mirror of
https://github.com/bherbruck/solidcraft.git
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Ladder 12: sheet metal, from a base flange to a bracket with a lip, each answer from its flat area
Base flange; an edge flange at 90 deg; four made together, the corners closed on the mitre plane with the rule's gap, at 90, 72 (leaning out, the ends run on along a slant) and 108 deg (leaning in, cut back); round, rectangular and tear reliefs; a hem; a fold, unfolded and refolded; the tray's flat pattern (outline size and area, bend lines); a bracket with a hole and a flange on a flange. K = 0.5, so every volume is T x the flat area. The 108 deg tray is a sheet-metal rig case too. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
jyviko
@@ -0,0 +1,24 @@
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{
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||||
"sources": [],
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"what": "a 100 x 60 base flange, 2 mm sheet",
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"source": "analytic",
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"method": "the sketch's rectangle extruded the rule's 2 mm up: V = 100 60 2, A = 2 (100 60 + 100 2 + 60 2); a box's 6 faces, 12 edges, 8 vertices",
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"body_count": 1,
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"volume_mm3": 12000.0,
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"area_mm2": 12640.0,
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||||
"faces": 6,
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"edges": 12,
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"vertices": 8,
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"bbox": {
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"max": [
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||||
]
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||||
}
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@@ -0,0 +1,46 @@
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{
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"commands": [
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{
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"command": "sheet.manage_rules",
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"params": {
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"name": "Sheet 2 mm",
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"thickness": "2 mm",
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"active": true,
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"bend_radius": "1 mm",
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"k_factor": 0.5,
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"gap": "0.5 mm"
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}
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},
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{
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"command": "sketch.create",
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"params": {
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"plane": "XY",
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"name": "Base"
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}
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||||
},
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{
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"command": "sketch.rectangle.two_point",
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"params": {
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||||
"p0": [
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||||
0,
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0
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||||
],
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"p1": [
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100.0,
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]
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}
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},
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{
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||||
"command": "sketch.finish",
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"params": {}
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},
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{
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"command": "sheet.flange",
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||||
"params": {
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"type": "base",
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"sketch": "Base"
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}
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}
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]
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}
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@@ -0,0 +1,21 @@
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{
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"sources": [],
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"what": "a 20 mm 90 deg edge flange along the base's front edge",
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"source": "analytic",
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"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). At 90 deg s0 = 3 and BA = pi: the base keeps 100 x 57, the bend pi x 100, the panel 17 x 100; V = 2 (5700 + 100 pi + 1700). The flange's outer face is flush with the edge (y = 0) and reaches z = 20. Faces: base top and bottom, its three free ends, the bend's two cylinders, the flange's inner and outer faces and its top: 10, each end of the L (x = 0, x = 100) one plane",
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"body_count": 1,
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"volume_mm3": 15428.318530718,
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"faces": 10,
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||||
"bbox": {
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||||
"min": [
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0,
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0
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||||
],
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"max": [
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60.0,
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20.0
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||||
]
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||||
}
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||||
}
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@@ -0,0 +1,20 @@
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{
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"base": "../../12-sheet-metal/001-base-flange",
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"commands": [
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{
