Taking 30 divisions, this will require the setting arm to pass 2400/30 holes per division, that is 80 holes, being one full turn plus 20 holes.

Whilst 2400 is a relatively large number the number of possible divisions is quite small and are all what one might call simple numbers. These are 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, and 1200.

Knowing the dividing head ratio together with the number of holes on the dividing plate it will be easy to determine if a division required is achievable. However, you are likely to have a set of dividing plates (or gears) that could result in a lot of calculations, albeit simple, until a suitable dividing plate is found, or maybe not found. Referring to the chart supplied with the dividing head will though help avoid the chore in many instances.

On some occasions though, your requirement may not be covered by the published charts, or you may not have all the plates quoted but have others. In this case you will have to resort to calculation. As already mentioned the ratio (R) times the number of holes (H) divided by the number of divisions required (D) must be a whole number (W), that is

R x H

W = -

D

This is a simple calculation if one has R, H and D but what if attempting to work out the number of holes (H) required on the dividing plate and the number of holes (W) to be traversed between divisions. Here, we have two unknowns (W and H) making the process to appear less than a straight forward. However, the value for W can be any number providing it is whole.

Let us consider the requirement for 26 divisions in which the formula will read

40 x H

W = -

26

The values for R and D, 40 and 26, should be simplified to their smallest values, reading

20 x H

W = -

13

that is dividing both by 2

From this it can easily be seen that W will be whole providing H is 13 or any multiple of this, 13, 26, 39, etc.

Having established the dividing plate to be used it will be necessary to calculate the number of holes traversed for one division. In this case, if choosing a plate with 39 holes, the number of holes traversed for a complete revolution of the workpiece will be 40 x 39 = 1560 and the number of holes per division will be 1560 / 26 = 60. Sixty holes then being achieved by one complete turn (39 holes) plus 21 holes.

Avoiding Counting Errors

In the above example it was necessary when using a 39 hole plate to traverse the input arm by one full turn plus 21 holes, doing this 26 times. Doing this unaided would be a demanding task and one which errors could easily be made.

The one full turn will present no problem but how does one count the 21 holes, doing this 26 times without making an error, very difficult.