HYPOCYCLOID This is the locus of a point on the circumference of a circle rolling around the inside of a large circle without slipping. Construction: Given r = 21m and R = 60 mm
Procedure: Draw the rolling circle radius 21mm centre at O
Divide it into a number of equal parts e.g. 12 equal parts.
Mark the arc of the large circle be equal to the circumference of the rolling circle using or using radius equal to one Q the divisions of the circle and stepping off the same number of equal units on the large arc.
Divide the arc into the same number of equal parts.
Centre at O1 product arcs from the divisions of the rolling circle and equal to the large arc.
Radiate lines from O1 passing through the divisions on the large arc as shown.
With the radius of the rolling circle, centres at the points of intersection of the radial lines and the central arc cut the corresponding arcs from the rolling circle.
Join the points of intersection to get the hypocycloid
ARCHIMEDIAN SPIRAL This is the locus of point which moves uniformly along a given line which rotates uniformly about fixed point.
To construct the spiral of Archimedes given the fixed line Ox = 100mm, op = 30mm (P is the point)
Procedure:
Centre at O radius OP draw a circle
Divide the circle into a number of equal parts e.g. 12
Divide px into the same number of equal parts i.e. 12