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"command": "sheet.flange",
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||||
"params": {
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||||
"type": "edge",
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"edges": [
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[
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50.0,
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],
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"height": 20.0,
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"angle": 90
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||||
}
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||||
}
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||||
]
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}
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+20
@@ -0,0 +1,20 @@
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{
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"sources": [],
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"what": "20 mm 90 deg flanges on all four edges, made together: the corners close with the rule's gap, notch relief",
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"source": "analytic",
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"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). Closing a corner (sheet.rs close_corner): every point of a panel's end keeps g/2 from the plane halving the two flanges' inner faces. For the flange on y = 0, its bend along x from the corner (s0, s0), a point s up its panel (rigid, turned theta about the bend axis T + R up) on the face z of the sheet keeps that distance from x = s0 - R sin(theta) - s cos(theta) + g/sqrt2 + (T - z) sin(theta) on; the inner face z = T needs least, so the end is the line x = s0 - e - s cos(theta), e = R sin(theta) - g/sqrt2: the panel runs on e past its bend's end at its foot and a further cos(theta) per mm up it (outward below 90 deg, cut back above). Each panel is the trapezoid leg x (L + 2e + leg cos(theta)), its bend BA x L, L the base's edge less 2 s0 (the bend ends square at the corner). At 90 deg: s0 = 3, BA = pi, leg 17, e = 1 - g/sqrt2 = 0.646447 (the panel ends T + g/sqrt2 short of the other's outer face line, gap g between the inner edges), no slant. Base 94 x 54, bends pi (2 94 + 2 54), panels 17 (2 (94 + 2e) + 2 (54 + 2e)); V = 2 x that = 22251.656329. The walls' outer faces stand on the edges: bbox 100 x 60 x 20. The notch relief cuts nothing: the bends end square at the corners",
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||||
"body_count": 1,
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||||
"volume_mm3": 22251.656328684,
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||||
"bbox": {
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"min": [
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],
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"max": [
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]
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}
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||||
}
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+36
@@ -0,0 +1,36 @@
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{
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||||
"base": "../../12-sheet-metal/001-base-flange",
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||||
"commands": [
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||||
{
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||||
"command": "sheet.flange",
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||||
"params": {
|
||||
"type": "edge",
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||||
"edges": [
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[
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50.0,
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]
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],
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"height": 20.0,
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||||
"angle": 90,
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||||
"corner_relief_shape": "notch"
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||||
}
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||||
}
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||||
]
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||||
}
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+20
@@ -0,0 +1,20 @@
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{
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||||
"sources": [],
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||||
"what": "20 mm flanges at 72 deg on all four edges, made together and closed at the corners, leaning out: the panel ends run on along a slant",
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||||
"source": "analytic",
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||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). Closing a corner (sheet.rs close_corner): every point of a panel's end keeps g/2 from the plane halving the two flanges' inner faces. For the flange on y = 0, its bend along x from the corner (s0, s0), a point s up its panel (rigid, turned theta about the bend axis T + R up) on the face z of the sheet keeps that distance from x = s0 - R sin(theta) - s cos(theta) + g/sqrt2 + (T - z) sin(theta) on; the inner face z = T needs least, so the end is the line x = s0 - e - s cos(theta), e = R sin(theta) - g/sqrt2: the panel runs on e past its bend's end at its foot and a further cos(theta) per mm up it (outward below 90 deg, cut back above). Each panel is the trapezoid leg x (L + 2e + leg cos(theta)), its bend BA x L, L the base's edge less 2 s0 (the bend ends square at the corner). At 72 deg: s0 = 3 tan36 = 2.179628, BA = 2.513274, leg 17.820372, e = 0.597503, the slant cos(theta) = 0.309017 a mm up. V = 2 x the flat area = 23902.891082. Bbox: the walls lean out: the outer face's far edge is H cos(theta) = 6.180340 outside each edge, and the inner face's far edge is highest, H sin(theta) + T cos(theta)",
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"body_count": 1,
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||||
"volume_mm3": 23902.891082184,
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||||
"bbox": {
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||||
"min": [
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-6.180339887498949,
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"max": [
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||||
}
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||||
@@ -0,0 +1,35 @@
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||||
{
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||||
"base": "../../12-sheet-metal/001-base-flange",
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||||
"commands": [
|
||||
{
|
||||
