Construction of Hypocycloid
Sample Problem 1:
Draw a Hypocycloid of a circle of 40mm diameter which rolls inside another circle of 200mm diameter for one revolution. Draw a tangent and normal at any point on it.
Steps for construction of Hypocycloid:
- To calculate θ : θ=r/R * 360º = 20/100 * 360º = 72°.
- Taking any point O as center and radius (R) 100mm, draw an arc PQ which subtends an angle θ = 72º at O.
- Let P be the generating point. On OP mark PC = r = 20mm = radius of rolling circle.
- With C as center and radius r (20mm) draw the rolling circle.
- Divide the rolling circle into 12 equal parts as 1,2,3,etc., in CM direction, since the rolling circle is assumed to roll CCW.
- Repeat Step Nos. 5 to 10 in problem 6 and draw a smooth Hypocycloid curve.
Tangent and Normal at a given point M.
- M as center and radius r=CP cut the locus of center at the point N.
- Join ON and extend it to intersect the base circle at S.
- Join MS, the Normal.
- At M, draw a line perpendicular to MS to get the required Tangent.