Geometry or Formuls to construct a circle to three entities.

[cropwell]

I googled the problem and found this https://planetcalc.com/1421/ you have to scroll down to the 'Segment defined by chord and height' and that will give you the radius of that circle that passes through the centers of the smaller circle. So you just add on the radius of the smaller circle.

Cheers,

Rob-T

[Neale]

I googled the problem and found this https://planetcalc.com/1421/ you have to scroll down to the 'Segment defined by chord and height' and that will give you the radius of that circle that passes through the centers of the smaller circle. So you just add on the radius of the smaller circle.

Cheers,

Rob-T

Rob - unfortunately, it's not quite that simple! I generally try to find some sort of sanity check when I'm doing sums like this - does it give the right answer for the extreme cases? Does the answer move the right way if I change one of the given values? In this case, if you increase the size of the small circle to be equal to the segment height, the answer should be "infinity" for the radius of the big circle as the circle becomes a straight line. With your approach (which will be fairly close if the size of the small circles is small). as the small circle size increases, R increases - but that means that it no longer touches the vertical line. What's needed is the chord length and height at the points of tangency with the small circles - which you don't know at this point.

If it's any consolation, I'm typing this rather than being in the workshop because I've just fouled up a job on the CNC router. I wanted to move the tool up and clear so that I could add an extra fixing screw towards the end of a 1.5hr machining operation. Due to a complete brain fade, I moved Z up using machine rather than work coordinates - which meant that it plunged down rather than going up before moving in X and dragging work and spoil board sideways, leaving a big gouge in the work. The only good thing was that at least it was a thick spoil board so that the cutter didn't reach the machine bed, and I didn't break the 2mm carbide cutter. We all have off days...

[cropwell]

I would have thought that, if the problem can be drawn on a sheet of paper then the calculator I found would be OK for all practical purposes. I don't think that extreme cases apply here. The chord length is the distance between the centres of the smaller circles. the height of the chord is the distance from the large circle minus the smaller circle radius. So we are calculating the radius of a circle concentric to the large one, where the periphery passes through the centres of the small circle. the large circle is this calculated radius plus the radius of the small circle.

I presume the OP knows all the dimensions and can substitute them in the calculation app.

The problem may be a fascinating exercise, but the practicalities of mathematics faded for me when it got to imaginary numbers. I was alright with algebra, geometry and calculus, but that was 60 years ago and I haven't had the need to do much more than arithmetic, sines, cosines and tangents and a bit of Pythagorean juggling in the intervening time.

This was my today project, from circuit diagram to pcb. It is a logic indicator circuit (Hi-Lo_Pulse) using a 4011.


Cheers,

Rob-T

[Doddy]

This was my today project, from circuit diagram to pcb. It is a logic indicator circuit (Hi-Lo_Pulse) using a 4011.


Cheers,

Rob-T

Thread-creep: I'm curious - I've had mixed results with isolation routing in the past (to the point that I refuse to entertain the idea any more and unlikely to change my mind) - but you go for complete copper removal... what cutting bits do you use/find useful for this?

[cropwell]

Thread-creep

I'll start a new thread.....