"command": "sheet.flange",
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||||
"params": {
|
||||
"type": "edge",
|
||||
"edges": [
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[
|
||||
50.0,
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"height": 20.0,
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||||
"angle": 72
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||||
}
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||||
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||||
]
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||||
}
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||||
+20
@@ -0,0 +1,20 @@
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||||
{
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||||
"sources": [],
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||||
"what": "20 mm flanges at 108 deg on all four edges, made together and closed at the corners, leaning in over the base: the panel ends are cut back along a slant where they would overlap",
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||||
"source": "analytic",
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||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). Closing a corner (sheet.rs close_corner): every point of a panel's end keeps g/2 from the plane halving the two flanges' inner faces. For the flange on y = 0, its bend along x from the corner (s0, s0), a point s up its panel (rigid, turned theta about the bend axis T + R up) on the face z of the sheet keeps that distance from x = s0 - R sin(theta) - s cos(theta) + g/sqrt2 + (T - z) sin(theta) on; the inner face z = T needs least, so the end is the line x = s0 - e - s cos(theta), e = R sin(theta) - g/sqrt2: the panel runs on e past its bend's end at its foot and a further cos(theta) per mm up it (outward below 90 deg, cut back above). Each panel is the trapezoid leg x (L + 2e + leg cos(theta)), its bend BA x L, L the base's edge less 2 s0 (the bend ends square at the corner). At 108 deg: s0 = 3 tan54 = 4.129146, BA = 3.769911, leg 15.870854, e = 0.597503, the slant cos(theta) = -0.309017 a mm up. V = 2 x the flat area = 20295.276640. Bbox: the walls lean in: what reaches furthest out is each bend's outer face a quarter turn in, s0 - (R + T) = 1.129146 inside the edge, and the outer face's far edge is highest, H sin(theta)",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 20295.276640444,
|
||||
"bbox": {
|
||||
"min": [
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||||
}
|
||||
@@ -0,0 +1,35 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/001-base-flange",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.flange",
|
||||
"params": {
|
||||
"type": "edge",
|
||||
"edges": [
|
||||
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|
||||
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|
||||
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|
||||
}
|
||||
@@ -0,0 +1,20 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "003's tray with a round corner relief 4 mm across at each corner",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). A corner relief (sheet.rs plan_relief) is cut from the base at the corner of the bends, size/2 = r along both edges: a quarter disc (round) or an r x r square (rectangular) at a square corner; both bends then start r from the corner, and the panels keep the ends the closing gave them. r = 2: each corner takes pi r^2/4 = pi of the base and 2 mm of each of its two bends (2 BA = 2 pi); V = 2 (003's flat area - 4 x that - 8 x 2 pi)",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 22125.99262254,
|
||||
"bbox": {
|
||||
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||||
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|
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||||
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|
||||
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||||
]
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,37 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/001-base-flange",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.flange",
|
||||
"params": {
|
||||
"type": "edge",
|
||||
"edges": [
|
||||
[
|
||||
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|
||||
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|
||||
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|
||||
],
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
"height": 20.0,
|
||||
"angle": 90,
|
||||
"corner_relief_shape": "round",
|
||||
"corner_relief": "4 mm"
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,20 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "003's tray with a rectangular corner relief 4 mm across at each corner",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). A corner relief (sheet.rs plan_relief) is cut from the base at the corner of the bends, size/2 = r along both edges: a quarter disc (round) or an r x r square (rectangular) at a square corner; both bends then start r from the corner, and the panels keep the ends the closing gave them. r = 2: each corner takes r^2 = 4 of the base and 2 mm of each of its two bends (2 BA = 2 pi); V = 2 (003's flat area - 4 x that - 8 x 2 pi)",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 22119.125363769,
|
||||
"bbox": {
|
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]
|
||||
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|
||||
}
|
||||
@@ -0,0 +1,37 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/001-base-flange",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.flange",
|
||||
"params": {
|
||||
"type": "edge",
|
||||
"edges": [
|
||||
[
|
||||
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|
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|
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|
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|
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|
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
]
|
||||
],
|
||||
"height": 20.0,
|
||||
"angle": 90,
|
||||
"corner_relief_shape": "rectangular",
|
||||
"corner_relief": "4 mm"
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,20 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "003's tray with torn corners: the bends run to the corner and each end is cut straight, in the flat, to where its panel's end starts",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). A torn corner (sheet.rs tear_corner) cuts nothing from the base: each bend zone's end runs straight from the corner, on its start line, to the panel's end at its far edge, e = 0.646447 further along (003's closing), so each torn end adds the triangle BA e / 2 to the bend zone; folded, the end is a helix and the column of sheet under each flat point still holds T of material (K = 0.5). V = 2 (003's flat area + 8 pi e / 2)",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 22267.903304036,
|
||||
"bbox": {
|
||||
"min": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
