Math Problem - 3 circles - generating an equation

[NXProf]

Hello,

I'm hoping to find an equation to solve for the distance of the center location of one circle from another circle given several variables of three circles and a given distance between intersecting points on the three circles. Please see the attached layout, which indicates the given variables (R₁, R₂, R₃, d₁, d₂) and the single variable (d₃) to find with an equation from the other variables.

Thank you very much for your help ahead of time.

 

[JohnRBaker]

Do you need an actual equation or rather a model where you can derive the value of d₃?

What version of NX are you running?

John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
Siemens PLM:
UG/NX Museum:

To an Engineer, the glass is twice as big as it needs to be.

 

[JohnRBaker]

Attached is an NX 5.0 model of your 3 Circles created as a sketch where you can edit the values of R₁, R₂, R₃, d₁ and d₂ and you will get the value of d₃. Just open the Expression editor and you will find the above 5 user-editable Expressions as well a single measurement Expression, d₃.

John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
Siemens PLM:
UG/NX Museum:

To an Engineer, the glass is twice as big as it needs to be.

 

[NXProf]

Thank you John for your help.

When I return to work on Monday, I'll have to review your sketch in NX 7.5 and edit the values for R₁, R₂, R₃, d₁, and d₂, while viewing the result for d₃.

But I should have been more clear since I was hoping to see the equation for finding d₃ given the other 5 variables.

Thank you again and I'll respond on Monday as well. Have a wonderful weekend!

Regards,
NXProf

 

[JohnRBaker]

Well, when I have a tool like NX with it's ability to create constrained sketches I don't really need an equation. I could 'bury' the sketch on an invisible layer and no one would be the wiser as to whether d₃ was solved using an equation or not.

John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
Siemens PLM:
UG/NX Museum:

To an Engineer, the glass is twice as big as it needs to be.