Dividing Head math help

I am working on a Dividing head calculator phone app and need some help with the math. 40-1 dividing head and I want to divide 7 times then I turn handle 5 turns and 35 holes on a 49 hole plate. I know that you divide 40 by 7 and get 5.71. so I am guessing that is the 5 turns but what math do I need to do to get the 35 holes on a 49 plate from the .71 or am I going about this all the wrong way? I have a Excel spread sheet that will do this but I just can not figure it out. Math is not my best subject so all help will be greatly appreciated.

Thanks

40/7= 5 5/7ths

find something that matches the holes that you have.

factor

10:14
15:21
20:28
25:35
30:42
35:49
40:56

If your going to be machining get a better understanding of mathematics it will help you in the long run.

Hi Stuff
As JS has pointed out, you need to throw the calculator on one side and
use old fashioned fractions, then as in your example for 7 divisions you look
to see if on the plate that is already mounted, there appears any one of the
rows of holes that are divisible by 7. So you look for 14,21,28,35,42,49 or 56.
You don't need to stick with your choice of 49. I lectured in Horology, and
students were forever cutting low numbered pinions used in cycloidal gearing
in clocks. . One student found himself a calculator that worked in fractions.
I seem to remember that it was a complete pain in the ar*e to use.

I presume that you know how to use the adjustable sector arms so you don't
need to count the holes every time.

Davycrocket

I'm not much hjelp on cooking up phone app algorithms (Al Gore gots rythem??)

Dare I suggest a slide rule to the knuckle draggers? It was always my favorite ratio tool. Set the C index on the ratio on D. Find the numerator on C opposite the denominator on D. All matches along the C/D scales are candidates ruling out a LOT that are close but no cigar. A slide rule is good for three significant digits. Use a calculator to prove canditate tooth counts, sector settings of holes in hole circles, etc.

Not every number will fit a dividing head's availabe hole circles. If the indexing tolerance will permit, you can add/drop "carry holes" when the indering error crosses 1/2 a hole circle interval. A spread sheet with its integer/remainder functions is a powerful tool for the dial twister.

Personally I prefer the likes of the DivisionMaster http://www.cartertools.com/divma.html for fancy indexing. With it you don't need no stinkin' sectors and hole plates and differential gearing even for large prime numbers. It also works for rotary feeds, angle incrementing, and feeds through arcs. $$

Dividing head setup

If you are working with a manual machine, rather than a cnc machine, the easiest way would be to get a copy of the 'Machinery Handbook". It has a detailed section on using the dividing head. The info would probably also be useful with a cnc machine.
Hugh

Ah, the 7-way division. The only simple polygon that cannot be constructed by compass and ruler.

40/7 = 5 + 5/7

To create 7ths we go 7 steps on a 49-hole plate. To make 5 7ths we go 5x7 = 35 steps on the plate.

Thus, the answer is 5 full turns plus 35 steps on a 49-hole plate. This will give you 1/7 of a circle.

Modulo

To continue on the "math" theme, consider getting friendly with the modulo function/operator in your preferred development environment. If you remember fractions with "remainders" from grade school, that's the "5/7" prior posters have mentioned. 40 mod 7 = 5, so the you know you have 5/7 as your remainder. Since you mention Excel, you might find the MOD() function in the sheet you're looking at. In this example, that portion of the formula would evaluate to: =MOD(40,7), and the value of a cell with that simple formula would be 5.

jscpm explained nicely how to handle the remainder when you're doing manual work - I'm going to need to need that some day ...

I come right back to the math because, as a college-educated guy who did well enough on entrance exams all those years ago not to need any math to fill out my GE requirements, I'm way behind your typical machinist (at least based on the sample here) when it comes to math, particularly trig. I suspect that if you're going to develop a useful phone app for machinists you're going to need some math, period.

John

stuff said:

I am working on a Dividing head calculator phone app and need some help with the math. 40-1 dividing head and I want to divide 7 times then I turn handle 5 turns and 35 holes on a 49 hole plate. I know that you divide 40 by 7 and get 5.71. so I am guessing that is the 5 turns but what math do I need to do to get the 35 holes on a 49 plate from the .71 or am I going about this all the wrong way? I have a Excel spread sheet that will do this but I just can not figure it out. Math is not my best subject so all help will be greatly appreciated.

Thanks

Click to expand...

One of those procedures that is largely forgotten these days, clearly a few of the guys here remember the process. You'll first need to make a fraction out of that decimal, for example 0.71 = 71/100 or 710/1000 and so forth. From there the numerator and denominator need to be factored by a common integer until the factored denominator matches one of your existing hole plates. The factor of the numerator will then be the number of sector holes.

Unhappily, I don't know of any rigorous mathematical procedure that accomplishes this. I'm not a programmer (just know enough to be dangerous) but usually this is accomplished with a "for ... next" loop, testing and incrementing the common factor by one until a satisfactory solution is reached. It's no big deal to do this with any computer language I know but telephone applications are unknown to this old brain (I can barely use a cellular telephone, LOL).

If it can be of any help, I can send you a spread-sheet that I devised which does that stuff. It can solve for exact ratios or can provide an approximation that is within a user-specified tolerance. PM me with an e-mail address that will accept an attachment if interested.

Cheers,
Randy C

edited: Sorry - after posting I noted that you said you already had a spread sheet. It might even be the one to which I referred - I provided download links on a couple of hobby forums a month or two ago. One more thought: recent Hewlett-Packard calculators generally have a "fdisp" (fractional display) function that is helpful for problems like this one.

For example if by division, one comes up with a result of 3.3513514 and then press the "fdisp" function key, the result will be 3 - 13/37 which would be 3 turns and a sector spacing of 13 holes on a 37 hole plate.