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What is the inner/outer or mid radius of the 45 degree arc the following element makes?

https://www.bricklink.com/v2/catalog/catalogitem.page?P=65473 enter image description here

I tried to align several of the elements in 90 and 180 degree arcs in stud.io, the end of the arc never seems to align with any modules, so I'm inclined to think the radius is nonsensical. Is there any way two or more of these elements can be combined so the open ends align with in system modules?

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After a bit of fiddling in LeoCAD, I can confirm that the mid radius (i.e. the distance from the center of the torus to the axis of an axle) is 3.5 studs plus 2 LDUs (equal to 3.6 studs, or 72 LDUs).

Consequently, the inner radius is 2.6 studs (or 52 LDUs), and the outer radius is 4.6 studs (or 92 LDUs).

CAD drawing of a quarter-torus, annotated

Note that the odd offset (2 LDUs / 0.1 studs) is half of the "lip" of a headlight brick, or half the height of a stud's cylinder. There are techniques to achieve a 2 LDU offset; see e.g. this question. Here's a possible assembly, just to demonstrate:

torus-aligning assembly, perspective torus-aligning assembly, front


Edit: it has been noted that 72 LDUs is also the height of three bricks. This allows to, for example, align a 2x2 round tile using brackets like so:

torus aligned with a 2x2 tile at 3 bricks of height torus aligned with a 2x2 tile at 3 bricks of height

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    72 LDU is also 9 plates or 3 brick heights... makes a lot more sense now, thx May 16, 2023 at 16:50
  • However, I'm not that happy with your connection example. technic holes in bricks are 0.1 mm = 0.25 LDU offsetted to their bottom. Your connection example would likely be considered illegal (depends a bit on how you connect back...) May 16, 2023 at 17:03
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    It was a 10-minute hack in LeoCAD. Besides, I tend to forget about some of those really specific cases of illegal/stressed connections. May 16, 2023 at 17:10
  • It's 72 LDU not 72 studs (as the post says). May 16, 2023 at 20:30
  • Sorry, butter fingers :-) May 16, 2023 at 20:41

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