100.0,
|
||||
60.0,
|
||||
20.0
|
||||
]
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,36 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/001-base-flange",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.flange",
|
||||
"params": {
|
||||
"type": "edge",
|
||||
"edges": [
|
||||
[
|
||||
50.0,
|
||||
0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
100.0,
|
||||
30.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
50.0,
|
||||
60.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
0,
|
||||
30.0,
|
||||
2.0
|
||||
]
|
||||
],
|
||||
"height": 20.0,
|
||||
"angle": 90,
|
||||
"corner_relief_shape": "tear"
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,20 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "002's L with an 8 mm hem on the base's back edge, folded under it with a 1 mm inner radius",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). A hem (sheet.rs add_hem) is a 180 deg bend starting at the edge, its inner radius the gap, folded under the face it is picked on (the top here, so down), its length to the outer face: the leg is 8 - (1 + 2) = 5 and BA = pi (1 + 1) = 2 pi. V = 2 (002's flat area + 100 (2 pi + 5)). Bbox: the bend's outer face reaches R + T = 3 past the edge (y 63) and, a half turn round its axis 1 mm under the base, down to z = -(2 R + T) = -4",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 17684.955592154,
|
||||
"bbox": {
|
||||
"min": [
|
||||
0,
|
||||
0,
|
||||
-4.0
|
||||
],
|
||||
"max": [
|
||||
100.0,
|
||||
63.0,
|
||||
20.0
|
||||
]
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,19 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/002-edge-flange-90",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.hem",
|
||||
"params": {
|
||||
"edges": [
|
||||
[
|
||||
50.0,
|
||||
60.0,
|
||||
2.0
|
||||
]
|
||||
],
|
||||
"length": 8.0,
|
||||
"gap": 1.0
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,21 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "001's base folded 90 deg up along a sketch line across it at x = 70",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). A fold (sheet.rs add_fold) takes its bend zone out of the sheet, so the flat stays 100 x 60 and V = 2 x 6000 = 12000. Centred on the line x = 70 the zone runs from 70 - pi/2; the larger side stays, the 30 mm side folds up 90 deg about the axis at x = 70 - pi/2, z = T + R: its outer face (the flat bottom) stands at x = 70 - pi/2 + R + T = 71.429204 and its panel, 30 - pi/2 long, rises from z = R + T to 31.429204. Faces as 002's L: 10",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 12000.0,
|
||||
"faces": 10,
|
||||
"bbox": {
|
||||
"min": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
71.42920367320511,
|
||||
60.0,
|
||||
31.4292036732051
|
||||
]
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,23 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/001-base-flange",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.fold",
|
||||
"params": {
|
||||
"points": [
|
||||
[
|
||||
70,
|
||||
0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
70,
|
||||
60.0,
|
||||
2.0
|
||||
]
|
||||
],
|
||||
"angle": 90
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,20 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "010's fold unfolded: the flat 100 x 60 plate again",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). A fold (sheet.rs add_fold) takes its bend zone out of the sheet, so the flat stays 100 x 60 and V = 2 x 6000 = 12000. Centred on the line x = 70 the zone runs from 70 - pi/2; the larger side stays, the 30 mm side folds up 90 deg about the axis at x = 70 - pi/2, z = T + R: its outer face (the flat bottom) stands at x = 70 - pi/2 + R + T = 71.429204 and its panel, 30 - pi/2 long, rises from z = R + T to 31.429204. Unfolded every panel lies in the base's plane where it was cut from: the 100 x 60 x 2 plate, the base in its place",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 12000.0,
|
||||
"bbox": {
|
||||
"min": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
100.0,
|
||||
60.0,
|
||||
2.0
|
||||
]
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,9 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/010-fold-90",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.unfold",
|
||||
"params": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,21 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "011's flat refolded: 010's part again",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). A fold (sheet.rs add_fold) takes its bend zone out of the sheet, so the flat stays 100 x 60 and V = 2 x 6000 = 12000. Centred on the line x = 70 the zone runs from 70 - pi/2; the larger side stays, the 30 mm side folds up 90 deg about the axis at x = 70 - pi/2, z = T + R: its outer face (the flat bottom) stands at x = 70 - pi/2 + R + T = 71.429204 and its panel, 30 - pi/2 long, rises from z = R + T to 31.429204. Refolding gives the folded part back: 010's numbers",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 12000.0,
|
||||
"faces": 10,
|
||||
"bbox": {
|
||||
"min": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
71.42920367320511,
|
||||
60.0,
|
||||
31.4292036732051
|
||||
]
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,9 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/011-fold-unfolded",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.refold",
|
||||
"params": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,57 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "the flat pattern of 003's tray: its outline's size and area, and its four bend lines",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). The flat pattern is drawn in the base's frame (the base in its place). Each flange lies flat past its edge: s0 back from it, then BA and the leg, so it reaches H - s0 + BA - s0 = 20 - BD = 17.141593 past the edge (BD = 2 (R + T) tan45 - BA = 6 - pi): the outline is (100 + 2 x that) x (60 + 2 x that), its area 003's flat area (11125.828164, the notched corners open). The bend lines are the bend zones' centre lines, BA/2 out from the cut-back edges: y = 3 - pi/2 and 57 + pi/2 from x = 3 to 97, x = 3 - pi/2 and 97 + pi/2 from y = 3 to 57",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 22251.656328684,
|
||||
"flat_pattern": {
|
||||
"size_mm": [
|
||||
134.2831853071796,
|
||||
94.2831853071796
|
||||
],
|
||||
"area_mm2": 11125.828164341892,
|
||||
"bend_lines": [
|
||||
[
|
||||
[
|
||||
2.9999999999999996,
|
||||
1.429203673205103
|
||||
],
|
||||
[
|
||||
97.0,
|
||||
1.429203673205103
|
||||
]
|
||||
],
|
||||
[
|
||||
[
|
||||
98.57079632679489,
|
||||
2.9999999999999996
|
||||
],
|
||||
[
|
||||
98.57079632679489,
|
||||
57.0
|
||||
]
|
||||
],
|
||||
[
|
||||
[
|
||||
2.9999999999999996,
|
||||
58.5707963267949
|
||||
],
|
||||
[
|
||||
97.0,
|
||||
58.5707963267949
|
||||
]
|
||||
],
|
||||
[
|
||||
[
|
||||
1.429203673205103,
|
||||
2.9999999999999996
|
||||
],
|
||||
[
|
||||
1.429203673205103,
|
||||
