Archemedian Spiral
The steps  used to obtain an Archemedian spiral is shown in figure 3 with the help of the problem given below. 
Problem:  A point moves away from the pole O and reaches a distance of 50 mm while moving around it once.
 Its movement from O is uniform with its movement around.  Draw the curve. 
Solution: Draw a circle with diameter 50 mm and divide it into a number of equal segments, (say six).  Label the intersections between
the radius and the circle as points 1 through 6.  Divide radius 0-6 into the same number of equal parts (i.e. six).
 Mark points on the radius as 1΄, 2΄, etc.
With O as the center,  draw an arc of radius 01΄, between 06 & 01.  Mark the point of intersection of the arc with radius 01.
  Then draw an arc of radius 02΄, between 06 &  02. Repeat this process until arcs have been drawn from all the points on the radius    0-6.
Using French curve, connect the intersection points in the order, they were marked i.e. point on 01, point on 02 radius, point on 03….

 

Figure 3. Steps in drawing an Archemidian spiral