View Full Version : maths help please

I am trying to dimension a CA toolholder so I can make some up, since they are so heavy freighting them from the US is out of the question...

The formula I have is

90-ø

S = M + D(cot ------- +1)

2

M = 40.38

D = 10

ø = 60

I also know the answer as I cheated and used google but S =67.7

But as algebra was not my strong suit at school I want to know where I am going wrong doing it manually

90-60

40.38+10 (cot ------ +1)

2

50.38 (cot15+1)

50.38 (3.732+1)

50.38 X 4.732 = 238.4 wrong answer

Where am I going wrong? I understand the BOMDAS rule, that was drummed into us pretty hard at school...

The forum software does not seem to like my attempt at fractions.... But I think you get the drift....

form_change

08-23-2011, 06:57 AM

To get an answer of 67.7, the formula would have to be

S=M+(D((cot__)-1))

67.7 = 40.38 +( 10 ((cot 15)-1))

Not knowing where it was from I can't say whether it is correct or not.

Michael

On edit - extra brackety goodness added

philbur

08-23-2011, 08:20 AM

90-60=30 degrees so you should be using cot (30) not cot(15). Using cot(30) gives the stated correct answer, providing you follow Michael's arrangement for the equation.

Oops, I think Micheal's equation should be ((cot 30)+1)) not ((cot15)-1), although they give the same answer.

Phil:)

I am trying to dimension a CA toolholder so I can make some up, since they are so heavy freighting them from the US is out of the question...

The formula I have is

90-ø

S = M + D(cot ------- +1)

2

M = 40.38

D = 10

ø = 60

I also know the answer as I cheated and used google but S =67.7

But as algebra was not my strong suit at school I want to know where I am going wrong doing it manually

90-60

40.38+10 (cot ------ +1)

2

50.38 (cot15+1)

50.38 (3.732+1)

50.38 X 4.732 = 238.4 wrong answer

Where am I going wrong? I understand the BOMDAS rule, that was drummed into us pretty hard at school...

The forum software does not seem to like my attempt at fractions.... But I think you get the drift....

90-60=30 degrees so you should be using cot (30) not cot(15). Using cot(30) gives the stated correct answer, providing you follow Michael's arrangement for the equation.

Phil:)

Hi Phil, It is 90-60/2... But then that gives you 60/2=30 and 90 from that is 60....

arghhhhh....

Forrest Addy

08-23-2011, 12:36 PM

What the hell are we doing? Calculating pin sizes over dovetails?

philbur

08-23-2011, 12:51 PM

You need to be clearer about your original post

You state:

90-ø

and

ø = 60

So 90-60 =30 so what!!!!! Where does this value fit in the equation? Does this value belong in the equation?

Your equation states cot............ What angle is .............

What is the relevance of 90-60/2. Where did divide by 2 come from it's not identified in your first post.

Phil:)

Hi Phil, It is 90-60/2... But then that gives you 60/2=30 and 90 from that is 60....

arghhhhh....

rohart

08-23-2011, 03:40 PM

Sorry to say it, but this is a bit of a mess.

What I do spot, however is that you say M = 40.38, and D = 10.

You say S = M + D (anything)

and then you say S = 50.38 times something.

No.

You must do the multiplications first, and then add separate terms.

So, in words, if S equals M plus D times something, work out the D times something first, and then add it to the M.

The D times something doesn't even want to know about M, so there's no way you can add M and D. AT ALL ! Absolutely strict rule.

You need to be clearer about your original post

It would be but you try to enter a fraction with the forum software.... It will not allow it and instead reformats what I type...

dockrat

08-23-2011, 04:05 PM

It would be but you try to enter a fraction with the forum software.... It will not allow it and instead reformats what I type...

alt-0188 ¼

alt-0189 ½

alt-0190 ¾

for the basics anyway

Here is the formula out of the book

http://img.photobucket.com/albums/v606/OzRinger/dovetail.jpg

Mike Burdick

08-23-2011, 06:59 PM

.RC.

