mirror of
https://github.com/bherbruck/solidcraft.git
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Kernel rig: everyday rounds of an L-bracket's bend
Inside bend r3, outside r5, both concentric (r3 and r8), the inside r35 using up both inside faces, r36 refused naming 35, and the inside bend Type: Curvature. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
jyviko
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{
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"sources": [],
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"what": "an L-bracket's inside bend rounded r3, then its outside bend r8 = 3 + its thickness: concentric rounds, a bend of even thickness",
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"source": "analytic",
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"method": "L-bracket: the legs 40x20x5 (x 0..40, z 0..5) and 5x20x40 (x 0..5, z 0..40) joined, 20 deep in y: V0 = 4000 + 4000 - 500 = 7500, 8 faces. Both rounds' centre lines are (8, y, 8): V = 7500 + 20 (1-pi/4) 9 - 20 (1-pi/4) 64 = 7263.9380. Check: in the square [0,8]^2 the bend is the quarter annulus pi (64 - 9)/4 against the L's 64 - 9 = 55 there: 20 (pi 55/4 - 55) = -236.0620. Faces 10.",
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"volume_mm3": 7263.937979737193,
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"faces": 10,
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{
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"sources": [],
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"what": "an L-bracket's inside bend rounded curvature-continuous (Type: Curvature) size 3",
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"source": "analytic",
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"method": "L-bracket: the legs 40x20x5 (x 0..40, z 0..5) and 5x20x40 (x 0..5, z 0..40) joined, 20 deep in y: V0 = 4000 + 4000 - 500 = 7500, 8 faces. The concave edge between two planes square to each other, its ends on the planar faces y = 0 and 20: the section is the quintic Bezier of setback 3 (fillets/862), area 113/756 9 = 1.345238, added along 20: V = 7526.9048. Faces 9; both seams G2.",
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"body_count": 1,
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"volume_mm3": 7526.9047619047615,
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"faces": 9,
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"order": "g2"
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@@ -0,0 +1,49 @@
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"type": "curvature"
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{
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"sources": [],
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"what": "the inside bend of an L-bracket rounded r3",
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"source": "analytic",
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"method": "L-bracket: the legs 40x20x5 (x 0..40, z 0..5) and 5x20x40 (x 0..5, z 0..40) joined, 20 deep in y: V0 = 4000 + 4000 - 500 = 7500, 8 faces. The concave edge (x = 5, z = 5) gains the spandrel (1-pi/4) 9 = 1.931417 along its 20: V = 7500 + 38.6283 = 7538.6283. Faces 9.",
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"body_count": 1,
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"volume_mm3": 7538.628330588459,
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"faces": 9,
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"continuity": {
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"order": "g1"
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}
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}
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@@ -0,0 +1,48 @@
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+21
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{
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"sources": [],
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"what": "an L-bracket's inside bend rounded r35, exactly as long as both inside faces: the round uses them up and meets the legs' ends at their edges",
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"source": "analytic",
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"method": "L-bracket: the legs 40x20x5 (x 0..40, z 0..5) and 5x20x40 (x 0..5, z 0..40) joined, 20 deep in y: V0 = 4000 + 4000 - 500 = 7500, 8 faces. The inside faces run 35 from the bend (x = 5..40 on the foot's top, z = 5..40 on the upright's inner face); the r35 round is tangent to them at their far edges (x = 40, z = 40), so both are used up. Added = 20 (1-pi/4) 35^2 = 5257.7450. V = 12757.7450. Faces 8 - 2 + 1 = 7. No continuity check: with both faces it was tangent to used up, the round meets only the legs' end faces (x = 40, z = 40), square to it (creases), so no tangent seam is left to measure.",
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"body_count": 1,
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"volume_mm3": 12757.744996762518,
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"faces": 7,
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+48
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@@ -0,0 +1,8 @@
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{
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"sources": [],
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"what": "an L-bracket's inside bend rounded r36, past both inside faces (35 long): refused, naming the largest radius that fits",
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"source": "invariants",
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"method": "a concave round adds material, and an r36 one would touch the inside faces 36 from the bend, past their 35: it would hang over the legs' ends. Owner rule: concave overflow stays refused, naming the largest that fits: 35 (every-l-bracket-inside-bend-r35-uses-both-faces), at the request's three significant digits (step 0.01).",
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"outcome": "refused",
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"refusal": "the largest radius that fits is 35 mm"
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}
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@@ -0,0 +1,48 @@
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}
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@@ -0,0 +1,24 @@
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{
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"sources": [],
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"what": "the outside bend of an L-bracket rounded r5",
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"source": "analytic",
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"method": "L-bracket: the legs 40x20x5 (x 0..40, z 0..5) and 5x20x40 (x 0..5, z 0..40) joined, 20 deep in y: V0 = 4000 + 4000 - 500 = 7500, 8 faces. The convex edge (x = 0, z = 0) loses the spandrel (1-pi/4) 25 = 5.365046 along its 20: V = 7500 - 107.3009 = 7392.6991. Faces 9.",
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"body_count": 1,
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@@ -0,0 +1,48 @@
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Reference in New Issue
Block a user