An Application to create dividing head tables

[AjohnwParticipant @ajohnw51620]

Good for you Gordon. I was concerned about ancient os users who may also have out of date virus checkers. Maybe even none.

It's a good application for people who want to produce a table of what they can do, The PC screen is fine but I prefer mine in a clear plastic envelope.

It doesn't display entirely correctly on linux but if the edge of the window it throws up is dragged that clears up.

John

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[Andy AshParticipant @andyash24902]

Hi Bazyle,

I said I would have a look at what you had done, and comment. I still don't have much time today, but I did look.

I think I can see what you're getting at.

So as far as I can tell, there's still nothing actually wrong with my spreadsheet, but I do now understand that it might not have been generating some of the options (the ones that carry an error) that you might have expected. It's not something I had thought about but I can see now that there is an issue here.

The first thing I would say is that if you turn the proximity down to zero, if there is nothing hilighted, then there are no "properly accurate" selections. Those that are shown are accurate to the available precision of the floating point unit on the computer. I think excel uses the IEEE 754 double precision floating point value (**LINK**). If the selection is that accurate then to my mind it is "spot on". Those are the choices one should always use if possible. They have both integral and differential precision perfectly.

Then there are the choices that carry an error. Of those, the way my sheet works it will only return choices where the hole count is slightly short, never slightly over. It is fair to say that for any given selection there might be a closer (more accurate) choice which is slightly over rather than slightly under. My spreadsheet would not necessarily notice those if they existed.

I think all I would say about that, is that if you have the compromise in mind (as you possibly should), then once you have found a candidate that you like, then you will have calculated if it is accurate enough for your purposes.

I didn't have time to look at your longer function in detail. I possibly still might. Equally I think I have seen what you are getting at. I might have a go at expressing an adjustment for the flaw you have identified and see if I come up with the same answer. Also it will be interesting to see if it actually makes much difference.

Andy.

Edited By Andy Ash on 18/05/2016 21:11:40

[BazyleParticipant @bazyle]

Andy. I don't think there is anything wrong with your program per se and I played with the variable error. It was just when I put in the plates I happen to have and a 60 worm and looked to see what I couldn't get I noticed some things weren't showing up like 15 divisions using a 15 plate which is an exact division. I figured that was a side effect of the MOD function so tried an alternative.

[Andy AshParticipant @andyash24902]

I am completely confident about the principle I described before.

I seem to remember someone saying that there is an article about division coming up in the ME, and I wouldn't be surprised to find that they explain what I'm struggling to.

Perhaps you don't realise it, but you have caused me to realise there is a deficiency which could be improved. Whilst I'm in there I think I'll add the capability to do a variable worm because others have been fiddling with that. Then I know it's all covered properly. I probably will add an "exact flag" so that you can switch between exact and the current proximity, to compare the highlights. I might even be able to the exact ones a different colour.

I have to say I wasn't completely sure of the example you cited before, of the target division being a multiple of the plate. I think I tried 32 and 64 seemed to give answers that I expected, so I wasn't quite sure what the specific problem was. Irrespective I looked at what you changed and saw a problem with what I had done.

As for 15 divisions on a 15 hole circle with a 60 worm, surely that's just four whole revolutions and no holes.

60 / 4 = 15

I'll try and do an updated sheet with more searching oomph!

[AjohnwParticipant @ajohnw51620]

I've just done some checking too – using the usual way T=Worm Teeth/Division Needed. So taking an awkward number say 11 T= 60/11 = 5 & 5/11 so 5 complete turns and 5/11 of a turn, So plate hole counts of 11,22,33,44… etc will do it. Or say 13, T=60/13 – 4 & 8/13 so hole circles of 13,26,39….. etc will do it.

This is where decimal seems to fall down because the only way of expressing prime fractions exactly is with prime fractions so to get round that Andy has to but a quality factor in as many divisions wont give an exact answer in decimal. It's what I expected actually and is why I did it a different way on the first sheet I posted – numbers all over the place because of the way it's generated though which is nvg. It just multiplies unique factors of both the worm and plate circle counts.

Make me wonder given how easy the sum is in fractions if it is worth using software.

However if some on is designing something with a gear train it's nice to have a list of the divisions it can do. If you look at the last table I posted it seems I can't do 11 or 13 but as the plates have both 39 and 66 hole circles I can. The other chart I posted earlier for B&S plates tells me that I can do 11 and 13 but not how to do it. The decimal approach tells me I can't.

My Dore Westbury dividing head and plate came with a table some had done long hand but the divisions it will do are a little limited. He chose hole counts of 40 to 70 in steps of 5. It's not that bad a choice actually for many things.

