A conic section is a curve obtained by cutting a right-circular cone with the help of a plane in different positions relative to the axis.
- e = 1 for parabola
- e = 3/2 for hyperbola
- e = 2/3 for ellipse
Problem: Draw a parabola when the distance between its focus and directrix is 50 mm. Also, draw a tangent and a normal at a point 70 mm from the directrix.
Problem: Draw a hyperbola when the distance of its focus from its directrix is 50 mm and eccentricity is 3/2. Also, draw a tangent and a normal to the hyperbola at a point 25 mm from the directrix.
Problem: Draw an ellipse when the distance of its focus from its directrix is 50 mm and eccentricity is 2/3. Also, draw a tangent and a normal to the ellipse at a point 70 mm away from the directrix.
ENGINEERING CYCLOIDAL CURVES
- Cycloid
- Epicycloid
- Hypocycloid
Problem: Draw a cycloid of a circle of diameter 50 mm for one revolution. Also, draw a tangent and a normal to the curve at a point 35 mm above the base line.
Problem: Draw an epicycloid of a circle of diameter 50 mm, which rolls outside a circle of diameter 180 mm for one revolution. Also, draw a tangent and a normal to the epicycloid at a point 135 mm from the centre of the directing circle.
Problems: Draw a hypocycloid of a circle of diameter 50 mm, which rolls inside a circle of diameter 180 mm for one revolution. Also, draw a tangent and a normal to the hypocycloid at a point 50 mm from the centre of the directing circle.
INVOLUTE
Prolem: Draw an involute for a triangular plane od side length 30mm also draw tangent and normal at a point 55mm from the center of the triangle.
Problem: Draw an involute of a hexagon of side 25 mm.
Problem: Draw an involute of a circle of diameter 50 mm. Also draw normal and tangent at a point 100 mm from the centre of the circle.
