### Author Topic: 5"sine bar  (Read 5197 times)

#### wheeltapper

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• Posts: 61
##### 5"sine bar
« on: July 15, 2013, 01:31:05 PM »
Hi
I thought I'd see how accurate I can be so I made this.

I'm quite pleased with how it came out.

Roy.
I used to be confused, now I just don't know.

#### b.lindsey

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• Dallas, NC, USA
##### Re: 5"sine bar
« Reply #1 on: July 15, 2013, 02:02:42 PM »
Looks very nice Roy!!  So how were you able to check the accuracy?

Bill

#### wheeltapper

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• Posts: 61
##### Re: 5"sine bar
« Reply #2 on: July 15, 2013, 03:48:07 PM »
Hi
I know the two rollers are 1/2" diameter exactly ( as exactly as I can be with a micrometer ) and the distance between the inside edges is 4 1/2" , again, as exact as I can be.

parallelism was checked by placing it on the mill table and running a dial gauge along the top.
I've previously checked the mill table with a gauge and get no discernable difference along it .

so as I see it its as accurate as I can make it.

Roy.
I used to be confused, now I just don't know.

#### mklotz

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• Posts: 2433
• LA, CA, USA
##### Re: 5"sine bar
« Reply #3 on: July 15, 2013, 04:19:57 PM »
It's worth checking what its effective length is.

Borrow an accurate angle plate of angle 'A'.  Put it on the bar and use gage blocks to pack the bar up until the angle plate is horizontal as measured with your DTI.  Call this stack height 'h'.  Now the effective length of the bar is:

EL = h / sin(A)

The effective length should be very close to your design value of 5".
---
Regards, Marv

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#### b.lindsey

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• Dallas, NC, USA
##### Re: 5"sine bar
« Reply #4 on: July 15, 2013, 04:20:17 PM »
Thanks Roy, pretty much as i had assumed, just thought I might have missed something.

Bill

#### arnoldb

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• Posts: 1340
• Windhoek, Namibia
##### Re: 5"sine bar
« Reply #5 on: July 15, 2013, 08:45:15 PM »
Very nice indeed Roy.  That's a handy bit of kit I've wished I'd already made on many occasions.

Kind regards, Arnold
Building an engine takes Patience, Planning, Preparation and Machining.
Procrastination is nearly the same, but it precludes machining.
Thus, an engine will only be built once the procrastination stops and the machining begins!

#### wheeltapper

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• Posts: 61
##### Re: 5"sine bar
« Reply #6 on: July 15, 2013, 09:22:16 PM »
It's worth checking what its effective length is.

Borrow an accurate angle plate of angle 'A'.  Put it on the bar and use gage blocks to pack the bar up until the angle plate is horizontal as measured with your DTI.  Call this stack height 'h'.  Now the effective length of the bar is:

EL = h / sin(A)

The effective length should be very close to your design value of 5".

Thanks for the formula, I haven't really got anything that accurate to test this properly yet but I'll paste this into my 'things to remember ' folder.

I did do a quick check, I used 30 degrees which needs a stack 2.5" high.
I made a stack that measured 2.5" with a micrometer with brass blocks and a feeler gauge .
then I set the bar on a flat surface and put one of those electronic angle gauges on top, zeroed the gauge then put the stack under the gauge.
I got exactly 30 degrees.

so I know I'm in the zone.

further testing will follow.

Roy.
I used to be confused, now I just don't know.

#### pgp001

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• Posts: 681
• West Yorkshire - UK
##### Re: 5"sine bar
« Reply #7 on: July 15, 2013, 10:27:43 PM »
Just trying to understand what you meant by:- (and the distance between the inside edges is 4 1/2")

I assume you mean the gap between the two 1/2" diameters and not the distance between the two locating corners, otherwise you have made a 4 1/2" sine bar

It does not really matter it just makes the maths a bit different, I actually have a little 2 1/2" sine bar, and my sine table is 8" centres.

It looks to be a nice bit of workmanship by the way.