57.0
|
||||
]
|
||||
]
|
||||
]
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,9 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/003-four-flanges-90-closed-corners",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.flat_pattern",
|
||||
"params": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,20 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "a bracket: a 30 mm flange on the front edge, a 10 mm lip turned out on its far edge, a d10 hole through the base",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). The flange (as 002, H 30) stands on y = 0 up to z = 30. The lip is picked on that flange's far edge on its outer face (y = 0), the panel's bottom face, so it bends down there, turning out over y < 0; its outer virtual sharp is on the edge (z = 30, y = 2, the flange's top-face plane), so the flange's panel is cut back s0 = 3 more (30 - 3 - 3 = 24) and the lip's outer face is the plane z = 30, its panel 10 - 3 = 7, reaching y = 2 - 10 = -8. The hole (d10 at (50, 35)) is a cut-out of the flat. V = 2 (100 57 + 100 pi + 100 24 + 100 pi + 100 7 - 25 pi). Bbox: x 0..100, y -8..60, z 0..30",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 18699.557428756,
|
||||
"bbox": {
|
||||
"min": [
|
||||
0,
|
||||
-8.0,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
100.0,
|
||||
60.0,
|
||||
30.0
|
||||
]
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,46 @@
|
||||
{
|
||||
"base": "../../12-sheet-metal/001-base-flange",
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.flange",
|
||||
"params": {
|
||||
"type": "edge",
|
||||
"edges": [
|
||||
[
|
||||
50.0,
|
||||
0,
|
||||
2.0
|
||||
]
|
||||
],
|
||||
"height": 30.0,
|
||||
"angle": 90
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "sheet.flange",
|
||||
"params": {
|
||||
"type": "edge",
|
||||
"edges": [
|
||||
[
|
||||
50.0,
|
||||
0,
|
||||
30.0
|
||||
]
|
||||
],
|
||||
"height": 10.0,
|
||||
"angle": 90
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.hole",
|
||||
"params": {
|
||||
"position": [
|
||||
50.0,
|
||||
35,
|
||||
2.0
|
||||
],
|
||||
"diameter": 10
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -219,6 +219,26 @@
|
||||
],
|
||||
"tier": "11-cumulative-parts",
|
||||
"what": "parts combining every tier"
|
||||
},
|
||||
{
|
||||
"cases": [
|
||||
"ladder/12-sheet-metal/001-base-flange",
|
||||
"ladder/12-sheet-metal/002-edge-flange-90",
|
||||
"ladder/12-sheet-metal/003-four-flanges-90-closed-corners",
|
||||
"ladder/12-sheet-metal/004-four-flanges-72-leaning-out",
|
||||
"ladder/12-sheet-metal/005-four-flanges-108-leaning-in",
|
||||
"ladder/12-sheet-metal/006-corner-relief-round",
|
||||
"ladder/12-sheet-metal/007-corner-relief-rectangular",
|
||||
"ladder/12-sheet-metal/008-corner-relief-tear",
|
||||
"ladder/12-sheet-metal/009-hem-on-the-back-edge",
|
||||
"ladder/12-sheet-metal/010-fold-90",
|
||||
"ladder/12-sheet-metal/011-fold-unfolded",
|
||||
"ladder/12-sheet-metal/012-fold-refolded",
|
||||
"ladder/12-sheet-metal/013-flat-pattern",
|
||||
"ladder/12-sheet-metal/014-bracket"
|
||||
],
|
||||
"tier": "12-sheet-metal",
|
||||
"what": "sheet metal: flanges, closed corners, reliefs, hems, folds and the flat pattern"
|
||||
}
|
||||
],
|
||||
"what": "the kernel complexity ladder: tiers in order of complexity, each building on the shapes before it; cases within a tier in order of measured time (cargo xtask kernel-cases --ladder --record)"
|
||||
|
||||
+20
@@ -0,0 +1,20 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "a 100 x 60 tray with four 20 mm flanges at 108 degrees (leaning in over the base), closed at the corners: the panel ends are cut back on a slant where they would overlap",
|
||||
"source": "analytic",
|
||||
"method": "T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). Closing a corner (sheet.rs close_corner): every point of a panel's end keeps g/2 from the plane halving the two flanges' inner faces. For the flange on y = 0, its bend along x from the corner (s0, s0), a point s up its panel (rigid, turned theta about the bend axis T + R up) on the face z of the sheet keeps that distance from x = s0 - R sin(theta) - s cos(theta) + g/sqrt2 + (T - z) sin(theta) on; the inner face z = T needs least, so the end is the line x = s0 - e - s cos(theta), e = R sin(theta) - g/sqrt2: the panel runs on e past its bend's end at its foot and a further cos(theta) per mm up it (outward below 90 deg, cut back above). Each panel is the trapezoid leg x (L + 2e + leg cos(theta)), its bend BA x L, L the base's edge less 2 s0 (the bend ends square at the corner). At 108 deg: s0 = 3 tan54 = 4.129146, BA = 3.769911, leg 15.870854, e = 0.597503, the slant cos(theta) = -0.309017 a mm up. V = 2 x the flat area = 20295.276640. Bbox: the walls lean in: what reaches furthest out is each bend's outer face a quarter turn in, s0 - (R + T) = 1.129146 inside the edge, and the outer face's far edge is highest, H sin(theta)",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 20295.276640444,
|
||||
"bbox": {
|
||||
"min": [
|
||||
1.1291457614135192,
|
||||
1.1291457614135192,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
98.87085423858647,
|
||||
58.87085423858648,
|
||||
19.021130325903073
|
||||
]
|
||||
}
|
||||
}
|
||||
+76
@@ -0,0 +1,76 @@
|
||||
{
|
||||
"commands": [
|
||||
{
|
||||
"command": "sheet.manage_rules",
|
||||
"params": {
|
||||
"name": "Sheet 2 mm",
|
||||
"thickness": "2 mm",
|
||||
"active": true,
|
||||
"bend_radius": "1 mm",
|
||||
"k_factor": 0.5,
|
||||
"gap": "0.5 mm"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "sketch.create",
|
||||
"params": {
|
||||
"plane": "XY",
|
||||
"name": "Base"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "sketch.rectangle.two_point",
|
||||
"params": {
|
||||
"p0": [
|
||||
0,
|
||||
0
|
||||
],
|
||||
"p1": [
|
||||
100.0,
|
||||
60.0
|
||||
]
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "sketch.finish",
|
||||
"params": {}
|
||||
},
|
||||
{
|
||||
"command": "sheet.flange",
|
||||
"params": {
|
||||
"type": "base",
|
||||
"sketch": "Base"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "sheet.flange",
|
||||
"params": {
|
||||
"type": "edge",
|
||||
"edges": [
|
||||
[
|
||||
50.0,
|
||||
0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
100.0,
|
||||
30.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
50.0,
|
||||
60.0,
|
||||
2.0
|
||||
],
|
||||
[
|
||||
0,
|
||||
30.0,
|
||||
2.0
|
||||
]
|
||||
],
|
||||
"height": 20.0,
|
||||
"angle": 108
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -1282,14 +1282,151 @@ case(T11, "004-housing", "the running part with every tier: back wall, boss, slo
|
||||
"10/008 less the M16 groove on the boss: its cylinder runs from the r1 root round (z 21, a shoulder: the groove stops w = %.6f clear of it) to the 1 mm top chamfer "
|
||||
"(z 29, run out through it, a free end); the groove's root r 6.917 stays outside the boss's 1.5 wall's inside (r 6.5), so it cuts the wall only. Bbox: the part's" % w16, base=C10)
