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finding the center of a circle


s.e.charles

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I want to develop a system for making pulleys from styrene stock.

I have a punch set which will net .189", .157", .128", & .096". for my most used scales of 1/25 & 1/24, these will be close enough to 5", 4", 3", & 2 1/2" discs respectively. I know these are not exact but this isn't the conundrum.

to wit: after the discs are punched, i'll want to stack them on a piece of .020" brass rod for aligning & mounting.

Q: how can I get consistent centered holes in the discs?

unfortunately, my punch is a rough steel & plexiglass unit which all but prohibits me from scribing crosshairs and cutting them concentrically. it is similar to the micro-mark unit, but has guide posts on both ends of a single row of holes.

thanks for any help, jigs, or formulas.

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Best bet is a 'centre finder', it's an engineering tool. Basically a V with a second part bisecting the V. You place the circle in the V the bicenting part gives a line through the center scribe the line, rotate 120 degrees, scribe again, and again. The three scribe lines will give you the centre However for your purposes I think you're going to have to make one as the engineers tool is quite large. You could just cut squares drill the centres out then knock the corners off (octegons) running them onto the wire before turning them, save using the punch set.

Colin

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Nice and simple method for larger circles.

How to find the centre of a circle:

For these tiny bits of styrene i'd drill the holes first, mount them on a mandril shaft in a hobby drill and the apply a sanding stick to the outside diameter till the correct size is reached.

poor man's lathe!

Edited by andygif290368
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I ended up getting a set of transfer punches. I slipped the styrene into my punch set, used the transfer punch, and then the cutter punch. gave me a disc with the center marked. then I drilled .020" for rod and strung the discs on held with a dollop of acc. chucked in the moto-tool and used a 400 grit sanding stick to smooth.

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  • 11 months later...

Use Euclidean geometry. Create a chord on the circle... a straight line joining one part of the circumference to the other. Best to have a shortish chord, one that is roughly 1/4 of the circumference. Now bisect the chord. Place the point of a pair of compasses on one end of the chord, open them out to approx 2/3rds of the way along the chord and scribe a large arc from top to bottom, one which starts this side of half way, and finishes this side of half way. Then swap ends and repeat the process to form a mirror arc. The arcs will intersect top and bottom. Join the two intersects with a straight line and lengthen it towards and through the centre of the circle. Because the centre WILL be somewhere along that line. Now draw another chord about 1/3rd of the way around the circumference from the first and repeat the process. Where the two lines intersect is the exact centre of the circle.

This SOUNDS complicated, but it isn't. Using this method you can find the centre of any circle in less than a minute.

Edited by Badder
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The Euclidean method is the business but I don't think I'd trust my eyes (or my compasses!) to get it right on a circle with a diameter of .096"!

I know, I was just showing off the fact that although I left school 33 years ago and haven't used geometry in all the time since, I can still remember it!

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Badders - less of your cheek please. Just for that, I'd like you to come to the front of the class and show us how to construct the internal tangent to two given circles. ;-)

Edit to add: because I've completely forgotten...

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Badders - less of your cheek please. Just for that, I'd like you to come to the front of the class and show us how to construct the internal tangent to two given circles. ;-)

Edit to add: because I've completely forgotten...

Stands at the front of the class of 81 with my stupid hair, heavy metal cut-off denim with studs, chains and band patches and says , 'To find the common internal tangent between two given circles, simply draw a line connecting the two circle centres.... then draw a line which intersects THAT line but also touches the circumferences of both circles. I thank you. Metallica rock!' and exits.

Edited by Badder
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  • 1 month later...

To my mind there's a quick, easily repeatable way to do this...

Measure the diameter of your circles.

Cut a square out of a small piece of plasticard with sides of that length or ever so slightly bigger.

Drop your punched circle in to that square hole.

Use a ruler and a sharp pencil to draw two lines between the opposite corners of that square, across your circle.

Where the lines cross is your centre.

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  • 3 weeks later...

To my mind there's a quick, easily repeatable way to do this...

Measure the diameter of your circles.

Cut a square out of a small piece of plasticard with sides of that length or ever so slightly bigger.

Drop your punched circle in to that square hole.

Use a ruler and a sharp pencil to draw two lines between the opposite corners of that square, across your circle.

Where the lines cross is your centre.

this is a good trick to remember; thanks.

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As mentioned transfer punches may be the way to go.

If you load material in your punch set, you can use the correct size TP to mark a center divot , then punch out the disc.

And remember TP's are designed to be LIGHTLY struck.

Done and done.

Edited by krow113
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