Engineering Curves

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Engineering Curves Part I


Conic Section


Ellipse, Parabola and Hyperbola are called conic sections because these curves appear on the surface of a cone when it is cut by some typical cutting planes.

observe illustrations given below...


conic section

 

Common definition of  parabola ellipse and hyperbola:

these are the locus of points moving in a plane such that the ratio of it' s distances from s fixed point (focus) and the fixed line( directrix) always remains constant. the ratio is called ECCENTRICITY. ( e )

For Ellipse E < 1


    For Parabola E = 1


      For Hyperbola E > 1


Parabola: A parabola is a plane curve where any point is at an equal distance from a fixed point ( the focus ) and a fixed straight line ( the directrix ).


Ellipse: It is a locus of a point moving in a plane such that the sum of it' s distance from two fixed points always remains constant. And this sum equals to the length of a major axis. These two fixed points are FOCUS 1 & FOCUS 2.

Hyperbola: Hyperbola is a set of all points such that the difference of the distances between any point on the hyperbola and two fixed points is constant. The two fixed points are called the foci of the hyperbola.

Engineering Curves Part II


Involute:




  1. involute of a circle

    • String length = πD

    • String length > πD

    • String length < πD



  2. Pole having a Length composite shape.

  3. Rode rolling over a semicircular pole.


Cycloid

  1. General Cycloid

  2. Trochoid ( superior )

  3. Trochoid ( inferior )

  4. Epi-Cycloid

  5. Hypo-Cycloid


Spiral:

  1. Sporal of one Convolution.

  2. Spiral of two Convolution.


Helix:

  1. On Cylinder.

  2. On a Cone.


 
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