and B.

14. PARABOLA
Mark a few points, say, 1, 2, 3, … on VC’ and erect perpendiculars through them meeting CB produced at 1’, 2’, 3’, …
With F as a centre and radius = 1–1’, cut two arcs on the perpendicular through 1 to locate P1 and P1’. Similarly, with F as a centre and radii = 2–2’, 3–3’, etc., cut arcs on the corresponding perpendiculars to locate P2 and P2’, P3 and P3’, etc.
Draw a smooth curve passing through V, P1, P2, P3 … P3’, P2’, P1’.

15. PARABOLA

16. HYPERBOLA
Hyperbola (Applications) Hyperbolic shapes finds large number of industrial applications like the shape of cooling towers, mirrors used for long distance telescopes, etc

17. HYPERBOLA
Constructing a Hyperbola (Eccentricity Method) Construction of hyperbola by eccentricity method is similar to ellipse and parabola. Let we construct a Hyperbola where the eccentricity, e = 3/2 and the distance of the focus from the directrix = 50 mm.