From your values:

S = 40.38+ 10(COT ((90-60)/2)) +1)

S= 40.38 + 47.32

S= 87.70

Your value for the trig part of the equation was correct, you just substituted the wrong values for the others.

Greg Q

08-23-2011, 07:02 PM

Can't you just measure the male dovetail on the toolpost?

rohart

08-23-2011, 07:04 PM

OK, so now I understand the heiroglyphics - the 90 and the 2.

As I said, the problem is you're adding M to D before multiplying by cot(15) + 1.

You must multiply cot(15) + 1, which as you say is 3.73 + 1, or 4.73, by 10, to get 47.3. Then you add the 40.38.

So the answer is 87.68.

I don't know how you got the google answer, but that system will have strict bracketing requirements too.

philbur

08-23-2011, 07:07 PM

You have errors all over the place. you are not reading what is on the paper.

(90-60)/2 is not the same as 90 -60/2

In any case ø is not 60 degrees it is 30 degrees.

The calculation for the cot angle is then (90-30)/2 which equals 30, then the equation 40.38 +( 10 ((cot 30)+1)) is correct and gives the result 67.7

Phil:)

Hi Phil, It is 90-60/2... But then that gives you 60/2=30 and 90 from that is 60....

arghhhhh....

philbur

08-23-2011, 07:32 PM

Oops, now I'm not reading what's on the paper, ø is 60 degrees for the female taper.

Edit: For the female dovetail I don't think it is possible to calculate S using only M and the included angle ø and the rod diameter D. The height of the dovetail can still been any value and therefore so can M without any change in S. Also how does D have any relevance. I can half the value of D with out changing the actual size of S. I think the equation needs to use the m value not the M value.

I think machinery's Handbook has the correct equation.

Phil:)

Forrest Addy

08-23-2011, 10:05 PM

When caalculating dovetails you calculate to theoretical corners. Since this is an intersection of two planes the corner is a theoretical point in space therefore impossible to measure directly; thus pins and calculation. When measureing dovetails you have to set a referance face for the flank angle to intersece with. The exterior flat of the male (projecting) dovetail is the reference face. Plins can be placed agoinst dovetails and a measurement over the pins will produce a number that by mathematics will produce an accurate dimenstion to the theoretical charp corners of the dovetial.

The female dovetail has no convenient internal angle of intersection. Since 99% ot the time the dovetail meet in the interior angle of rthe diverging flanks and the clearance for the projecting flat of the male dovetail. If this flat is accurately nachined it can be measured for depth and the resultant pin reading can be used to calculat the theoretical sharp ange forme by the diverging flanks and the reference surface.

If the female interior flat is not a usable secondary reference surface you will have to trap the pins/ Start wight a flat placed on the female dovetail ref surface and clamp the pons to it using a manufaactured piece whose angles trap the pin beteen the flat and flank, I usually made the piece of wood. If the pins extend a bit from the dovetail they can be measured (carefully) with a mike.

Its take calculating to get there but you have to start with a clear idea of the geometry and the significancve of the pin reading before you can determine the all important theoretical sharp corner.

oldtiffie

08-23-2011, 11:12 PM

I agree with you Forrest.

Perhaps this item last item of a HTML file may assist the OP as well:

http://homemetalshopclub.org/news/dec02/dec02.html

bborr01

08-23-2011, 11:21 PM

Can't you just measure the male dovetail on the toolpost?

That's what I was thinking too.

Maybe it is an exercise in math but simple usually works for me.

Brian

The dovetail on the tool post has the same problem as this one that being it is chamfered so the true measurement can only be guessed...

It was really a test of mathematics then anything.... As mentioned I have the answer already but wanted to make sure I could do it manually...

Seems the equation is wrong as was my arithmetic..

The height is 12.5mm for those interested... That must be why calculator I used asked for the height measurement..

philbur

08-24-2011, 04:24 AM

This is why you use distance between pins.

Phil:)

The dovetail on the tool post has the same problem as this one that being it is chamfered so the true measurement can only be guessed...