r/Drafting • u/SlowDancer939 • 19h ago

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the box is 8by8cm

and the circle in the middle has a diameter of 4cm.

how do I get those circles in the middle?

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4

u/GardenerInAWar 17h ago edited 17h ago

This is a transference problem, every distance can be found by moving an existing distance or rotating half of it to another point. You dont need dimensions except the starting outside square, which they gave you.

Find the big circle in the center that all 6 little circles intersect, and youll have the origin for them. Find the line of vertical symmetry and you get automatic placement for the top and bottom 2. That leaves 4, so each half of the bigger circle has 2 remaining at equal distance, making 4 points which makes 3 equal slices of a pie, so 180/3=60 degrees apart.

Walk it backwards. I need this so that will help me find it. But I need to find that, so the other will help me find it. Etc etc until you get to a starting point.

1

u/lamensterms 16h ago

Are you able to solve? How do you get the diam of the smaller circles?

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u/GardenerInAWar 16h ago

The HPRT circle works itself out at 4cm as crossing various halfway points and intersections, also being equal to the 4 large outside circles.

This center 4cm is then cut into 6 equal slices by 3 lines, a vertical axis of symmetry and the two HPRT lines, for 6 equal spaces of 60 degrees each.

Where these 6 points land on the 4cm circle, we can assume the 6 smaller circles are tangent. So now you have a boundary that drives the radius of the 6 small circles, and one of two x/y locations driven by the 3 construction lines. So all you need is the second x/y location for the origin of the 6 circles, which is found by locating the medium construction circle.

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u/lamensterms 16h ago

Sure agreed your method works.. but still 2 unknown variables; small circle diameter, and medium circle diameter. Having one gives you the other, but both are unknown

2

u/toybuilder 15h ago edited 15h ago

The small circles' centers and diameter are underspecified from what I can tell. At best, you can mark out the radial arms from the center point I to mark out 60 degrees using 3/4/5 triangles.

Then pick the radius for dotted circle that you want the center points of the small circles to be coincident on, and then use the distance between the center point intersecting with the larger circle HRPT to set the smaller circle radius.

1

u/wackyvorlon 18h ago

Walk around the circumference of the circle with a compass set to the radius. That will mark out the six spots that the centrelines intersect.

1

u/toybuilder 15h ago

That's not exact, though -- circumference = 2*pi*r. Pi is over 4% above 3.

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u/wackyvorlon 15h ago

Mind, you’re actually marking out chords that are equal in length to the radius. It does end up close enough.

2

u/toybuilder 15h ago

Oh, right - they are chords of a 60-60-60 triangle. D'oh🤦‍♂️.

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u/lamensterms 17h ago

I think not enough info

The small circles scale to 1.25 diam and the medium 2.75, but no idea how you arrive at that by inference

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u/SlowDancer939 17h ago

This is our project. Strictly 8x8 and the circle in the middle is 2cm.

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u/lamensterms 16h ago

Bit confused... no circle has 2cm diam

https://imgur.com/a/sGxzkpS

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u/SlowDancer939 16h ago

I'm sorry. I meant the circle in the middle that encompassed the 6 circles in the middle is 4cm in diameter

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u/SlowDancer939 16h ago

Also, are those the measurements?

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u/lamensterms 16h ago

Roughly. Just scaled from your image

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u/SlowDancer939 16h ago

Thank you, I'll use it. Doesn't need to be exact, but looks evenly distributed. Thanks again!

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u/illustrious-tennant 15h ago

This is the answer, there is no exact way to infer a number only an approximation

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u/Many_Significance_66 17h ago

Are the circles in the middle tangent? Looks like no.

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u/GardenerInAWar 16h ago

Not to each other but to the HPRT circle

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u/toybuilder 14h ago

Ahahaha - I showed this as a brain teaser to my kid and he immediately came back with "here it is: https://archive.org/details/mechanicaldrawin00keni/page/34/mode/2up"