Rusty Math-Need to figure where circles touch

[Walt]

I'm making a bike light. The box that holds everything together is getting milled out of a chuck of aluminum. The chunk of aluminum needs holes in it for the light to shine out, power to come in, switches to mount (got those done), and a small, removable cover so I can stuff the switch and electronics board inside.

The cover will also function as a mount and heat sink for the electronics board. Due to the small size of the light, there's no place else to put it. In order to mount the board, a 1" circle, I will use a boring tool to make a shallow blind hole in the underside of the cover, with a narrow shoulder on it.




The electronics board has components sticking out both sides and needs a small, raised pad machined so it sits proud of the surrounding material. That's the rectangular shape in the drawing with an angle cut out of the upper right side. Since I'll be doing this with a small end mill, how do I calculate where to crank the x-y table to in order to cut the aluminum from the bottom of the hole, but not run into the sides of the circle? I should know this stuff, but math classes were a long time ago, and I've forgotten a lot.

Walt

 

[Ray C]

I'd try to help you but your image/attachment is not showing-up.

Can you re-post the graphic?

Ray

 

[Walt]

I looked up "tangent circles" on Google and got this page from Wikipedia:

http://en.wikipedia.org/wiki/Tangent

I was worried that I was going to be faced with some calculus, but fortunately it's not that hard of a problem. Good thing for me, 'cause I don't remember much calculus at all!

The general formula for internal tangent circles is (x1-x2)^2+(y1-y2)^2 = (r1-r2)^2

(The ^ symbol is the way I was taught to indicate powers. x^2 is x squared, x^1/2 is the square root of x.)

This is going to need to end up as x,y coordinates for the milling machine, but the calculation can be simplified if we let the bore hole be circle 2 and be centered on 0,0.

Then we end up with x1 = (( r1-r2)^2 - y1^2)^1/2

It's pretty easy to put this in an Excel spreadsheet.



The x-figures actually represent two points (actually four points when the bottom half of the bore is calculated), they are that amount +- from the center of the bore hole, and also the center of the bore hole needs to be translated to the 0,0 point of the part, but that's not hard. I'll work something up and post a complete spreadsheet if anyone is interested.

Walt

- - - Updated - - -

I'd try to help you but your image/attachment is not showing-up.

Can you re-post the graphic?

Ray

I'll try re-posting the graphic when I get home from work, sorry for the bad post.

Walt

 

[Walt]

Here's maybe a better picture of what I'm trying to do. I'm boring a blind hole into a piece of aluminum, then machining a raised feature into the bottom of it. Hopefully, without accidentally cutting into the sides of my bore. No need to respond to this Ray, I think I've figured it out on my own. Thanks.

Walt

 

[markknx]

Walt,
If you are boring first the why not Clamp you part in the rotary table align center with the end mill. then run the table back !/2 your inside Dia. or until you touch the inside of the bore. then you can mill the first arch. set the rotary's stops to leave the proud area wide. crank the table forward and use a larger end mill and swing the arch again. this will keep the bore then all you have to do is mill the rectangle.

 

[Walt]

Walt,
If you are boring first the why not Clamp you part in the rotary table align center with the end mill. then run the table back !/2 your inside Dia. or until you touch the inside of the bore. then you can mill the first arch. set the rotary's stops to leave the proud area wide. crank the table forward and use a larger end mill and swing the arch again. this will keep the bore then all you have to do is mill the rectangle.

Thank you Mark. I would definitely do that if I had a rotary table. I've been drooling over pictures of them, maybe now is the time to get one!

Walt