Conic Section (Ellipse, Parabola & Hyperbola) Orthographic Projection ENGINEERING GRAPHICS Unit 1 Conic Section (Ellipse, Parabola & Hyperbola) Cycloids &Involutes Orthographic Projection www.arpradeep.tk

Introduction Engineering Drawing is the language of Engineers. It is a graphical language used for effective communication among engineers. www.arpradeep.tk

DRAFTING TOOLS Drawing Board Mini drafter or T- square Drawing Instrument box Drawing Pencils Eraser Templates Set squares Protractor Scale Set French curves Drawing clips Duster piece of cloth (or) brush Sand-paper (or) Emery sheet block Drawing sheet www.arpradeep.tk

Drawing Board & Minidrafter Standard Size : 650mm x 470mm www.arpradeep.tk

Set squares & French curves Compass & Divider Set squares & French curves www.arpradeep.tk

Drawing Pencils with grade www.arpradeep.tk

Drawing sheet size Designation Dimension, mm Trimmed size A0 841 x 1189 A1 594 x 841 A2 * 420 x 594 A3 ** 297 x 420 A4 210 x 297 www.arpradeep.tk

Drawing sheet & Title block www.arpradeep.tk

Types of Lines & Applications www.arpradeep.tk

Open type Closed type Closed and filled Oblique stroke Types of Arrow head Open type Closed type Closed and filled Oblique stroke www.arpradeep.tk

Symbols for Shape Indication R : Radius Square SR: Spherical Radius  = Diameter www.arpradeep.tk

Engineering Curves www.arpradeep.tk

Conic Sections - Circle When the cutting plane AA is perpendicular to the axis and cuts all the generators, the section obtained is a circle www.arpradeep.tk

Conic Sections - Ellipse When the cutting plane BB is inclined to the axis of the cone and cuts all the generators on one side of the apex, the section obtained is an Ellipse www.arpradeep.tk

Conic sections - Parabola When the cutting plane CC is inclined to the axis of the cone and parallel to one of the generators, the section obtained is a Parabola www.arpradeep.tk

Conic Sections - Hyperbola When the cutting plane DD makes a smaller angle with the axis than that of the angle made by the generator of the cone, the section obtained is a Hyperbola www.arpradeep.tk

Eccentricity Method- construction of Ellipse, Parabola & Hyperbola Distance of the moving point from the focus e = Distance of the moving point from the directrix Note If the e < 1, curve obtained is Ellipse If the e = 1, curve obtained is Parabola If the e > 1, curve obtained is Hyperbola www.arpradeep.tk

Eccentricity Method www.arpradeep.tk

Exercises – Conic Sections Draw an ellipse when the distance of focus from the directrix is equal to 35 mm and eccentricity is 3/4. Draw a tangent and normal at a point P located at 30mm above the major axis. Draw a hyperbola when the distance of focus from the directrix is equal to 40mm and eccentricity is 5/3. Draw a tangent and normal at a point P located at 30mm above the major axis. A point moves such that its distance from a fixed straight line to its distance from a fixed point is equal. Draw the locus of the curve traced by that point. Add a normal and tangent to the curve at 40mm above the axis www.arpradeep.tk

Cycloid It is a curve traced by a point on the circumference of a circle which rolls along a straight line without slipping. Engineering Applications: Used in small gears in instruments like dial gauges and watches www.arpradeep.tk

Exercises – Cycloid A coin of 40 mm diameter rolls over a horizontal table without slipping. Draw the curve trace by a point on the circumference of the coin for the 3/4th of the revolution. Draw a cycloid formed by a rolling circle 50 mm in diameter. Use 12 divisions. Draw a tangent and normal at a point on the curve 30 mm above the directing line. www.arpradeep.tk

Involute Involute is a single-curved line traced out by an end of a string when unwound itself from straight line or a circle or a polygon, the string being always kept taut. Engineering Applications: Casings of centrifugal pumps and Cams are of involute shape. www.arpradeep.tk

Involute of a circle www.arpradeep.tk

Involute of a Square www.arpradeep.tk

Involute of a Pentagon www.arpradeep.tk

Exercises – Involutes A coir is unwound from a drum of 30 mm diameter. Draw the locus of the free end of the coir for unwinding through an angle of 360o. Draw also the tangent and normal at any point on the curve. Draw the curve traced out by an end of a thick wire unwound from a square of side 25 mm. Draw one turn of involute of a hexagon inscribed in a circle of 30mm diameter www.arpradeep.tk

Orthographic Projection ORTHO means Right-angle; GRAPHIC means Drawing; ORTHO GRAPHIC means Right-angled Drawing www.arpradeep.tk

Orthographic Projection www.arpradeep.tk

Orthographic Projection www.arpradeep.tk

Orthographic Projection www.arpradeep.tk

Orthographic Projection – Exercise 1 www.arpradeep.tk

Exercise 1 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 2 www.arpradeep.tk

Exercise 2 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 3 www.arpradeep.tk

Exercise 3 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 4 www.arpradeep.tk

Exercise 4 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 5 www.arpradeep.tk

Exercise 5 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 6 www.arpradeep.tk

Exercise 6 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 7 www.arpradeep.tk

Exercise 7 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 8 www.arpradeep.tk

Exercise 8 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 9 www.arpradeep.tk

Exercise 9 – Answer www.arpradeep.tk

Orthographic Projection – Exercise 10 www.arpradeep.tk

Exercise 10 – Answer www.arpradeep.tk

The End www.arpradeep.tk