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metal master engg
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Join Date: Aug 2008
Location: india
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Geometry Calculation of Balls

09/13/2010 4:52 PM

Dear all , for one of my development of mechanical machine part , i make wire feeding clutch or say go no go taper feeder part , like collet with steel balls inside .

i need to know calculation or formula of calculating diameter of outer radius of steel balls

3 ball or circles are equally divided by 3 point divider

please see attached drawing and let me know what will be the diameter of outer radius,circle , of three balls surrounding one ball, i may keep changing dimensions , but the theory should be the same .

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Pathfinder Tags: Auto Cad calculation of size drawings geometry mech engineering
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Tornado
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#1

Re: geometry calculation of balls

09/13/2010 5:42 PM

If the 4 small balls are all the same radius r, the outer circle radius R = 3r.

If the center ball is different (radius r'), then R = r' + 2r.

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rickwil
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#2
In reply to #1

Re: geometry calculation of balls

09/14/2010 6:50 AM

"If the 4 small balls are all the same radius r, the outer circle radius R = 3r."

The three balls are not touching each other across their diameter, they are contacting at something less. The distance can't be 3r, it would have to be less but I'm not that much of a mathamatician to figure out the distance.
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Geode Hunter
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#3
In reply to #2

Re: geometry calculation of balls

09/14/2010 7:42 AM

I would seem if they did not touch at the diameter, they would be loose in the constraining circle.

I believe the Tornado has it nailed.

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rickwil
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#4
In reply to #3

Re: geometry calculation of balls

09/14/2010 8:18 AM

Yep, I drew it out and measured. I see it now. Any two balls hold the center ball another ball's diameter from the side mking it 3r. It took me a while to get it.
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dkwarner
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#5
In reply to #2

Re: geometry calculation of balls

09/14/2010 10:22 AM

I initially thought something along the same line, but I also tried, and Tornado is indeed right!

This drawing should make it clear: these were originally Ø 1.0" circles surrounding a Ø 0.5" circle.

Dick

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Apprentice-1
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#6

Re: Geometry Calculation of Balls

09/14/2010 10:54 AM

If the central circle is excentric this will change the formula, as in the figure:
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