Trying to understand dividing plates/heads/ratios... My head hurts.

[Twmaster]

In a Thread by Brian Rupnow Marv posted the following...

With a 90:1 RT, you have to turn the RT handle 90 full turns to make the part turn one complete revolution. Now let's suppose you want to make a 21 tooth gear. That requires turning the part 1/21 revolution for each tooth. That means you have to turn the handle

(1/21) * 90 = 90/21 = 4 & 6/21 turns

for each tooth. That's four complete turns of the handle and 6 spaces (note I didn't say holes) on the 21 hole plate.

Put the pin in one of the holes and bring the beveled edge of one of the sector arms around to touch the left side of the pin. Now, counting the hole the pin is in as zero, count off 6 holes and place another pin. Verify that there are indeed six inter-hole spaces between the two pins. Bring the other sector arm around so its beveled face touches the right side of this last-placed pin. Tighten the locking mechanism that retains this angular separation of the two arms.

Now, when you want to index, swing the locked sector arm assembly so as to put the beveled edge of the sector arm pair against the left side of the indexing pin. Pull the pin and turn it 4 full turns, then continue to the hole that lies next to the other sector arm on the 21 hole ring. Voila, you've moved the handle 4 and 6/7 turns and you only had to count to four. Really, once you understand it, I think you'll agree that it's a very ingenious mechanism.

-----

For any other gear, with N teeth, simply compute:

90/N

and express it in a fraction with a denominator that matches the number of holes in one of your hole circles. Then proceed as above to set the sector arms.

I will have the following to make my parts with:

30:1 ratio head. 50 hole plate. I need to make a part with 50 divisions....

So, using the above.... I end up with the number .6 (1/50 x 30) So would that be 6/10 of a rotation or 30 holes on my dividing plate to make that happen?

This unit will not have sector arms. A very simple device.

This is making my head hurt.

 

[wizardofwood]

Hi Mike
6/10 is right, but if you leave it as 30/50 it tells you how many holes to move on your 50 hole plate.
So as Marv said, counting the current hole as 0, you move to the 30th hole and that is the required position.
hope this helps, I am a visual learner so sometimes my descriptions are very muddy.
Byrne

 

[Twmaster]

Thanks Byrne,

I, like you, need visual aides to grok some of the concepts we use in the workshop.

Once I thought a bit more about this as 30/50 it now makes sense.

 

[Deanofid]

You've got your answer, Mike. Like most of these kind of problems, you can figure it from the other end, too. Your gear ratio needs 30 turns for one rotation. Your plate has 50 holes. 30 x 50 = 1500. The total number of holes your dividing device will pass for one full rotation is 1500, and you want to know how many holes for 50 spaces. 1500/50 = 30 holes per space in your piece. Same answer.

If you haven't made your index plate yet, one with a hole count of 60 might be more useful. You can do your 50 spaces with that, (36 holes), and you can do many useful numbers that divide "by 3's" that are so handy in many machining projects. 2,3,4,5,6,9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, etc. What ever divides into 1800.

Dean

 

[Twmaster]

Thanks Dean,

I have not made a plate yet. As I was having some difficulty understanding how the thing worked I just tossed that out as an example to help me 'get it'.

Now I get it!

 

[mklotz]

Mike,

If the math scares you, I strongly recommend you download the DIVHEAD program from my page. It can be set up to work for any dividing head by putting the gear ratio and available hole plates into the (ASCII) data file that accompanies the program. Once set up, you simply enter the number of divisions you require and it does all the thinking for you.

Here's an example output to show you what it returns. (The problem was 14 divisions on a head that had a 40:1 ratio.)

--------------------------
DIVIDING HEAD CALCULATIONS

Number of workpiece divisions [14] ?

DH Worm Gear Ratio = 40:1
Holes in rapid indexing plate on spindle = 24
Divisions of Workpiece = 14
Ratio/Divisions = 40/14 = 2.857142857
Turns required = 20/7 = 2 & 6/7

2 full turns of crank
and 18 holes on 21 hole plate
or 42 holes on 49 hole plate
--------------------------

Obviously, the program will tell you what you need to know directly, but far better is to do the calculation by hand and then use the program to check your answer. That way you'll learn how to do it for the time when you need to do it and the program isn't to hand.

 

[Twmaster]

Thanks Marv,

No, math does not scare me at all. I've always done well with math. I just have a brain disconnect that makes it hard for me to visualize some concepts when going from paper to real life.

Too bad your programs are all for the PeeCee.... All Unix-like OSes here.