Phil

#### ttrikalin

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• Posts: 155
##### Re: 5"sine bar
« Reply #8 on: July 15, 2013, 10:51:01 PM »
Say $h=2.5$ inches, the stack of gages you are using for a target angle of $A=30$ degrees ($\pi/6$), and $x = 5.0$ inches, the target length of the sine bar (we assume the rolls are dead on 1/2", though you can revise the calculations below).

The partial derivative of $A$ w.r.t. $x$ gives an indication of how off your actual angle would be for small mistakes in the knowledge of $x$. (good enuf calculation for what we do)

Code: [Select]
\frac{\partial}{\partial x}\text{asin}\big(\frac{h}{x}\big) = -\frac{h}{x^2 \sqrt{1-h^2/x^2}}
So, if you are off in the length of the bar by small amounts that you should be able to measure, then the percentage (%) you are off in the angle is very small.

If you are wrong 0.001" in x, the angle is off by 0.022%
If you are wrong 0.005" in x, the angle is off by 0.11%
If you are wrong 0.010" in x, the angle is off by 0.22%

Unless you have a very expensive electronic angle gizmo, I doubt that it has an accuracy that can get close to getting 0.22% around a 30 degree angle...

You should be happy with the sine bar, and enjoy it without fear!

tom
take care,

tom in MA

#### ttrikalin

• Full Member
• Posts: 155
##### Re: 5"sine bar
« Reply #9 on: July 15, 2013, 10:52:42 PM »

I am a lover of life, not a mathematician.

take care,

tom in MA

#### wheeltapper

• Full Member
• Posts: 61
##### Re: 5"sine bar
« Reply #10 on: July 15, 2013, 11:03:55 PM »
Say $h=2.5$ inches, the stack of gages you are using for a target angle of $A=30$ degrees ($\pi/6$), and $x = 5.0$ inches, the target length of the sine bar (we assume the rolls are dead on 1/2", though you can revise the calculations below).

The partial derivative of $A$ w.r.t. $x$ gives an indication of how off your actual angle would be for small mistakes in the knowledge of $x$. (good enuf calculation for what we do)

Code: [Select]
\frac{\partial}{\partial x}\text{asin}\big(\frac{h}{x}\big) = -\frac{h}{x^2 \sqrt{1-h^2/x^2}}
So, if you are off in the length of the bar by small amounts that you should be able to measure, then the percentage (%) you are off in the angle is very small.

If you are wrong 0.001" in x, the angle is off by 0.022%
If you are wrong 0.005" in x, the angle is off by 0.11%
If you are wrong 0.010" in x, the angle is off by 0.22%

Unless you have a very expensive electronic angle gizmo, I doubt that it has an accuracy that can get close to getting 0.22% around a 30 degree angle...

You should be happy with the sine bar, and enjoy it without fear!

tom

I did mean the distance between the 1/2" rollers.
also, I did not understand one single thing in your post

when I see lots of numbers together my brain runs into a corner and whimpers

Roy
I used to be confused, now I just don't know.

#### ttrikalin

• Full Member
• Posts: 155
##### Re: 5"sine bar
« Reply #11 on: July 15, 2013, 11:09:05 PM »
[...] I did not understand one single thing in your post
when I see lots of numbers together my brain runs into a corner and whimpers

Then you are a fellow lover of life, my friend...

This is the message to take home...

If you are off by 0.001" in  the length of the sine bar, the target angle of 30 degrees is missed by 0.022% -- peanuts.

take care,

tom in MA

#### mklotz

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• Posts: 2433
• LA, CA, USA
##### Re: 5"sine bar
« Reply #12 on: July 15, 2013, 11:25:42 PM »
Tom's computations are implemented in my SINEBAR program - no thinking on your part required.  It will tell you the angle error resulting from a small error in either the stack height or in the length of the sine bar.

[It will also tell you the stack height required for a given angle and the blocks from a standard set needed to form that height.]
---
Regards, Marv

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