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Vertex Dividing-Head - basic help please

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BERT ASHTON04/01/2021 09:14:25
75 forum posts
58 photos

I have a photostat copy of the B & S dividing head manual.

If anybody wants a copy inbox me.b & s dividing head 006.jpg

not done it yet04/01/2021 09:57:40
6806 forum posts
20 photos

What is it with people and simple maths!

Take a somewhat simplified example.

Say 1). the table turns is 90 per full revolution

2). Ten teeth are required.

Very clearly the answer will be 10 turns per tooth, but lets do the calculation, just as a demonstration....

Clearly we would want to choose a 10 hole (space) plate for this.🙂

For 90 turns of the handle 900 holes would pass the starting point (simple enough for everyone? 90 x 10 = 900)

if 900 holes is turned for 10 teeth, one tooth would need 90 holes (that’s right, 900/10 = 90).

We know that each turn of the handle is 10 holes, so 90 holes is 90/10 turns. = 9 turns. Surprise, surprise?



Some more examples, a little more challenging:

say 19 teeth with a 40 turn rotary table/dividing head (an unlikely real life example)

We clearly choose a 19 hole plate for this, so 40 turns is 40 x 19 holes in total (= 760)

760 holes has to make 19 teeth so each tooth will require 760/19 holes = 40 holes per tooth.

With a 19 hole plate that will be 2 turns and 2 holes for each tooth. JOB DONE. One could use a plate circle of 38 or 57 and both would work (but unlikely those numbers would be found on your dividing plates🙂 )

Now, if a 38 tooth plate was used the answer would work out to 2 complete turns and 4 holes. Exactly the same result in practice.

The simplest maths is: take table turns ratio, multiply by holes in plate, then divide by the number of teeth required. If the answer is greater than the hole number chosen it will need more than one turn and you can work out how many and the remainder.

Another: 45 teeth with a 72 turn table

Let’s choose a 15 hole circle (as that is a factor of 45 (15 x 3 = 45)). There unlikely to be a 3, 5, 9 or 45 hole circle on your plates.🙂

72 turns of 15 holes = 72 x 15 = 1080 holes for 45 teeth.

1080 divided by 45 will give holes per tooth = 24

(The calculator operations needed are 72 x 15/45 = 24)

We have a 15 hole circle so require one complete turn and 9 holes per tooth. Job done.

Notes: if your correctly calculated answer does not equal an exact whole number, you’ve chosen the wrong plate circle! Prime numbers are always included on the plate circles or they can not be cut.


Only three numbers to be inputted to one’s calculator, basically. Nothing is difficult about that. BUT choosing a suitable plate circle seems likely to be the major stumbling block? (The answer to the question posed above).

Lets look at a 63 tooth gear. Possible factor pairs of 63 are (1, 63) (3, 21) and (7, 9).

A 63 hole plate would be easy (one hole/tooth), but 63 hole plates are thin on the ground. 1 and 3 are not sensible choices so 7, 9 and 21 are possibilities (even though 7 and 9 are not usually found on plates). Just trying them with your table turns, to see if the answer is an exact whole number, is one way to find a possible solution.

90 turn plate:

90 x 7/63 = 10 Works OK but unlikely an option

90 x 9/63 = 12.86 Does not work out to a whole number, so not OK.

90 x 21/63 = 30 Works OK

72 turn plate:

72 x 7/63 = 8 Works OK but not likely an option

72 x 9/63 = 10.29 Does not work out to a whole number, so not OK

72 X 21/63 = 24. Works OK

40 turn table:

40 x7/63 = 4.44 Does not work out to a whole number, so not OK

40 x 9/63 = 5.71 Does not work out to a whole number, so not OK

40 x21/63 = 13.3 Does not work out to a whole number, so not OK

(with a 40 turn table one would require a 63 hole plate!).

36 turn table:

36 x7/63 = 4 Works OK but not likely an option

36 x 9/63 = 5.14 Does not work out to a whole number, so not OK

36 x 21/63 = 12 Works OK

Note that for all the OKs, the ‘other’ factor is also a factor of the table turns ratio.🙂 Helps when deciding on a plate circle to check out. As one’s table will be of a known turns ratio, you would soon work out the possible options fairly easily. The plates are made with the least number of useful circles (why 7 and 9 are not usually found) and will include all possible prime numbers. Numbered hole circles will work for any turns ratio for that same number of teeth - the answer for the number of holes/tooth will be the same as the turns ratio (no calculation needed).

