CBSE Book Class 11 Engineering Graphics Special Curves

SPECIAL CURVES

3.1 INTRODUCTION

In several articles of daily use we notice that they have straight edges which may form various rectilinear figures such as triangle, square, rohmbus, parallelogram, trapezium etc. Look around or recall from your past experience such articles and name them. Then we also have articles/objects whose shape is circular, spherical, cylindrical, prisms and pyramids, conical etc. You have studied about the various orbits of the planets of solar system. What is their shape, called as ? Oval objects are also quite common. Name a few. In Engineering we shall come across many objects/ parts which are combination of these various shapes. We are going to study about these special curves.

3.2 ELLIPSE

One the most common curve in Engineering will be the oval/an egg shape. This we shall call as Ellipse. Let us know about the ellipse in details. Now study the figure (3.1) shown and answer the simple questions by choosing the correct option from the choices given. (Major Axis, Minor Axis, Centre, Semi-Major Axis, Semi-minor axis, Focus.

Q1. The point C is the .................... of ellipse.

Q2. Length A–A’ is the ...................... of ellipse.

Q3. Length B–B’ is the .................... of ellipse.

Q4. Length CA = CA’ and is called ........................ of the ellipse.

Q5. Length CB = CB’ and is called ..................... of the ellipse.

Q6. The points F and F’ each is known as .............. of the ellipse. We call them focii while refering to both. In engineering we are required to draw the curve ellipse. We shall now learn how to contruct the ellipse by various methods.

3.2.1 CONSTRUCTIONS OF THE ELLIPSE BY VARIOUS METHODS

(i) By the concentric circles method :

Example : Draw an ellipse whose major axis = 80 mm and minor-axis = 50 mm by the concentric circles method. Solution : Refer Fig. 3.2 (i) Draw a circle of φ 80 mm and another circle of φ 50 mm. (ii) Divide both the circles in 12 equal parts either by 30° and 60° angles or by compass method of constructing 60° angles. (iii) From divisions (1, 2 ...........) of the outer circle draw vertical lines as shown (iv) Similarly from the inner circle divisions draw horizonal to intersect the vertical lines already drawn. (v) The point of intersection of these vertical and horizonal lines will give us (a, b, c, d .........) points on ellipse (vi) Draw a smooth ellipse passing through thesepoints either by free hand or by French curves (It is better to practice free hand drawing of curves.) In good drawing there should not be any kink or dip on the entire curve).

(ii) Intersecting arcs methods :

Example : Draw an ellipse whose semi major axis is 35 mm and semi-minor axis is 20 mm by intersecting arcs method. Solution : Refer Fig. 3.3 : (i) On a horizontal line mark centre C of the ellipse. Cut CA = CA’ = 35 mm on this line (ii) Draw a perpendicular line through C on AA’ to obtain B and B’ such that CB = CB’ = 20 mm (iii) Now B as centre and radius = semi major axis = 35 mm obtain the focii F and F’ on the major axis A-A’. (iv) Take random points 1, 2, 3, approximately, equidstant between C and F on CA. Now take A’1, A’2 and A’3 as radii and centre as F’ draw arcs above and below line CA (v) Now take A1, A2 and A3 as radii and F as F’ as centre, cut the previous arcs drawn to obtain points of intersection (1, 2, 3, 5, 6 & 7) (vi) Similarly the points are to be obtained on the left. Draw a smooth ellipse through all these points of intersecting arcs.

(iii) Intersecting lines method :

Example : Draw an ellipse whose major axis = 60 mm and the minor axis = 40 mm by intersecting lines method. Solution : Refer Fig. 3.4 : (i) Draw a rectangle (60 × 40) such that AA’ is the major axis and BB’ is the minor axis which are obtained by joining the mid-points of opposite sides of the rectangle. Mark centre as C. (ii) Now divide both the semi-major axes into four equal parts and name the points 1, 2 and 3 (iii) Similarly divide both the sides of rectangle parallel to semi minor axes in four parts, naming them 1’, 2’ and 3’ (iv) Join these points on sides with B and B’ as shown. Further Join1, 2 and 3 with B and B’ as shown (v) Extend these lines to

Please refer to the link below for - CBSE Class 11 Engineering Graphics Special Curves