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CURVES IN ENGINEERING
An attempt on lucidity & holism PON.RATHNAVEL
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SyllabusConics – Construction of ellipse, Parabola and hyperbola by eccentricity method – Construction of cycloid and involutes of square and circle – Drawing of tangents and normal to the above curves. 10 hours
SynopsisIntroduction to Curves – Classification of Curves – Introduction to Conics, Roulettes and Involutes Terminology in Curves - Properties of Conics, Roulettes and Involutes - Construction of ellipse by eccentricity method - Construction of Parabola by eccentricity method - Construction of hyperbola by eccentricity method – Construction of cycloid – Construction of Involute of square – Construction of Involute of Circle 05 periods
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WHY CURVES?
CIVIL ENGINEERINGBridges, Arches, Dams, Roads, Manholes etc.
MECHANICAL ENGINEERINGGear Teeth, Reflector Lights, Centrifugal Pumps etc
ECEDesign of Satellites, Missiles etc, Dish Antennas, ECG & EEG Machines
CSE & ITComputer Graphics, Networking Concepts
ENGINEERING GRAPHICS EXAM2 Marks - 4 & 15 Marks - 1
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JUMBLE ?
U O L CS
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LOCUS
SET OF POINTS
GIVEN CONDITIONS
PATH Vs LOCUS
Locus is a collection of points which share a property.
It is used to define curves in a geometry.
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CURVE
A curve is considered to
be the locus of a set of points that satisfy an
algebraic equation
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CLASSIFICATIONCURVES
CONIC SECTIONS ENGINEERING CURVES
1. CIRCLE2. ELLIPSE3. PARABOLA4. HYPERBOLA5. RECTANGULAR HYPERBOLA
1. CYCLOIDAL CURVES/ROULETTESa.Cycloidb.EpiCycloidc.Hypocycloidd.Trochoids(Superior & Inferior)e.Epitrochoids(Superior & Inferior)f.Hypotrochoids(Superior&Inferior)2. INVOLUTE3. SPIRALSa.Archimedianb.Logarithmicc.Hyperbolic4. HELICESa.Cylindricalb.Conical5. SPECIAL CURVES
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STICKING TO SYLLABUS
Theory
CONICSROULETTESINVOLUTES
Practical
ELLIPSEPARABOLA
HYPERBOLACYCLOID
INVOLUTE OF SQUAREINVOLUTE OF CIRCLE
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CONIC SECTIONS (A) CONICS
The curves obtained by the intersection of a cone by cutting plane in different positions are called conics.
The conics are1. CIRCLE2. ELLIPSE3. PARABOLA4. HYPERBOLA5. RECTANGULAR HYPERBOLA
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DEFINING CONICS
Curve Position of Cutting Plane
Circle Perpendicular to axis and parallel to the base
Ellipse Inclined to the axis and not parallel to any generator. Angle of Cutting Plane > Angle of Generator
Parabola Inclined to axis, parallel to generators and passes through the base and axis
Hyperbola Inclined to the axis and not parallel to any generator. Angle of Cutting Plane < Angle of Generator
Rectangular Hyperbola
Parallel to the Axis and Perpendicular to the Base
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ELLIPSE
Ellipse is defined as the locus of points the sum of whose distances from two fixed points, called the foci, is a constant.
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PARABOLA
Parabola is defined as the locus of points whose distances from a fixed point, called the focus, and a fixed line, called the directrix, are always equal.
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HYPERBOLA
Hyperbola is defined as the locus of points whose distances from two fixed points, called the foci, remains constant.
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ROULETTES
A cycloid is a curve generated by a point on the circumference of a circle as the circle rolls along a straight line without slipping.
The rolling circle is called generating circle and the line along which it rolls is called base line or directing line.
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ROULETTES
CYCLOID – THE QUARREL CURVE OR THE HELEN OF GEOMETRY
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ROULETTES
CYCLOID – THE QUARREL CURVE OR THE HELEN OF GEOMETRY
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ROULETTES
An epicycloid is a curve generated by a point on the circumference of a circle which rolls on the outside of another circle without sliding or slipping.
The rolling circle is called generating circle and the outside circle on which it rolls is called the directing circle or the base circle.
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ROULETTES
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ROULETTES
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ROULETTES
A hypocycloid is a curve generated by a point on the circumference of a circle which rolls on the inside of another circle without sliding or slipping.
The rolling circle is called generating circle/hypocircle and the inside circle on which it rolls is called the directing circle or the base circle.
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ROULETTES
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ROULETTES
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ROULETTES
A trochoid is a curve generated by a point either inside or outside the circumference of a circle that rolls along a straight line without slipping.
When the point is inside the circumference of the circle, it is called inferior trochoid. If it is outside the circumference of the circle, it is called superior trochoid.
An inferior trochoid is also called prolate cycloid.A superior trochoid is also called curtate cycloid.
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ROULETTES
An epitrochoid is a curve generated by a point either inside or outside the circumference of a circle that rolls along the outside of an circle without slipping.
When the point is inside the circumference of the circle, it is called inferior epitrochoid. If it is outside the circumference of the circle, it is called superior epitrochoid.
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ROULETTES
A hypotrochoid is a curve generated by a point either inside or outside the circumference of a circle that rolls along the outside of an circle without slipping.
When the point is inside the circumference of the circle, it is called inferior hypotrochoid. If it is outside the circumference of the circle, it is called superior hypotrochoid.
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INVOLUTES
An involute is a curve traced by a point as it unwinds from around a circle or polygon.
The concerned circle or polygon is called as evolute.
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INVOLUTES
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INVOLUTES
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INVOLUTES