Construction of Spiral Curves

SPIRAL CURVES

Spiral is a curve generated by a point moving continuously in one direction along a straightline while the straightline revolves about a fixed point.

The fixed point about which the line revolves is called pole and the line joining any point on the curve and the pole is known as the radius vector. One complete revolution of the spiral forms one convolution.

Two types of spiral curves are : 

i) Archimedes spiral 

ii) Logarithmic spiral

1. Construction of Archimedes spiral

Data known : 

(i) Radius

(ii) Number of convolutions

Example 10: Draw an Archimedian spiral of one convolution given the radius as 60mm.

Procedure:

1) Mark a point O and draw a circle of radius 60mm.

2) Draw horizontal diameter, and mark the intercept of horizontal diameter with the circle at A. When the line OA revolves about O for one revolution, point A moves uniformly to O.

3) Divide the line OA and the circle into same number of equal parts (say 12), marking the divisions as 1, 2 etc., on AO from A and 1', 2' etc. on the circumference of circle from A in anticlockwise direction.

4) When the line OA revolves 1/12 of a revolution, (ie., from 0-A to 0-1'), A moves towards O by a distance equal to 1/12 AO. Hence to get the position of A on 0-1', draw an arc with O as centre and 0-1 as radius to cut the radial line 0-1' at P1.

5) Similarly obtain the points P2, P3.... etc., by taking O as centre and O-2, 0-3... etc. by radius to cut the radial lines 0-2, 0-3'.... etc. respectively.

6) Join the points A, P1, P2 .... P11 and O by a smooth curve which is the required spiral curve.