Engineering Graphics ''Epicycloid''

Epicycloid

Definition :-

EPI-CYCLOIDS : IT IS A LOCUS OF A POINT ON THE PERIPHERY OF A CIRCLE ROLLING ON ANOTHER CIRCLE FROM OUTSIDE











Construction

Step 1. When smaller circle will roll on larger circle for one revolution it will cover πD distance on arc and it will be decided by included arc angle .
Step 2. Calculate θ by formula θ = (r/R) x 3600.

Step 3. Construct angle θ with radius OC and draw an arc by taking O as center OC as radius and form sector of angle θ.

Step 4. Divide this sector into 8 number of equal angular parts. And from C onward name them C1, C2, C3 up to C8.

Step 5. Divide smaller circle (Generating circle) also in 8 number of equal parts. And next to P in clockwise direction name those 1, 2, 3, up to 8.

Step 6. With O as center, O-1 as radius draw an arc in the sector. Take O-2, O-3, O-4, O-5 up to O-8 distances with center O, draw all concentric arcs in sector. Take fixed distance C-P in compass, C1 center, cut arc of 1 at P1. Repeat procedure and locate P2, P3, P4, P5 unto P8 (as in cycloid) and join them by smooth curve.