I included the 40 turns ratio table examples to demonstrate why they are not a popular choice (9 degrees per turn of the handle!) for either the user or (more importantly) the manufacturers🙂 .

This boils down to: pick the highest factor of the tooth count, that is on your plates, and just work it out.

Remember that holes really means spaces in all the above...

I didn’t get a chart with either of my rotary tables and I would not trust them (or the internet) when it is so easy to sort it out myself. I use so few settings that keeping a chart for it would be pointless for me.

Andrew Johnston04/01/2021 10:31:22
6601 forum posts
701 photos

Posted by not done it yet on 04/01/2021 09:57:40:

...........but 63 hole plates are thin on the ground.

For my traction engines I needed to cut 63 and 69 tooth gears, neither value is listed under simple indexing for my industrial 40:1 dividing head. My dividing head is universal, but rather than set up compound or differential indexing it was easier to make a 63 and 69 hole plate:

Division Plate


Nigel McBurney 104/01/2021 11:29:15
1000 forum posts
3 photos

I dont see how making a two row index plate is easier than setting the differential indexing gear train I assume cnc was used to space out the holes in a new plate,but there is still the steel to locate,turn to size and drill and c/bore the screw holes. I last used differential indexing for a customer job a couple of years ago that was a 63 t gear .

Andrew Johnston04/01/2021 12:52:04
6601 forum posts
701 photos

While I have a full set of change wheels and the banjo I don't have the expanding arbor that fits in the back of the spindle (the late JohnS couldn't find it). So it was easier to make a division plate as I already had an offcut of aluminium of the correct size and thickness. The holes were drilled using the bolt function on the DRO.


Bazyle04/01/2021 13:56:49
6323 forum posts
222 photos
Posted by not done it yet on 04/01/2021 09:57:40:

What is it with people and simple maths!

Take a somewhat simplified example.

Say 1). the table turns is 90 per full revolution

2). Ten teeth are required.

Very clearly the answer will be 10 turns per tooth, but lets do the calculation, just as a demonstration....


eh? is there a version of this in English?

I think there were lots of reasons not just lack of calculators that drove the likes of B&S and Elliott and Machinery Handbook to issue tables that even us mathematically challenged could look up division rations in. These can be found on the 'net aswell as the table in the link given by MG for the Vertex earlier.

The standard set of 3 plates fro B&S had 18 circles of holes and Elliott 23 I think. However both offered extra plates with more primes, inclucing 63, but of course these are rare on the used market. Odd that I'm not immediately seeing such extras for the BS0 clones.

BTW it is always worth checking if your maths is up to it. The Elliott table for differential indexing 201 divisions is wrong - but I doubt anyone has ever wanted to make a 201 tooth gear.

Hopper05/01/2021 02:26:20
6383 forum posts
334 photos

Ah, the joys of having a GH Thomas Versatile Dividing head with the extra fine adjustment that allows you to advance the index plate itself by a measured extra amount for doing primes etc.

I wonder if its possible to set up a similar thing on these commercial units? Its a simple 60T wormwheel and worm with a micrometer dial. But it means mounting the indexplate on a moveable hub.


Seen in use here with a single row of 60 holes used with the fine adjustment to make all the remaining circles of holes for a set of three indexing plates. Accurate to within one thousandth of a degree according to George.


not done it yet05/01/2021 06:52:18
6806 forum posts
20 photos

with more primes, inclucing 63,

Just to keep the record straight (for the non-maths types). 63, having factors (other than 1 and itself) is not a prime number.

If a particular dividing head, such as a 40 turn item, needs a plate with the exact number of holes that does not make that number a prime.

Bazyle05/01/2021 09:06:57
6323 forum posts
222 photos

Indeed, a slip on my part but obviously it is an useful number. Out of interest the extra plates provided by Elliott are as follows and ot all primes:

53 57 59
63 67 69
73 77 79
83 87 89
93 97 99

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