|
||||
|
||||
# ---------------------------------------------------------------- 12 sheet metal
|
||||
# A sheet body is its flat pattern (crates/doc/src/sheet.rs): the base, and per flange a bend zone
|
||||
# BA = theta (R + K T) wide and its panel. Folded, a panel moves rigidly and a bend zone of
|
||||
# thickness T becomes an annular sector, theta/2 ((R + T)^2 - R^2) per mm = theta T (R + T/2): with
|
||||
# K = 0.5 that is T x BA, so the folded part holds exactly the flat area x T. Rule: T = 2, R = 1,
|
||||
# K = 0.5, corner gap g = 0.5. An edge flange at the default position has its outer virtual sharp on
|
||||
# the picked edge: the base is cut back s0 = (R + T) tan(theta/2) and the bend starts there; its
|
||||
# height H runs from that sharp along the outer face, so the panel past the bend is H - s0 long.
|
||||
T12 = "12-sheet-metal"
|
||||
TS, RS, KS, GS = 2.0, 1.0, 0.5, 0.5
|
||||
WS, DS, HS = 100.0, 60.0, 20.0
|
||||
SQ2 = math.sqrt(2)
|
||||
RULE = C("sheet.manage_rules", name="Sheet 2 mm", thickness="2 mm", active=True, bend_radius="1 mm", k_factor=KS, gap="0.5 mm")
|
||||
def sm_ba(deg):
|
||||
return math.radians(deg) * (RS + KS * TS)
|
||||
def sm_s0(deg):
|
||||
return (RS + TS) * math.tan(math.radians(deg) / 2)
|
||||
SMETH = ("T = 2, R = 1, K = 0.5, the corner gap g = 0.5. A bend zone is BA = theta (R + K T) wide in the flat; folded it is an annular sector holding theta T (R + T/2) a mm "
|
||||
"of bend, T BA with K = 0.5, and every panel moves rigidly, so V = T x the flat area. An edge flange's outer virtual sharp is on the picked edge: the base is cut "
|
||||
"back s0 = (R + T) tan(theta/2), the bend starts there, and its panel is H - s0 long (H from the sharp along the outer face). ")
|
||||
case(T12, "001-base-flange", "a 100 x 60 base flange, 2 mm sheet", [RULE] + sketch("XY", C("sketch.rectangle.two_point", p0=[0, 0], p1=[WS, DS]), name="Base") +
|
||||
[C("sheet.flange", type="base", sketch="Base")],
|
||||
{"body_count": 1, "volume_mm3": WS * DS * TS, "area_mm2": 2 * (WS * DS + WS * TS + DS * TS), "faces": 6, "edges": 12, "vertices": 8,
|
||||
"bbox": {"min": [0, 0, 0], "max": [WS, DS, TS]}},
|
||||
"the sketch's rectangle extruded the rule's 2 mm up: V = 100 60 2, A = 2 (100 60 + 100 2 + 60 2); a box's 6 faces, 12 edges, 8 vertices")
|
||||
S1 = up(T12, "001-base-flange")
|
||||
ba90, s90 = sm_ba(90), sm_s0(90)
|
||||
A2 = WS * (DS - s90) + WS * ba90 + WS * (HS - s90)
|
||||
case(T12, "002-edge-flange-90", "a 20 mm 90 deg edge flange along the base's front edge",
|
||||
[C("sheet.flange", type="edge", edges=[[WS / 2, 0, TS]], height=HS, angle=90)],
|
||||
{"body_count": 1, "volume_mm3": TS * A2, "faces": 10, "bbox": {"min": [0, 0, 0], "max": [WS, DS, HS]}},
|
||||
SMETH + "At 90 deg s0 = 3 and BA = pi: the base keeps 100 x 57, the bend pi x 100, the panel 17 x 100; V = 2 (5700 + 100 pi + 1700). The flange's outer face is flush "
|
||||
"with the edge (y = 0) and reaches z = 20. Faces: base top and bottom, its three free ends, the bend's two cylinders, the flange's inner and outer faces and its top: 10, "
|
||||
"each end of the L (x = 0, x = 100) one plane", base=S1)
|
||||
S2 = up(T12, "002-edge-flange-90")
|
||||
FOUR = [[WS / 2, 0, TS], [WS, DS / 2, TS], [WS / 2, DS, TS], [0, DS / 2, TS]]
|
||||
def tray_area(deg):
|
||||
"""The flat area of 001 with flanges H high at `deg` on all four edges, closed at the corners: each
|
||||
panel end runs on (or is cut back) on the mitre plane halving the two inner faces, g/2 clear of it."""
