Tangent with circles at an angle

Rhino
1

Problem Tangents.3dm.zip (17.0 KB)

Screen Shot 2021-08-24 at 12.14.37 PM
Screen Shot 2021-08-24 at 12.14.37 PM1142×874 14.4 KB

I am trying to find a construction to do the following. I want to have two lines tangent to the three circles roughly as shown. However, I need a 60 degree angle between the lines.

The black circles cannot move. The red circle can move tangent to the line to the right of it.

How then would one position the red circle along the line so that the tangents would be at 60 degrees?

2

I do not see any solution to that - the black circles need to move to hold the 60 degrees, or the angle needs to increase to leave the black circles in place.

-Pascal

3

If you move the red circle up, tangent angle decreases. As it is now, it’s about 66d. You can move it up a little and it goes through 60d

Here’s the same with more construction lines and the circle moved up.

Screen Shot 2021-08-24 at 12.53.00 PM
Screen Shot 2021-08-24 at 12.53.00 PM1249×1459 17.8 KB

4

Ah, Ok - so you are allowing rotation of the lines… still the solution looks likely to be iterative, to me - I am not sure that there is an exact construction for this.

-Pascal

5

My solution

  1. sketch 2 black circless
  2. connect its centers with line (line A)
  3. sketch line B with arbirary length from midpoint of line A
  4. sketch line C from any black circle center with angle 30° to intersect line B
  5. sketch perpendicular line ti line C with start point in the from circle center to get intersection
  6. ofset line C through the intesection
    to get the tangent line (line D)
  7. mirror sketch line D with respect to line A, you should get two tangent lines with inner angle 60°
  8. sketch the 3rd circle with option tangent and click on the line D, input the radius and click on the mirrored line
    ViewCapture20210825_121428
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6

Hi @miano
I know it’s cheating, but here’s the SolidWorks solution.
Problem Tangents SWX.3dm (173.1 KB)

-Jakob
Sorry - wrong file uploaded - BRB!
THERE we go; now it’s the right file!

7

i think offsetting the problem by 0.035 will offer some constructions with a circle / inscribed angle for the 60 degrees

… maybe this is the starting-point for a better solution ?

my / the somehow brute-force solution is to draw surfaces, that represent all possible positions in the z-direction

ViewCapture20210826_132021
ViewCapture20210826_1320211079×926 84.6 KB

the orange curves represent the 0.035 offset with the inscribed angle / circle for 60 degree
the violet surface shows all possible tangents
the cyan surface is to construct the rails for the green surface
the green surface should be a (non-existing) sweep2 with road like top option - and this is where this approach gets un-precise…
the green, final circle is 3x tangent, but has a radius of 0.0348889 inches (instead of 0.035)…

Problem_Tangents_3d_search_tom.3dm (218.2 KB)

any more precise pure rhino ideas ?

9

as far as i understood the question - using @Normand SW solution - the constraints are
5x tangent
1x Radius … inch stuff ;-(
1x Angle 60degree

Screenshot 2021-08-26 at 16.33.39
Screenshot 2021-08-26 at 16.33.391058×945 29.9 KB

10

Yeah, @Tom_P - that’s the way I understood it as well. Easily done in SWX, but not sure if there’s a way to construct it without dependencies/parametry.
-Jakob

11

well see my post above :cold_face:

12

Hi @Tom_P
Sorry! I totally missed the picture and the lower part of the message :flushed: Cool way to go about it!!!
-Jakob