John

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[ZebethyalParticipant @zebethyal]

Here is a link to my spreadsheet: LINK.

I had to wait to upload it from home as work blocks access to all file sharing sites.

[BazyleParticipant @bazyle]

Posted by Andy Ash on 18/05/2016 22:54:21:

.

I have to say I wasn't completely sure of the example you cited before, of the target division being a multiple of the plate. I think I tried 32 and 64 seemed to give answers that I expected, so I wasn't quite sure what the specific problem was. Irrespective I looked at what you changed and saw a problem with what I had done.

As for 15 divisions on a 15 hole circle with a 60 worm, surely that's just four whole revolutions and no holes.

60 / 4 = 15

Thanks for the efforts you are putting into this chaps. (TIm – work blocks download too )

Andy sorry my mistake I should have said I was using 40 worm and B&S plates 15,16,17,18,18,20. Allowing for the worm only needs a trivial change to column B in your sheet.
We know that there must be a zero error solution for each division equal to those hole counts . However 15 &19 don't cough up 10 and 2 like they should, while 16,17,18 are correct. This is what I was attributing to the MOD function.

[Michael GilliganParticipant @michaelgilligan61133]

I'm a bit bewildered by all the evident enthusiasm for tabulating 'possibilities'.

I accept that it's a nice technical exercise, but [no offence intended] it does seem rather pointless.

[Admittedly, if one was selling plates, it would be useful]

It seems to me that the more useful question is: "I have this particular ratio in my dividing arrangement, so what do I need, to get 'N' divisions on the work?"

MichaelG.

[AjohnwParticipant @ajohnw51620]

That one reckons I can do 11 and 13 divisions etc Timothy. LibreCalc doesn't like some of the formatting but that's no problem.

One strange thing – on the first sheet. Say I enter 60:1 worm wheel and a division of 11. It picks the correct plate but tells me 5 turns and 105 holes on a 33 hole plate ?

John

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[ZebethyalParticipant @zebethyal]

I will have a look at that – the other sheet says 5 turns and 15 holes for 11 divisions using a 33 hole plate when using a 60:1 worm.

Looks like the maths on the first sheet needs bringing into line with that on the second sheet – I had thought I did them the same, obviously not

[ZebethyalParticipant @zebethyal]

@Michael – As I mentioned in one of my earlier posts, having a table of what is possible can be useful in looking for an intermediate solution.

Take for example the 125 division problem mentioned, it only took me a few seconds to look along the 125 division line to see which sets of holes on a plate could achieve this (25 or 50 holes), then look along the 25 and 50 division rows to see if I could easily make either of these using the plates that I already have (columns in green).

I can then make a temporary 25 hole plate in acrylic or even thin plywood, which in turn will allow me to make the 125 divisions required.

[Michael GilliganParticipant @michaelgilligan61133]

Understood, Timothy

But the few lines of BASIC that I wrote in 1993 would also give me an answer.

[the old Commodore 64 code runs perfectly on the CBM HandBasic App on my iPad]

It's not the calculation that troubles me … it's the apparent desire to make lists.

What [I think] we need is a simple way to get an answer to one specific question at a time.

I mean no offence to the 'list makers' … it's just a different mind-set; asking a slightly different question.

Please feel free to ignore my opinion.

MichaelG.

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Edit: For info. here's the no-frills output from mine, for your example:

90 :1  125 DIV
 0 + 18 / 25 

READY.

Edited By Michael Gilligan on 19/05/2016 21:28:48

[AjohnwParticipant @ajohnw51620]

The reason I needed a list Michael was to work through clock trains that I can actually cut with what I have. I don't want to have to check that I can cut every one I just want to pick them out. It would be much the same if I wanted any sort of gear train.

As freeing the last rusty brake on a car was an absolute pig I have had a day off and amongst other things had a play with spread sheet sums. There is no need to involve 360 degrees at all however it looks like generating a tidy output list would need a macro. There may be another method though – exporting a sectional coma separated list which takes very little effort to tabulate in a word processor.

The sums and the validity check can be done with the quotient and mod functions which essentially means that only integer values will produce results.

I didn't think you meant any offence to list makers – lists serve a certain need and in my case I might not want to bother going near my pc to find a division I can cut so like paper. I suppose I could use a spread sheet to work through clock trains but feel I may as well do that long hand on paper.

