Exercise [Rouletters (Cycloid, Epicycloid, Hypocycloid, Involute), Spiral curves, Helix]

EXERCISE

Cycloid

1) Construct a cycloid generated by a rolling circle of 60 mm in diameter. Draw a tangent and a normal at a point on the curve 40 mm above the base line.

2) A circular wheel of 40 mm diameter rolls without slipping along a straight line. Draw the curve traced by a point P, lying on the rim for 1.25 revolutions of the wheel. Name the curve traced. Also draw a tangent and a normal at a point P, when the wheel has travelled 80 mm from its starting position.

Hint: The curve is cycloid. For 1.25 revolutions, draw cycloid for one complete revolution and quarter part of the second revolution.

3) A circular wheel of diameter 55 mm rolls without slipping along a straight line. Draw the curve traced by a point P on its rim for one revolution of the wheel. Draw tangent and normal to the curve at a point located 35 mm above the line.

Epicycloid

4) Draw an Epicycloid generated by a point P on the circumference of a rolling circle of 50 mm diameter when it rolls outside a directing circle of 150 mm diameter for one complete revolution. Draw a normal and a tangent to the curve at any convenient point on the curve.

5) A rolling circle having 40 mm diameter rolls on a fixed disc with 60 mm diameter with external contact. Draw the loci of path traced by a point on the circumference of circle for one complete revolution.

6) The points of intersection of an epicycloid with the directing circle subtend an angle of π/2 radians at the centre of the directing circle. If the directing circle has a diameter of 130 mm, draw the epicycloid.

Hypocycloid 

7) A circle of 50 mm diameter rolls along the inside of another circle of 200 mm diameter. Draw the path described by a point on the circumference of the rolling circle for one complete revolution. Draw tangent and normal at a point on the third quarter of the curve.

8) A circus man rides on a motor cycle inside a globe having a 6 m diameter. The motor cycle wheel is 1m in diameter. Draw the locus of a point lying on the circumference of the wheel of the motor cycle for one complete turn.

9) A circle having a 50 mm diameter rolls within a circle of 150 mm diameter with internal contact. Draw the locus of a point lying on the circumference of the rolling circle for its complete turn. Draw a tangent and normal to the curve at a point 40 mm from the centre of base circle. 

10) Construct a hypocycloid taking the diameter of the generating circle and radius of directing circle as 60 mm.

Involute :

11) Draw the involute of a circle having diameter 40 mm. Draw tangent and normal at a point on the curve located at a radial distance of 100 mm.

12) Draw the involute of a square of side 25 mm and mark the tangent and normal at the mid point of the third segment of the curve.

13) Draw the curve traced out by an end of a thick wire unwound from an equilateral triangle of side 20mm, the wire being kept tight.

14) Construct an involute of pentagon for one turn, side of pentagon being 30mm. 

Sprial:

15) Construct an Archimedian spiral of one convolution in a circle of diameter 140mm. 

Helix :

16) Draw one turn of a helix of pitch 60mm upon a cylinder of 80mm diameter and 100mm height.