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A circle of 60 mm diameter rolls along a straight line without slipping. Draw the locus of point P for one complete revolution of the circle.


A circle of 60 mm diameter rolls along a straight line without slipping. Draw the locus of point ‘P’ for one complete revolution of the circle. The point ‘P’ is 38 mm above the straight line and towards the right of the vertical centre line. Name the curve.

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Ans –

Given Data:-

Diameter of rolling circle Φ = 60 mm

Point P = 38 mm above straight line.

Assumption – Circle is rolling towards right side (Show the direction)

Procedure:-

1) Draw a circle of 60 mm diameter.

2) Draw horizontal and vertical axis and mark centre of the circle say C

3) Divide the circle into 12 equal parts and name each division 1, 2, 3, ….12 as per shown in fig.

4) Draw a straight horizontal line of length πD from the contact surface of circle and ground.

5) Mark the point P at a distance of 38 mm above horizontal line.

6) Measure distance 1-P on circle in compass and mark that much distance on horizontal line taking contact surface (Point 4) as center . (See figure.)

7) Mark that point 1’.

8) Measure distance P-12 on circle in compass and mark that much distance on horizontal line taking end point (Point P’) as center . (See figure.)

9) Mark that point 12’.

10) Now 1’-12’ is the total distance to divide into 11 dicision. (1 division get covered in 1-P and P-12).

11) Divide the line into 11 equal parts 1’, 2’, 3’…..12’.

12) Draw again a circle of 60 mm diameter at πD distance with centre C’.

13) Draw horizontal and vertical axis for 2nd circle.

14) Draw horizontal lines from points (1,7) (2,6) (3,5), 4, (8,12), (9,11) and 10 up to vertical axis of 2nd circle.

15) Draw vertical lines from point 1’, 2’, 3’,…. P’ up to horizontal axis and name it C1, C2, C3….Cp respectively.

16) Taking C1 as centre and 30 mm radius (radius of rolling circle) cut the horizontal line passing through point on the circle near point P. Mark that point P1.

17) Repeat the same procedure up to Cp and accordingly marks points up to Pp.

18) Draw smooth curve passing through all points (P1, P2, ….. Pp) and name the curve

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