 

[mklotz]

Too bad your programs are all for the PeeCee.... All Unix-like OSes here.

Well, the C source code is included with the program.

Just kidding. If you grok the math, it's a trivial calculation.

 

[Twmaster]

Too bad that source is looking for files like dos.h....

 

[mklotz]

If you're going to make your own plates, my DPLATES program (part of the DIVHEAD archive) will tell you which hole circles you will need.

As an example, in order to do all divisions through fifty, you will need...


REQUIRED DIVIDING HEAD HOLE PLATES

DH worm gear ratio [40] ? 30
Maximum number of divisions needed [50] ?

Hole plates required for all divisions up to 50
5,6,9,13,14,16,17,19,22,23,29,31,37,41,43,47,49,

Note that these numbers are the minimal requirement - they represent the minimum hole-drilling effort. However, integer multiples of these will work.

 

[mklotz]

Just to prove that that selection of hole plates will indeed cover all the divisions up through 50, I used my DIVHEADT program to automatically construct the turns and holes table for a 30:1 ratio table with that selection of hole plates...

-------------------------------------

Turns & holes/plate for dividing head with worm gear ratio = 30:1

Available hole plates =
5, 6, 9, 13, 14, 16, 17, 19, 22, 23, 29, 31, 37, 41, 43, 47, 49,

2 => 15 & 0
3 => 10 & 0
4 => 7 & 3/6 or 7/14 or 8/16 or 11/22
5 => 6 & 0
6 => 5 & 0
7 => 4 & 4/14 or 14/49
8 => 3 & 12/16
9 => 3 & 2/6 or 3/9
10 => 3 & 0
11 => 2 & 16/22
12 => 2 & 3/6 or 7/14 or 8/16 or 11/22
13 => 2 & 4/13
14 => 2 & 2/14 or 7/49
15 => 2 & 0
16 => 1 & 14/16
17 => 1 & 13/17
18 => 1 & 4/6 or 6/9
19 => 1 & 11/19
20 => 1 & 3/6 or 7/14 or 8/16 or 11/22
21 => 1 & 6/14 or 21/49
22 => 1 & 8/22
23 => 1 & 7/23
24 => 1 & 4/16
25 => 1 & 1/5
26 => 1 & 2/13
27 => 1 & 1/9
28 => 1 & 1/14
29 => 1 & 1/29
30 => 1 & 0
31 => 0 & 30/31
32 => 0 & 15/16
33 => 0 & 20/22
34 => 0 & 15/17
35 => 0 & 12/14 or 42/49
36 => 0 & 5/6
37 => 0 & 30/37
38 => 0 & 15/19
39 => 0 & 10/13
40 => 0 & 12/16
41 => 0 & 30/41
42 => 0 & 10/14 or 35/49
43 => 0 & 30/43
44 => 0 & 15/22
45 => 0 & 4/6 or 6/9
46 => 0 & 15/23
47 => 0 & 30/47
48 => 0 & 10/16
49 => 0 & 30/49
50 => 0 & 3/5

-------------------------------------

For those of you with dividing heads with other ratios and hole plates, note that this program can be used to produce a table for use with your machine. Print it out, laminate it and keep it with the table.

 

[arnoldb]

Mike, Marv has done great work in bringing us all these applications.

You can run most (well, most likely all; I have just tested the majority) of them under Linux/Unix and most likely OS-X using DosBox

:-[ I had great ambitions in re-doing at least some of Marv's applications for Linux using FreePascal. I only succeeded in doing one so far; this happens to be his DIVHEAD as that is a much-used one for me. If you want, I'll post a link to it for download.

And I'll publicly eat humble pie. Last year when I asked Marv if he minded if I used his programs to port to FreePascal Linux based apps, he mentioned his reservations about myself and other people doing similar conversions. Marv, it appears you are correct so far :-[. Building tools & engines is a most welcome distraction from spending days writing programs!

Regards, Arnold

 

[Twmaster]

Oh absolutely Arnold. Marv offers us all great stuff. Lots of work saved.

I also appreciate the pointer to DosBox. It works great on my old G4!

 

[mklotz]

And I'll publicly eat humble pie. Last year when I asked Marv if he minded if I used his programs to port to FreePascal Linux based apps, he mentioned his reservations about myself and other people doing similar conversions. Marv, it appears you are correct so far :-[. Building tools & engines is a most welcome distraction from spending days writing programs!

Told you so. :big:

In all fairness, I can't say I blame you. Porting software has to be one of the most unrewarding jobs on earth. Especially so if one delights in constructing new stuff.

 

[wla421]

My head hurts just reading all that.

George