John

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[ZebethyalParticipant @zebethyal]

@Michael – just curious, what would your app give as a result for 35 divisions? would it give (some/all of the following)

1 + 4 / 7, 1 + 8 / 14, 1 + 12 / 21, 1 + 16 / 28, 1 + 20 / 35, 1 + 24 / 42, 1 + 28 / 49, etc

Does it know what hole sets you already have and try to give results for those, or does it give the lowest possible answer and leave it up to you to multiply it up to then see if you have a suitable plate?

I have 21 and 49 holes, but may not realise straight away that I actually have plates that will work for this requirement based on an answer of 1 + 4 / 7, because I would also not remember what sets of holes I have without checking the plates themselves, or a list of what holes I have.

I agree it is all personal preference, some people like a chart they can print out and refer to, others like an app or spreadsheet.

Personally, it depends on what I am doing as to which works best at the time, for a one off, entering data works fine, for looking up multiple items or comparing results, a chart or spreadsheet is often easier to simply scroll up/down/across.

I have a similar list for gear trains for thread cutting on my lathe, sure I can enter all my gears into an app and see what comes out for a given tpi or metric pitch, but a chart with pre-worked answers is much faster.

 

Edited By Timothy Moores on 20/05/2016 08:15:27

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Timothy Moores on 20/05/2016 08:12:51:

@Michael – just curious, what would your app give as a result for 35 divisions? would it give (some/all of the following)

1 + 4 / 7, 1 + 8 / 14, 1 + 12 / 21, 1 + 16 / 28, 1 + 20 / 35, 1 + 24 / 42, 1 + 28 / 49, etc

Does it know what hole sets you already have and try to give results for those, or does it give the lowest possible answer and leave it up to you to multiply it up to then see if you have a suitable plate?

.

Timothy,

I may have to hide in the corner for a while

As you guessed; my routine [quite deliberately] only delivers the 'first' answer for any query; and [also intentionally] it doesn't know what plates are available.

That's not the reason for my embarassment though …

I have just run your query, and I'm getting

2 + 4 / 7 not 1 + 4 / 7

Must find out what's amiss

MichaelG.

[ZebethyalParticipant @zebethyal]

Hi Michael,

No reason to hide in embarassment, that is for me to do – your answer is correct – It would appear that I can't read – I wrote the first solution down wrong and then propagated the error with the other solutions

I started the solution with the worm set to 60, then realised my mistake and changed to 90.

I updated the holes part correctly in my above post but did not realise that the turns had changed from 2 to 1 as such all of the above should read 2 + whatever, not 1 + whatever.

Edited By Timothy Moores on 20/05/2016 11:33:54

[Michael GilliganParticipant @michaelgilligan61133]

Phew … That's a relief

[AjohnwParticipant @ajohnw51620]

I've part done a spreadsheet of my own using quotient and mod so that it only uses integers. In need of a life I checked the basics by verifying that the plates I want to use will do all divisions up to 60.

I now have a series of cells that tell me which plate and hole count can do a division and sums for the numbers to go with it. Scanning them may need a macro but have been looking to see if it can be done with the basic spreadsheet functions. I'm sure much older ones would do this.

John

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[AjohnwParticipant @ajohnw51620]

Not the place for a lesson on writing functions to use from a speadsheet but I spent a few hours reading doc's and as wonderful as the facilities are they are a long way from what Basic should be. I did find a couple of examples then and came up with this for a diving head division calculator. Just the start getting the info in it and getting results back which at the moment are just what was input.

REM ***** BASIC *****

Option Explicit
Option Compatible

REM Public RowData(29) as variant

Public Function DivHead (Count as integer,RowRange as variant )
Dim CellValue as variant
Dim Counter as integer
Dim AllValues (Count-1) as integer 'The -1 will(?) cause probs with MS

if not isarray (RowRange) then
MsgBox "2nd Value Must be a Range"
exit function
end if

for each CellValue in RowRange
MsgBox "b " & CellValue
AllValues(Counter)=CellValue
Counter=Counter+1
next

DivHead = StringIt ( AllValues ) 'Covert array values to a string
' so lots can be returned
End Function

Public Function StringIt ( InputArray as Integer )
Dim ReturnString as String
Dim Avalue as Integer
Dim Row as Integer

For Row = LBound ( InputArray,1 ) to Ubound ( InputArray,1 )
Avalue = InputArray ( Row )
Rem MsgBox "String " & Avalue
ReturnString = ReturnString & Avalue & ";"
Next

Stringit = ReturnString

End Function

'A 2 dimensional arrat of cells – copied from a guide and not tried
' It sums numbers > 0 in the array eg used with Addup (B6:D12) etc
'
'Punlic Function AddUp( Range )
' Dim TheSum As Double
' Dim iRow As Integer
' Dim iCol As Integer

' TheSum = 0.0

' For iRow = LBound(Range, 1) To UBound(Range, 1)
' For iCol = LBound(Range, 2) To UBound(Range, 2)
' If Range(iRow, iCol) > 0 Then TheSum = TheSum + Range(iRow, iCol)
' Next
' Next

The lower commented out AddUp function is just another way of reading a range of cells other than the one I used in DivHead. where for each in is used. It seems functions can only return one entity hence converting and array of values to a string ie text. My idea. I will see if it's possible to write directly to any number of cells from a function but it may not be.

