Introduction of Geometrical Constructions

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Introduction of Geometrical Constructions - Curves & Involutes.
I. Geometrical Constructions consists of basic concepts and procedures for drawing simple diagrams such as dividing a line, drawing of curves and involutes etc.,
II. Basic concepts have already been discussed in playlist II(Basic Shapes) of this course and hence in this section curves used in engineering practice will be covered. (CONICS & SPECIAL CURVES).
III. Conic is a curve formed along the section plane obtained by cutting the cone. Depending upon the section plane’s angle, conic can be a circle, or an ellipse, or parabola or hyperbola.
iv. Some important special curves are:
a) Cycloid
b) Epi-Cycloid
c) Hypo-Cycloid
d) Involutes (of various figures).
Cycloid: Cycloid is a curve traced by a point on the circumference of a rolling circle on a straight line.
Epi-cycloid: Epi-Cycloid is a curve traced by a point on the circumference of a rolling circle outside a generating circle.
Hypo-cycloid: Hypo-Cycloid is a curve traced by a point on the circumference of a rolling circle inside a generating circle.
Involutes: Involute of a shape is a curve traced by following the path of a thread or string while it is being unwounded from the circumference/periphery of the shape.
Complete Exercise based on Geometrical Constructions:
1.Draw an ellipse by using Concentric Circle Method with major axis 8cm and minor axis 6cm
Ellipse by using Concentric Circle Method: • Ellipse by using Conce...
2.Draw an ellipse by using Eccentricity Method with eccentricity 2/3. Take focus at a distance of 6cm from directrix.
Ellipse by using Eccentricity Method: • Ellipse by using Eccen...
3.Draw a parabola by using Eccentricity Method. Take focus at a distance of 5cm from directrix.
Parabola by using Eccentricity Method: • Parabola by using Ecce...
4.Draw a parabola by using Rectangular Method. Consider base to be 70mm and height 30mm.
Parabola by using Rectangular Method: • Parabola by using Rect...
5.A ball is thrown in the air from the ground, such that, it reaches the maximum height of 70m and it falls at a distance of 30m from initial ground position. Draw the path traced by the ball.
Path traced by a ball. • Path traced by a ball.
6.Draw a hyperbola by using Eccentricity Method with eccentricity 3/2. Take focus at a distance of 5cm from directrix. At a distance of 3cm, draw a tangent and normal to this hyperbola.
Hyperbola: • Hyperbola by using Ecc...
7.Draw a cycloid which has been generated by a rolling circle of 50mm diameter for one complete revolution. Also, draw tangent and normal to this cycloid at a point 35mm from the base line.
Cycloid: • Cycloid
8. Draw an epi-cycloid which has been generated by a rolling circle of 40mm diameter on a 120mm directing circle for one complete CW revolution. Also, draw tangent and normal to this cycloid at a point 90mm from the center of directing circle.
Epicycloid: • Epi-cycloid
9. Draw a hypo-cycloid which has been generated by a rolling circle of 40mm diameter inside of a 160mm directing circle for one complete CW revolution. Also, draw tangent and normal to this cycloid at a point 60mm from the center of directing circle.
Hypocycloid: • Hypo-Cycloid
10. Draw the involutes formed by unwinding a thread on the following figures:
(i) Circle (30mm diameter) (ii) Equilateral Triangle (25mm side) (iii) Square (25mm side) (iv) Pentagon (25mm side).
Involutes : • Involutes Of Circle, T...