CONSTRUCTION OF ELLIPSE

Transcription

1 CONSTRUCTION OF ELLIPSE Procedure: The procedure for drawing an ellipse by the Concentric Circle method is described below: Two circles are drawn with the major and minor diameters of 60 mm and 40 mm respectively (Fig. S1.8). Then the circle is divided into a number of equal radial divisions. They intersect both the inner and the outer circles of minor and major diameters respectively. Now from the intersecting points of the outer circle and the inner circle vertical and horizontal lines are drawn respectively. The intersecting points of the vertical and the horizontal lines give the locus of the ellipse. They are joined to obtain the required ellipse. Fig. S1.8 Procedure: The procedure of drawing an ellipse by the Parallelogram method is given below: AB and CD are the major and minor diameters of the ellipse. A parallelogram PQRS is drawn with the major and minor diameters (Fig. S1.9). Now AB is divided into a number of equal parts and then PQ and RS are also divided into the same number of equal parts. They are marked with 1, 2 and 3. Then through the points 1, 2 and 3, lines are drawn from C and D. The intersecting points of the lines are the locus of the ellipse. Now the required ellipse is completed. Fig. S1.9 Procedure: In order to draw an ellipse by the Four-Centered Approximate method, the steps as mentioned below are to be followed: PQ and RS are the major and the minor diameters of the ellipse. They intersect at the point O (Fig. S1.10). An arc is drawn with center O and radius OP. It intersects the extended minor axis at the point A. Now PR is joined and an arc of radius RA is drawn taking R as the center. It intersects PR at the point B. Then PB is bisected and a perpendicular is drawn through the bisecting point C. The perpendicular intersects the extended minor axis at the point D. CD intersects PO at the point E. OE is drawn equal to OE and OD / is drawn equal to OD. DE /, D / E and D / E / are added and extended.

2 Taking D and D / as the centers and DR or D / S as the radius two arcs MRN and KSL are drawn respectively. Also taking E and E / as the centers and PE or QE / as the radius another two arcs KPM and NQL are drawn respectively. Thus the required ellipse is completed. Fig. S1.10 CONSTRUCTION OF PARABOLA Procedure: The procedure to draw a parabola by the parallelogram method is given below: The rectangle PQRS with sides PQ and QR is drawn first. The axis of the parabola OA is drawn parallel to QR passing through the mid-point of PQ (Fig. S1.13). Now QR is divided into a number of equal divisions, which are marked with 1, 2, 3 and 4. QO is divided into the same number of equal divisions and they are also marked with 1, 2, 3 and 4. Then the points 1, 2, 3 and 4 on QR are joined with the point O. From the points 1, 2, 3 and 4 on OQ lines are drawn parallel to OA. They intersect with the respective lines from QR. Now the curve is drawn through the intersecting points as in the figure to obtain the required parabola. Fig. S1.13 CONSTRUCTION OF AN INVOLUTE PROFILE Procedure: The procedure of drawing an involute profile is given below: The base circle of diameter 65 mm is drawn and a point a is taken on its circumference, then a tangent am is drawn through the point a on the base circle (Fig. S1.15). Now from the point a the line am and the circumference are divided equally into a number of points b, c, d, e, f and b 1, c 1, d 1, e 1, f 1 respectively.

3 Next to find the locus of the involute profile a tangent is drawn through the point f 1 on the base circle and the circle is drawn through the point f with center o. They intersect at the point f 2. Similarly the other points b 2, c 2, d 2, e 2 are obtained and a smooth curve is drawn through the points to find the required involute profile. Different Lines: Fig. S1.15 Sl No. Types of Line Usage 1 Visible line / object line 2 Hidden line / dashed line to indicate all visible outlines of an object. It shows the shape of an object. to represent the hidden edge of an object. It must begin and end with a dash touching the visible lines. Dashes that show hidden lines usually touch each other at intersection. 3 Center line to show the center line of holes, pitch line. Sl No. Types of Line Usage 4 Extension line, dimension line and Leaders to show dimension of an object extension line, dimension line and leaders are used.

4 5 Section line to indicate the cut portion of an object. 6 Cutting plane line to show the imaginary cutting of an object 7 ISO Cutting Plane Line 8 Break line to show a break on the object. It shortens the view of a long part. 9 Phantom line/repeat line to show the alternate position of an object or the position of an adjacent part. DIMENSIONING

5 2.3.1 Extension Line (1) A gap of 1 mm has to be kept in between the extension line and the visible line. (2) An extension line should extend about 3 mm from the outermost dimension line. (3) Extension lines may cross each other without a break. They may also cross the visible lines without a break. If the extension lines cross arrowheads or dimension lines close to arrowheads, a break may be permissible. (4) Centerlines may be used as extension lines. However, it should not be broken while passing the circle. (5) Extension lines are usually drawn perpendicular to dimension lines, where there is overcrowding extension lines may be drawn at an oblique angle Dimension Line (1) Dimension line should be approximately 10 mm away from the visible line. The spacing between the consecutive parallel dimension lines may also be considered as 10 mm. (2) Dimension lines are broken near the middle to allow space for dimension. (3) Dimension lines should usually be placed outside the view unless it becomes necessary. (4) When the space in between the extension lines is too small to insert dimension line completed with arrowhead, it may be provided outside the extension line. (5) Dimension lines should not cross each other. To accomplish it the shortest dimension line should be placed nearest to the outline of the part. (6) Centerlines should never be used as dimension lines. (7) In case of extra long dimension line or crowding of dimensions, dimension lines inside the view may be permissible When several dimension lines are required side by side along a line, it is recommended to stagger them. (8) The dimension line for a part, which cannot be presented completely on the drawings due to its large distance, the free end is terminated in a double arrowhead pointing in the direction in which it could be completed Leaders (1) A leader should always be inclined at an angle of 60 0 preferably and 45 0 occasionally (not horizontal or vertical) with a 3 mm horizontal bar. (2) A leader is either terminated by an arrowhead on a line or a small dot of about 1.5 mm diameter within the outline of the part. (3) Leaders should not be drawn bent except special circumstances. (4) Leaders should not cross each other, however, they may be drawn parallel to each other. (5) To direct a circle or an arc the leader should be so drawn, if it is imagined to extend it must pass through the center of the circle or the arc. (6) All notes and dimensions in a leader have to be provided in the horizontal direction.

6 In Figures 2.3 to 2.8, some uses of extension lines have been presented. Figure 2.3: Crossing of Extension Lines Figure 2.4: Center Line as Extension Line Usage of Leaders Diameter Dimensioning

7 Multiple Diameter Dimensioning: ENGINEERING DRAWING Radius Dimensioning: Dimensioning in Cylindrical Holes Dimensioning on various types of cylindrical holes has been shown in Figures 2.21 to Figure 2.21: Through Hole Figure 2.22: Blind Hole

8 Figure 2.23: Group of Holes Figure 2.24: Group of Holes Some Practices: (Generate Orthographic views from isometric views)

9 Isometric Views With Solution (Try without using the solution):

10 Section Lining:

11 Symbols for Section Lining