Normal & Tangent to Epicycloid
According to Wikipedia, In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
Question: A circle of 50 mm diameter rolls on the circumference of another circle of 180 mm diameter and outside it. Trace the locus of a point on the circumference of the rolling circle, for one complete revolution. Name the curve formed. Draw a tangent to the curve at a point on it 125 mm from the center of the directing circle.Solution:
- Draw an Epicycloid according to the given data. (Don't know how to draw an epicycloid? To learn, kindly follow the given link: How to draw an Epicycloid?).
- On epicycloid take a point Q.
- Draw an arc of 25 mm on the arc passing through the center of the circle from point Q.
- From that point, draw a straight line to the center of the circle of having 90 mm radius (180 mm diameter).
- Name N point at which the straight line intersect big circle.
- Draw line QN, which will be the Tangent to the given epicycloid.
- Draw a perpendicular line to the line QN, which will the Tangent to the given curve.
Practice questions..
- A circle of 30 mm diameter rolls on the circumference of another circle of 150 mm diameter and outside it. Trace the locus of a point on the circumference of the rolling circle, for one complete revolution. Name the curve formed. Draw a tangent to the curve at a point on it 100 mm from the center of the directing circle.
- A circle of 45 mm diameter rolls on the circumference of another circle of 160 mm diameter and outside it. Trace the locus of a point on the circumference of the rolling circle, for one complete revolution. Name the curve formed. Draw a tangent to the curve at a point on it 110 mm from the center of the directing circle.