|
||||
th = math.radians(deg)
|
||||
s0, ba, leg = sm_s0(deg), sm_ba(deg), HS - sm_s0(deg)
|
||||
ext = RS * math.sin(th) - GS / SQ2
|
||||
lens = [WS - 2 * s0, DS - 2 * s0] * 2
|
||||
base = (WS - 2 * s0) * (DS - 2 * s0)
|
||||
return base + sum(ba * L + leg * (L + 2 * ext + leg * math.cos(th)) for L in lens), ext, s0, ba, leg
|
||||
CORNER = ("Closing a corner (sheet.rs close_corner): every point of a panel's end keeps g/2 from the plane halving the two flanges' inner faces. For the flange on y = 0, "
|
||||
"its bend along x from the corner (s0, s0), a point s up its panel (rigid, turned theta about the bend axis T + R up) on the face z of the sheet keeps that distance from "
|
||||
"x = s0 - R sin(theta) - s cos(theta) + g/sqrt2 + (T - z) sin(theta) on; the inner face z = T needs least, so the end is the line x = s0 - e - s cos(theta), "
|
||||
"e = R sin(theta) - g/sqrt2: the panel runs on e past its bend's end at its foot and a further cos(theta) per mm up it (outward below 90 deg, cut back above). "
|
||||
"Each panel is the trapezoid leg x (L + 2e + leg cos(theta)), its bend BA x L, L the base's edge less 2 s0 (the bend ends square at the corner). ")
|
||||
a3, e3, *_ = tray_area(90)
|
||||
case(T12, "003-four-flanges-90-closed-corners", "20 mm 90 deg flanges on all four edges, made together: the corners close with the rule's gap, notch relief",
|
||||
[C("sheet.flange", type="edge", edges=FOUR, height=HS, angle=90, corner_relief_shape="notch")],
|
||||
{"body_count": 1, "volume_mm3": TS * a3, "bbox": {"min": [0, 0, 0], "max": [WS, DS, HS]}},
|
||||
SMETH + CORNER + "At 90 deg: s0 = 3, BA = pi, leg 17, e = 1 - g/sqrt2 = 0.646447 (the panel ends T + g/sqrt2 short of the other's outer face line, gap g between the "
|
||||
"inner edges), no slant. Base 94 x 54, bends pi (2 94 + 2 54), panels 17 (2 (94 + 2e) + 2 (54 + 2e)); V = 2 x that = %.6f. The walls' outer faces stand on the "
|
||||
"edges: bbox 100 x 60 x 20. The notch relief cuts nothing: the bends end square at the corners" % (TS * a3), base=S1)
|
||||
S3 = up(T12, "003-four-flanges-90-closed-corners")
|
||||
for name, deg, what in [("004-four-flanges-72-leaning-out", 72, "leaning out: the panel ends run on along a slant"),
|
||||
("005-four-flanges-108-leaning-in", 108, "leaning in over the base: the panel ends are cut back along a slant where they would overlap")]:
|
||||
th = math.radians(deg)
|
||||
a, e, s0, ba, leg = tray_area(deg)
|
||||
if deg < 90:
|
||||
lo, zmax = -HS * math.cos(th), HS * math.sin(th) + TS * math.cos(th)
|
||||
bb = "the walls lean out: the outer face's far edge is H cos(theta) = %.6f outside each edge, and the inner face's far edge is highest, H sin(theta) + T cos(theta)" % -lo
|
||||
else:
|
||||
lo, zmax = s0 - (RS + TS), HS * math.sin(th)
|
||||
bb = ("the walls lean in: what reaches furthest out is each bend's outer face a quarter turn in, s0 - (R + T) = %.6f inside the edge, and the outer face's far edge "
|
||||
"is highest, H sin(theta)" % lo)
|
||||
case(T12, name, "20 mm flanges at %d deg on all four edges, made together and closed at the corners, " % deg + what,
|
||||
[C("sheet.flange", type="edge", edges=FOUR, height=HS, angle=deg)],
|
||||
{"body_count": 1, "volume_mm3": TS * a, "bbox": {"min": [lo, lo, 0], "max": [WS - lo, DS - lo, zmax]}},
|
||||
SMETH + CORNER + "At %d deg: s0 = 3 tan%g = %.6f, BA = %.6f, leg %.6f, e = %.6f, the slant cos(theta) = %.6f a mm up. V = 2 x the flat area = %.6f. Bbox: %s" %
|
||||
(deg, deg / 2, s0, ba, leg, e, math.cos(th), TS * a, bb), base=S1)
|
||||
RELIEF = ("A corner relief (sheet.rs plan_relief) is cut from the base at the corner of the bends, size/2 = r along both edges: a quarter disc (round) or an r x r square "
|
||||
"(rectangular) at a square corner; both bends then start r from the corner, and the panels keep the ends the closing gave them. ")
|
||||
for name, shape, take, how in [("006-corner-relief-round", "round", PI * 4 / 4, "pi r^2/4 = pi"), ("007-corner-relief-rectangular", "rectangular", 4.0, "r^2 = 4")]:
|
||||
case(T12, name, "003's tray with a %s corner relief 4 mm across at each corner" % shape,
|
||||
[C("sheet.flange", type="edge", edges=FOUR, height=HS, angle=90, corner_relief_shape=shape, corner_relief="4 mm")],
|
||||
{"body_count": 1, "volume_mm3": TS * (a3 - 4 * take - 8 * 2 * ba90), "bbox": {"min": [0, 0, 0], "max": [WS, DS, HS]}},
|
||||
SMETH + RELIEF + "r = 2: each corner takes %s of the base and 2 mm of each of its two bends (2 BA = 2 pi); V = 2 (003's flat area - 4 x that - 8 x 2 pi)" % how, base=S1)
|
||||
