A Man Using A Computer

LDD - (Erroneous) Gap using hinges to create 360 circle

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Hey there, everyone,

I've been working on a project with multiple 16-sided spires of various diameters.  For each of these spires, I am sandwiching the flooring between an array of hinges.  Each hinge has the same number of degrees -- 22.5° (360° / 16 sides = 22.5°) -- and each side has the same number of studs.  I made one of these that had two studs on each side and it worked fine -- the floor snapped into everything without a problem.

Today I tried to make one with 5 studs on each side w/ each hinge set at 22.5°.  When I went to add the flooring, it had hairline gaps that wouldn't be there in reality and nothing would snap together.  I tried to game the program by adjusting the hinge degrees slightly (22.53°).  This worked -- I was able to join the plates, but certain smaller plates on the underside, would not fit.  I designed each quadrant of these circles to be identical -- you rotate them by 90° and they fit into one another.

I know that if I had the pieces in front of me that I could get them to fit together, but that's not a cost-effective option currently.  I really want to make a clean design.

Attached is a picture to help you see what I'm dealing with.  I'm trying to join the 4x12 plates with an (offset) 6x6 plate where the white circle is.

Has anyone else dealt with these kinds of hairline gaps?  How did you manage?  Working radially definitely complicates things.  Thanks

Capture.JPG.5aa194a3e9fefb8f8c41658e25a75449.JPG

Edited by A Man Using A Computer
Adding attachement

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10 minutes ago, LM71Blackbird said:

Hmm... have you tried it with 4 or 6 studs on each side? Even numbers usually tend to be easier to work with.

It seems like the hairline gaps show up for many different versions, including 2 studs on each size.  I was able to get my design to work.  It isn't perfect, but at least I can continue to proceed.  

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These gaps aren’t erroneous, they are mathematical!

A regular polygon (same length sides, same angles) with an integer length for the sides doesn’t generally have an integer radius (either for the inscribed circle or the circumscribed circle).

When you build it in real life, the hinges adjust themselves and don’t all take the same 157.5° angle.

You need to either measure the angles on a real construct (good luck) or find them mathematically.  Personally, I use a geometry tool (Kig, under Linux/KDE) and end up with something like this for a 4-stud-sided hexadecagon:

hexadeca-angles.png

The angles you have to use in LDD will be those shown here, or 180° minus angle, or another complement, depending on how the hinge is placed and the angle measured.

 

(Quick explanation of the construct:

  • the points (0,0) and (8,8) are the fixed hinges (the vertical side [(0,-4);(0,0)] and horizontal side [(8,8),(12,8)] are connected with plates, as you wish to do),
  • the hinge points we are looking for are on 4-stud radius circles from these points,
  • the middle diagonal is the center of the middle unconnected side, the other diagonals are its hinge points (the ones we are looking for) and they are at 2 studs on each side, we want that side/segment to be at 45°,
  • we just find the intersections of the diagonals with the circles and find where the hinge points can be (two solutions), and therefore we find the angles.

)

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3 hours ago, SylvainLS said:

Personally, I use a geometry tool (Kig, under Linux/KDE)

Thank you very much!

To be clear, is Kig a program within KDE? Is KDE just a Linux program?

Where can I find something like Kig or KDE for Windows?

 

UPDATE:

I tried the degrees you recommended in LDD.  Unfortunately, the hinge tool only allows for two decimal places.  It automatically rounds up these figures and that causes the combined angles to be too steep to form the circle.  I'm open to trying other programs.  I'd prefer something that can handle over 30,000 bricks and will also import my LDD files.

Edited by A Man Using A Computer
new info

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Kig is a program, KDE is a desktop environment.  You can learn more here.  They talk about other similar tools that may exist for Windows.

As for the angles:

  1. two decimal places is enough,
  2. LDD only shows two but you can still enter three or more,
  3. LDD doesn’t measure the angles as shown on the construction, instead of 68.9057, you need to use 90 − 69.9057 = 21.0943 (or -21.0943, the sign depends on which subpart of the hinge you’re rotating), and instead of 156.094, you need to use 180 − 156.094 = 23.906.  (Again, two decimal places is enough.)

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2 hours ago, SylvainLS said:

LDD doesn’t measure the angles as shown on the construction, instead of 68.9057, you need to use 90 − 69.9057 = 21.0943 (or -21.0943, the sign depends on which subpart of the hinge you’re rotating), and instead of 156.094, you need to use 180 − 156.094 = 23.906.  (Again, two decimal places is enough.

So am I using both measurements to create a circle, alternating between the two?

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Let’s try with a picture:

hexadeca-quarter.jpg

  1. Place the big White plates.
  2. Place the leftmost Black-DBG hinge.
  3. Click and rotate the DBG subpart by 21.09°.
  4. Place the Red 1x4 plate underneath.
  5. Place the LBG-VLBG hinge.
  6. Click and rotate the VLBG subpart by 23.91°.
  7. Place the Orange 1x4 plate underneath.
  8. Clone the LBG-VLBG hinge and put on the rest of the Orange 1x4 plate.
  9. Place the Yellow 1x4 plate.
  10. Clone the Black-DBG hinge and connect the Yellow 1x4 plate and the right White plate.

Now you have a quarter of a hexadecagon.  Just clone once to have a half one, and clone the half to close the loop.

By the way, the angles are (obviously?) the same if you want longer (or shorter) sides.  Here the side is 4 and the polygon has a “diameter” of 22.  Side 5 means a “diameter” of 27.  (Diameter = 5 x side + 2)

Edited by SylvainLS
BTW

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5 minutes ago, SylvainLS said:

Let’s try with a picture:

First off, thanks so much for going through the trouble to create that diagram.  It helped a lot.  

This method worked.  Previously, I was trying to first build the entire outer ring using just 22.5° and then trying to place the plates.  Placing the plates and then building the ring with your specific hinge settings worked.

This was a huge help.  Thank you again.

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You’re welcome :classic:

Now you have both a method to build and a reason why Maths are useful in real life.  I don’t know why such constructions aren’t used as examples by teachers all over the world! :grin:

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I'm trying to do this again, but this time with 4 studs on 8 sides.  I tried multiplying the previous figures Sylvain gave me (21.09° and 23.91°) by two.  I can't get the plates to sync up.  This time I'm making rings, but no bases -- this is so that I can build vertical, octagonal towers.  I need to be able to button everything up at the end with a ring of four #24599 arches or something similar.  I seem to be off by half a stud, but I feel like I could get these all to fit if I had the pieces in my hands.

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First, you can’t use the hexadecagon values to make an octagon, the problems are totally different.

But the octagon problem is simpler: you have “on studs” vertical and horizontal sides and you want to connect them with only one diagonal side. That means both ends of the diagonal side have integer coordinates. And the only diagonals with integer coordinates are hypothenuses in Pythogorean triangles. And there are no Pythagorean triangles with a hypothenuse of 4.

Problem solved: you can’t.

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