Author Topic: Dividing head calculations  (Read 10014 times)

Offline Allen Smithee

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Dividing head calculations
« on: June 03, 2015, 06:36:04 PM »
Last night in an idle moment I was messing about on a spreadsheet (mainly because I knew how much it would annoy Marv) to produce tables that, for a given gear ratio and number of division holes, would give the angular results for all combinations of turns and number of holes. The sheet has columns for each ring of holes, and the next step is to add a "search box" so that the nearest few combinations for any desired angle are highlighted. This is all easy stuff which I'm sure lots of people have done, although if anyone wants a copy I'll happily upload it when I've finished it and tidied it up.

But I wanted the sheet to display the angles both in decimal degrees and degree/minute/second numbers. This is again not rocket science, and there were lots of possible spreadsheet formulas for doing it using successive truncation or similar (which are all simple, but long and tedious). But it occurred to me that spreadsheets understand "hours/minutes/seconds" formats and can work with these directly, and they're numerically identical to degrees/minutes/seconds number systems. So I started playing with simply using a custom cell format to reformat the displayed number without changing the underlying numbers.

This should also be very, very simple, and some quick googling told me that if I set the cell format to "custom" and typed [h]° mm' ss\" into the "Type" box it would do what I wanted. And it did - the format looked right, but the actual numbers were massively wrong. Where the decimal degrees column read 0.6° the D/M/S column read 14° 24' 00"!!

After much head scratching the penny finally dropped, and my reason for typing all this blather is to pass on the tip for anyone who is doing something similar - this data type in excel doesn't convert decimal HOURS to hours/minutes/seconds - it converts decimal DAYS to hours/minutes/seconds. So it was assuming that my 0.6 was actually 0.6 days rather than 0.6 hours, and so gave the answer 14 hours and 24 minutes. All that is needed to use this trick for easy conversions is simply to divide the value by 24 to convert it into decimal days which (in our case here) means it displays any decimal-degree angle in degrees, minutes and seconds...

 :facepalm: :facepalm: :facepalm:

Incidentally (if anyone is interested) in the data type [h]° mm' ss\" the square brackets around the [h] tell excell not to roll-over the number at midnight and to count total elapsed hours (which as we're using it for degrees rather than hours is definitely useful). The backslash in ss\" is telling excel to just att the double quote marks as text rather than treating them as closing quotes in the type definition.

AS
« Last Edit: June 03, 2015, 07:43:25 PM by Allen Smithee »
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Online steamer

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Re: Dividing head calculations
« Reply #1 on: June 03, 2015, 07:42:21 PM »
Actually Allen, I've written a rotary table spreadsheet....I can post it here....but later when I get home....in degrees, minutes and seconds.


Dave
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Re: Dividing head calculations
« Reply #2 on: June 03, 2015, 07:46:19 PM »
I did post this before....but here it is.

Dave
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Offline mklotz

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Re: Dividing head calculations
« Reply #3 on: June 03, 2015, 07:55:53 PM »
Last night in an idle moment I was messing about on a spreadsheet (mainly because I knew how much it would annoy Marv) to produce tables that, for a given gear ratio and number of division holes, would give the angular results for all combinations of turns and number of holes. The sheet has columns for each ring of holes, and the next step is to add a "search box" so that the nearest few combinations for any desired angle are highlighted.

Well you've certainly succeeded in that regard.  A monstrous collection of tables so big it needs a search function?  Sort of "steampunk" mathematics.  But keep up the good work - it will keep you out of the bars.

Why not take your desired angle, divide it into 360 and truncate the result to an integer, then use normal dividing head math to find the turns and holes?  Better yet, use a rotary table and input the desired angle directly.



The DIVHEAD program on my website will calculate turns and holes for any dividing head. You supply it (via a text file) the gear ratio and a list of the hole plates you have, then, at run time specify the number of divisions required and it returns the turns and holes. Here's an example output:

DIVIDING HEAD CALCULATIONS

Number of workpiece divisions [14] ? 24

DH Worm Gear Ratio = 40:1
No rapid indexing plate available
Divisions of Workpiece = 24
Ratio/Divisions = 40/24 = 1.666666667
Turns required = 5/3 = 1 & 2/3

1 full turns of crank
and 18 holes on 27 hole plate
or 22 holes on 33 hole plate
or 26 holes on 39 hole plate
or 30 holes on 45 hole plate

If the number of divisions specified is not possible given the specified hole plates the program will tell you the hole plate you need.

Also included in the archive is a program that calculates the minimum-drilling set of hole plates you need to make all divisions up to some user-specified number.
Regards, Marv
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Offline Allen Smithee

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Re: Dividing head calculations
« Reply #4 on: June 03, 2015, 08:06:47 PM »
Input from a text file? How quaint! Does it output on punch-cards as well?:stir:

My reasons for doing it were mainly to provide a table in both decimal and DMS so that when looking through old drawings I could quickly find how close I could get to it with the plates I already have. And as my dividing head and headstock divider have different gear ratios it can also tell me if one or other method can get closer to the desired value.

And of course it would wind you up, which opportunities should not be passed up lightly....

 :mischief: :mischief:

AS
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Re: Dividing head calculations
« Reply #5 on: June 03, 2015, 08:12:08 PM »
OK guys.......Don't make me flick the switch on this thread as well.....OK?

Dave
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Offline Allen Smithee

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Re: Dividing head calculations
« Reply #6 on: June 03, 2015, 08:29:13 PM »
Apologies - it was only intended as mild joshing.

Joking aside, my primary reason for doing this was because I intend to use the resulting spreadsheet to produce a table of angles against plates and divisions.

ie a list of angles with the corresponding plate, division set, hole numbers and handle turns required to achieve them. I can see this as being a useful chart to have on the wall in the workshop, so that when I want a particular angle I have a quick reference on which combination of plate and holes will achieve it, or get close enough for the purpose in hand (say if I don't actually need better than +/-.25 degrees can I get close enough with the plate that's currently fitted etc). I can also use the same table when designing, so I can design things I can actually make easily.

A spreadsheet is an easy way of doing this, and more to the point maintaining it - it would be very easy to add in the additional values if I made/bought a different plate.

AS
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Offline mklotz

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Re: Dividing head calculations
« Reply #7 on: June 03, 2015, 09:05:06 PM »
OK guys.......Don't make me flick the switch on this thread as well.....OK?

OK, I'll just add Allen to the list and move along.
Regards, Marv
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Offline Don1966

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Re: Dividing head calculations
« Reply #8 on: June 03, 2015, 10:53:28 PM »
Allen try this sheet and see if it helps. It will convert your degrees to minutes and seconds and will hunt for the nearest hole plate.
It works on a 60 to 1 ratio.  f yours is different just change the 60's in the E10 to E26 columns to your table ratio. Also the C8 cell from 60 to your ratio. The hole plate number if they don't match yours just insert your values in the C10 to C26 column where the green numbers are.
If you have the Versatile Dividing Head (VDH) look in Plans and Drawings for the one I posted.
Don

 

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