Hypocycloid.ppt

Engineering graphics: Hypocycloid

1. Presentation Topic CURVES - Hypocycloid Group No. – E22 Roll No. – 337 & 338 Division - E C.K.Pithawala C ollage of Engineering & Technology

2. Problem - Draw hypocycloid, rolling circle 60mm diameter and directing circle 160mm diameter. Draw a tangent and normal to it at a point 40mm from the centre of the directing circle. Given data : d = 60mm R = 160/2 = 80mm When rolling circle rolls by one revolution, the distance covered by it inside the directing circle will be = ∏d = 3.14 * 60 = 188.571mm The angle subtended for directing circle of radius R is calculated as follows : Angle = ∏d/R = (3.14 * 60)/80 = 135 degree

3. Step:1:  Construct angle  = 135 degree with radius OP = 80mm and draw an arc by taking O as center OP as radius(R) and form sector of angle  . 135 degree O P 80 mm

4. Step:2: Now divide this 135 degree circle in 12 nos. 135 degree O P 80 mm

5. Step:3: Now draw a circle of d = 60mm on OP from P point and named it’s centre C. 135 degree P 80 mm C

6. Step:4: Now divide this d=60mm circle in 12 parts and name the points as shown in figure. Draw one circular line also from point C. 135 degree P 80 mm C 1 2 3 4 5 6 7 8 9 10 11 O 12

7. Step:5: Now joint 12,1-11,2-10,….,6 points as shown in figure. Draw one circular line also from point C and name points as shown in figure. 135 degree P 80 mm C 1 2 3 4 5 6 7 8 9 10 11 O 12 C C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

8. Step:6: Now with centres C1,C2,….C12 and r = 30mm draw arcs to intersect with arc lines through 1,2,…12 and name points as shown in figure. 135 degree P 80 mm C 1 2 3 4 5 6 7 8 9 10 11 O 12 C C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 P P2 P1 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12

9. Now, how to draw a tangent and a normal to a hypocycloid: Step:7: With centre O & radius 40mm, mark a point M on the hypocycloid. Now draw an arc with centre M and r = 30mm to intersect with the centre line at point T. Join OT and extend line to point N as shown in figure. 135 degree P 80 mm C 1 2 3 4 5 6 7 8 9 10 11 O 12 C C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 P P2 P1 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 M T N

10. Step:8: Now join MN points, which be the normal to the hypocycloid. Now draw line X-M-X’, passing through M and perpendicular to MN, which be the tangent to the hypocycloid. 135 degree P 80 mm C 1 2 3 4 5 6 7 8 9 10 11 O 12 C C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 P P2 P1 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 M T N X X’

11. The End