## 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.

This is **EPI – CYCLOID**.