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INSTRUCTIONS
============
This spreadsheet contains calculators for dividing heads and rotary tables. A calculator for converting any number of degrees to circle divisions is also provided.
The dividing head calculator is based on a standard 60:1 turns ratio. Your dividing head may be equipped with dividing rings having different numbers of holes to those shown here. If that is the case, refer to the item below "Changing the number of indexing holes".
IMPORTANT
=========
This spreadsheet has been protected to prevent accidental corruption of formulae. If you need to change any of the protected cells, refer to item "Changing the number of indexing holes" below.
DIVIDING HEAD CALCULATOR
=======================
The primary purpose of a dividing head is to divide a circle into any number of equal segments (sometimes referred to as divisions) as is required for gear cutting, machining spokes, etc.
Depending on the range of indexing circles, almost any division is possible. It may even be possible to divide into unequal segments. For example, a dividing head fitted with a 51 hole indexing ring can divide a circle into 7 and one half segments (7 segments of 48 degrees and one of 24 degrees).
When using a dividing head it is best to think in terms of divisions rather than degrees. (You can convert degree to divisions using the converter immediately below the dividing head calculator at left).
To divide a circle into "n" divisions, enter the number n into the box titled "Divide a circle into this number of segments/divisions:"
The answer will be shown as the total number of revolutions of the crank handle plus the number of holes in the index plate. (See item below "Changing the number of indexing holes".)
Indexing rings that provide an exact solution are boldly displayed with the comment "you can use the X ring and advance the index by Y holes on the index plate" where X is the number of holes in the ring and Y is number of holes used. Y may take any value from zero to X. When a ring provides no solution, no text or numbers are displayed.
Use the Vrulers to count holes. Tighten them into a V that is exactly the number of holes apart that you are counting. Spin them until they hit the index pin, advance the pin to the other ruler.
The following examples are valid when the dividing head has a 60:1 crank to spindle ratio and is equipped with rings having the following numbers of holes: 46, 47, 49, 51, 58, 52 & 65. If your calculator has additional hole numbers, the solutions may contain additional options to those discussed below.
Example1:
7 equal divisions:
Enter 7 into the box.
Answer: Turn the crank 5 times plus 35 holes on the 49 ring of the index plate.
Example 2:
8 equal divisions:
The zero's indicate that this is a full revolution of the crank (5 turns only).
Example 3:
27 divisions
Observe that there is no exact solution if you only possess rings having 46, 47, 49, 51, 58, 62 & 65 holes.
Since these rings provide solutions for 26 and 28, one option may be to advance the head by divisions for 26 then 28 then 26, and so on. However this only works so long as the angular error is tolerable.
As can be verified using the Rotary Table Calculator, the angular difference between 26 and 27 is 0.5287 degrees (overshoot) and the difference between 27 and 28 is 0.4762 degrees (undershoot). The cumulative error for a 26+28 cycle of divisions is the difference between the two errors. Since the overshoot error is greater than the undershoot error the cumulative error will be about 0.0525 degrees of overshoot and will increase by the same amount after each successive division cycle.
To produce 27 divisions (segments of the circle), it is necessary to advance the dividing head by 13 cycles of 26 + 28 = 26 segments from the starting point. The 27th segment is then the remainder of the circle after the position of the 26th segment has been established. The total cumulative angular error after the 13 cycles will be 13 x +0.0525 = +0.6835 degrees. In other words the last segment will be narrow by 0.6835 degrees. All the other segments will be alternately wider by 0.5287 degrees or narrower by 0.4762 degrees compared to the desired width.
Changing the number of indexing holes.

Before you can change the number of indexing holes you will need to unprotect this spreadsheet. I have password protected it only to prevent accidentally overwriting cell contents and formulae. The password is "OPEN" (all caps). The password is entered under Tools/Protection/Protect Sheet.
The column of numbers from C10 to C16 represents the numbers of holes in the concentric rings of an index plate. Index plates are usually stamped with these numbers on the face.
Every index plate is different so it will be necessary to change those numbers if the index plate has a different number of holes (very likely). Likewise, if you have indexing plates that cater for more than seven rings you may need to expand the columns by strategically inserting rows and entering new numbers.
To change any number in the existing column, simply unprotect the spreadsheet (see first paragraph of this item) and type in the numbers that are on your index plate.
To add new numbers to the existing column, simply unprotect the spreadsheet (see first paragraph of this item) and add (insert) as many rows as you wish to add numbers. To ensure automatic creation of the necessary formulae during row insertion, insert the new row(s) within the existing column. In other words, insert the row(s) anywhere below the first number AND above the last number in the column.
I recommend that you then protect the page again to prevent accidentally overwriting a formula.
ROTARY TABLE CALUCLATOR
========================
Use the rotary table calculator at left to determine the angle of rotation when the circle is to be divided into any number of equally sized segments.
Geometrically speaking, the calculator gives the number of degrees included in each segment expressed as decimal degrees, degrees, minutes & seconds and radians.
Example: Divide a circle into 26 equal segments.
Answer: Each segment is:
13.646 decimal degrees
13 degrees, 50 minutes, 46.154 seconds
0.12083 radians
A rotary table can be employed as a dividing head provided you carry out the angular mathematics (using the calculator). This works best when the segments are whole degree fractions of the circle (see table below). However, when segments involve fractions of a degree it becomes easy to introduce errors when rotating the table to each successive position. In such cases it is preferable to use a dividing head.
Table 1: Circle segments that have whole numbers of degrees.

Segments: 1 2 3 4 5 6 8 9 10 12 15 18 20 24 30 36 45 60 72 90 120 180.
Degrees: 360 180 120 90 72 60 45 40 36 30 24 20 18 15 12 10 8 6 5 4 3 2
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