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WELCOMEEngineering Graphics - Lect 2

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OVERVIEW OF PLANE CURVES

Conic Section

Involute

Cycloid

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Conic sectionEllipse

Parabola

Hyperbola

OVERVIEW

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METHODS TO DRAW CONIC SECTION

Directrix Focus

Method

Ellipse

Parabola

Hyperbola

Ellipse

Concentric Circles Method

Rectangle or oblong Method

Arc of circle method

Parabola

Rectangle or oblong method

Tangent Method

Hyperbola

Directrix Focus

Method

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CONIC SECTIONWhen a right circular cone is cut by section plane in different positions with respect to the axis of the cone, the sections obtained are called as conics.

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CONIC SECTION When the section plane is inclined to the axis

and cuts all the generators on one side of the vertex we get an ellipse as section.

When the section plane is inclined to the axis and is parallel to the one of the generators we get parabola as section.

Hyperbola is obtained, When the section plane is inclined to the axis and cuts the cone on one side.

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DEFINITION It is a path generated by a point in one plane in

such way that ratio of its distance from fixed point (Focus) to its distance from fixed line (Directrix) remains constant.

This ratio is called as Eccentricity (e) If Ratio (e) < 1 it is Ellipse IF Ratio (e) =1 it is Parabola If Ratio (e) >1 it is Hyperbola

The line at right angle to the directrix and passing through a focus is called axis.

The point at which the conic curve cuts its axis is called as the vertex.

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DIRECTX FOCUS METHOD

To construct an ellipse when the distance of the focus from directrix is equal to 60mm and eccentricity = 2/3 by using directrix focus method.

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Draw a vertical line which represents directrix , At any point O, a right angle draw an axis OO2 and mark focus F on the axis so that OF=60mm

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Now divide OF into five equal parts

Mark vertex V on the 3rd part of from O so that VF/VO=2/3=e (VF=60x2/5=24mm,VO=60x3/5=36mm)

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Through V, draw a perpendicular VV´ to the axis, which is equal to the V1F.

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Draw a line joining O and V’, and extend it.

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Mark points 1,2,3…on the axis, and draw perpendicular lines to meet OA when produced at 1´

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With F as a centre and radius equal to 11´, Draw arcs to cut the perpendicular through 1 on the both sides of the axis.

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Repeat the same procedure for other points, e.g. for point 2, take radius equal to 22’ and F as a centre, draw arks to cut the perpendicular through 2 on the both sides of the axis.

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Finally, draw a smooth curve through all these points. Then this curve is required ellipse.