John

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Edited By Ajohnw on 23/05/2016 16:44:49

[AjohnwParticipant @ajohnw51620]

I call DiveHead with DIVHEAD(COLUMNS(H1:H11),H11:M11 in a cell. COLUMNS give's a count of them – not needed but at some point I will need to pass several numbers. H11:M11 contain a dividing plates hole counts.

I've used MsgBox to check what's going on.

Using the Basic editor in Libre Calc was interesting(?), If the run code button is used it throws up error messages where ever one of the variables being passed to the function is used. It does this because they aren't defined until the code actually runs. May as well just use the compile button once coding errors have gone. It only runs once when it's entered into the spread sheet. Pressing some key should make it run again. Easiest answer is to click on lt's cell, delete the last letter and type it in again then press return – it then thinks ahhh something has changes so runs it all again.

John

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Edited By Ajohnw on 23/05/2016 16:42:10

Edited By Ajohnw on 23/05/2016 16:43:14

[Andy AshParticipant @andyash24902]

I finally got an hour to look at what I previously did considering what Bazyle had said.

The numbers I was reporting were correct but the method of filtering was quite seriously flawed.

I think I've got it licked now. I think my spreadsheet now does what I originally thought it did, plus some new stuff.

I've no time tonight to explain and post it.

There is an update coming. ***Especially after I do some more checking!***

[AjohnwParticipant @ajohnw51620]

I don't think it's possible to guarantee results when it's done in decimal Andy. Hence me 'arting about with macro's. Once the detail are in one of those it can be done in pure integer so there can't be any rounding errors.

Curiously, not really, in the spread sheet Libre calc has arranged for the mod and quotient functions to work correctly with decimal input providing they are integers and essentially they are the only functions needed to do the sums. So converting divisions to degrees isn't a good idea as bang go the integers.. Excel is bound to be the same as far as the functions are concerned but checking through all of the divisions a plate might do will produce a rather massive spread sheet done the usual way.

The advantage of the macro function is that it can output just the divisions a plate can do rather than including the divisions that it can't. Well I see it as an advantage especially if I want to go up to the max divisions a plate can do, eg a 66 hole plate and a 60T worm works out at nearly 4000 divisions max. In practice it will probably only produce a few 100 or so actual divisions.

John

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[ZebethyalParticipant @zebethyal]

For anyone interested, I have just created the equivalent of Michael's app using 4 cells of a spreadsheet (plus headings) to find the lowest possible value to solve for a given division.

Cell format for B4 is 'Fraction – up to 3 digits'

You can then multiply this up to find a suitable plate – 4/22, 6/33, etc (I have a 33 hole plate).

As another example using 60:1 and 13 divisions, the answers would be 4 turns and 8/13 holes (16/26, 24/39, etc).

Edited By Timothy Moores on 24/05/2016 14:31:06

[Michael GilliganParticipant @michaelgilligan61133]

Well done, Timothy

Interesting technical exercise as it may be … I honestly don't see the need for a more detailed output.

MichaelG.

.

P.S. … The two little items that I have linked on Neil's 'Best Apps and Software' thread may be of interest.

 

Edited By Michael Gilligan on 24/05/2016 15:52:01

[Michael GilliganParticipant @michaelgilligan61133]

For anyone with 'BASIC' nostalgia:

Here's how I did it on the Commodore 64, in 1993

DIVIDING.BAS

100 PRINT CHR$(147)
110 PRINT "RATIO = ";
120 INPUT RATIO
130 PRINT "DIVISIONS = ";
140 INPUT DIVN
150 HOLES%=0
160 HOLES%=HOLES%+1
170 MAX=RATIO*HOLES%
180 LOT=MAX/DIVN
190 IF LOT=INT(LOT) GOTO 210
200 GOTO 160
210 TURNS=RATIO/DIVN
220 T%=INT(TURNS)
230 PLUS=LOT-(T%*HOLES%)
240 PRINT CHR$(147)
250 PRINT RATIO;":1 ";DIVN;"DIV"
260 PRINT T%;"+";PLUS;"/";HOLES%

MichaelG.

[Author]

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