Harold Hall


The Formula

SK. 1 shows a very simple example requiring to position 5 holes on a given diameter.


The formula for the X co-ordinates for this is as follows.


           (P - 1) X 360     

 X = R Cos-----------------   




R equals the radius (that is PCD/2)

P equals the hole number, e.g. 1, 2, 3, 4, 5, etc.

N equals the number of holes, 5 in this case.


Similarly for the Y co-ordinates


            (P - 1) X 360

Y = R Sin-----------------



Calculating these values, even when there are many more holes, will not be that arduous if you have a calculator having trigonometrical functions. Unlike printed tables, that  normally list values up to 90 degrees, a calculator will deal easily with the angles above 90 degrees, giving the value and whether it is positive or negative. I would suggest therefore that, with simple scientific calculators being available quite cheaply, one should be a standard item in the home workshop.  Even better though, it is likely that your PC has one already installed, try start>programs>accessories>calculator


A disadvantage of the method in Sk1 is that it involves both positive and negative co-ordinates making it somewhat difficult to equate the values to those to be read off the leadscrew dials. This though can easily be overcome by changing the reference point from the centre of the circle to a point equal to the extreme upper and left positions as in SK. 2. This making all co-ordinates positive. The formula then becomes-


           P - 1) X 360     PCD

X = R Cos--------------- + -----

               N             2


Workshop Processes