case(T12, "008-corner-relief-tear", "003's tray with torn corners: the bends run to the corner and each end is cut straight, in the flat, to where its panel's end starts",
|
||||
[C("sheet.flange", type="edge", edges=FOUR, height=HS, angle=90, corner_relief_shape="tear")],
|
||||
{"body_count": 1, "volume_mm3": TS * (a3 + 4 * ba90 * e3), "bbox": {"min": [0, 0, 0], "max": [WS, DS, HS]}},
|
||||
SMETH + "A torn corner (sheet.rs tear_corner) cuts nothing from the base: each bend zone's end runs straight from the corner, on its start line, to the panel's end at its "
|
||||
"far edge, e = %.6f further along (003's closing), so each torn end adds the triangle BA e / 2 to the bend zone; folded, the end is a helix and the column of sheet under each "
|
||||
"flat point still holds T of material (K = 0.5). V = 2 (003's flat area + 8 pi e / 2)" % e3, base=S1)
|
||||
hem_len, hem_gap = 8.0, 1.0
|
||||
hem_leg = hem_len - (hem_gap + TS)
|
||||
case(T12, "009-hem-on-the-back-edge", "002's L with an 8 mm hem on the base's back edge, folded under it with a 1 mm inner radius",
|
||||
[C("sheet.hem", edges=[[WS / 2, DS, TS]], length=hem_len, gap=hem_gap)],
|
||||
{"body_count": 1, "volume_mm3": TS * (A2 + WS * (PI * (hem_gap + KS * TS) + hem_leg)), "bbox": {"min": [0, 0, -(2 * hem_gap + TS)], "max": [WS, DS + hem_gap + TS, HS]}},
|
||||
SMETH + "A hem (sheet.rs add_hem) is a 180 deg bend starting at the edge, its inner radius the gap, folded under the face it is picked on (the top here, so down), "
|
||||
"its length to the outer face: the leg is 8 - (1 + 2) = 5 and BA = pi (1 + 1) = 2 pi. V = 2 (002's flat area + 100 (2 pi + 5)). Bbox: the bend's outer face reaches "
|
||||
"R + T = 3 past the edge (y 63) and, a half turn round its axis 1 mm under the base, down to z = -(2 R + T) = -4", base=S2)
|
||||
FL = [C("sheet.fold", points=[[70, 0, TS], [70, DS, TS]], angle=90)]
|
||||
fleg = WS - 70 - ba90 / 2
|
||||
FOLDB = {"min": [0, 0, 0], "max": [70 - ba90 / 2 + RS + TS, DS, RS + TS + fleg]}
|
||||
FMETH12 = ("A fold (sheet.rs add_fold) takes its bend zone out of the sheet, so the flat stays 100 x 60 and V = 2 x 6000 = 12000. Centred on the line x = 70 the zone runs "
|
||||
"from 70 - pi/2; the larger side stays, the 30 mm side folds up 90 deg about the axis at x = 70 - pi/2, z = T + R: its outer face (the flat bottom) stands at "
|
||||
"x = 70 - pi/2 + R + T = %.6f and its panel, 30 - pi/2 long, rises from z = R + T to %.6f. " % (FOLDB["max"][0], FOLDB["max"][2]))
|
||||
case(T12, "010-fold-90", "001's base folded 90 deg up along a sketch line across it at x = 70", FL,
|
||||
{"body_count": 1, "volume_mm3": WS * DS * TS, "faces": 10, "bbox": FOLDB},
|
||||
SMETH + FMETH12 + "Faces as 002's L: 10", base=S1)
|
||||
case(T12, "011-fold-unfolded", "010's fold unfolded: the flat 100 x 60 plate again", [C("sheet.unfold")],
|
||||
{"body_count": 1, "volume_mm3": WS * DS * TS, "bbox": {"min": [0, 0, 0], "max": [WS, DS, TS]}},
|
||||
SMETH + FMETH12 + "Unfolded every panel lies in the base's plane where it was cut from: the 100 x 60 x 2 plate, the base in its place", base=up(T12, "010-fold-90"))
|
||||
case(T12, "012-fold-refolded", "011's flat refolded: 010's part again", [C("sheet.refold")],
|
||||
{"body_count": 1, "volume_mm3": WS * DS * TS, "faces": 10, "bbox": FOLDB},
|
||||
SMETH + FMETH12 + "Refolding gives the folded part back: 010's numbers", base=up(T12, "011-fold-unfolded"))
|
||||
# The flat pattern of 003's tray: its outline (the size and the area) and its four bend lines, the
|
||||
# centre lines of the bend zones, half BA out from the base's cut-back edges.
|
||||
reach = HS - s90 + ba90 - s90
|
||||
cl = s90 - ba90 / 2
|
||||
case(T12, "013-flat-pattern", "the flat pattern of 003's tray: its outline's size and area, and its four bend lines", [C("sheet.flat_pattern")],
|
||||
{"body_count": 1, "volume_mm3": TS * a3,
|
||||
"flat_pattern": {"size_mm": [WS + 2 * reach, DS + 2 * reach], "area_mm2": a3,
|
||||
"bend_lines": [[[s90, cl], [WS - s90, cl]], [[WS - cl, s90], [WS - cl, DS - s90]], [[s90, DS - cl], [WS - s90, DS - cl]], [[cl, s90], [cl, DS - s90]]]}},
|
||||
SMETH + "The flat pattern is drawn in the base's frame (the base in its place). Each flange lies flat past its edge: s0 back from it, then BA and the leg, so it reaches "
|
||||
"H - s0 + BA - s0 = 20 - BD = %.6f past the edge (BD = 2 (R + T) tan45 - BA = 6 - pi): the outline is (100 + 2 x that) x (60 + 2 x that), its area 003's flat area "
|
||||
"(%.6f, the notched corners open). The bend lines are the bend zones' centre lines, BA/2 out from the cut-back edges: y = 3 - pi/2 and 57 + pi/2 from x = 3 to 97, "
|
||||
"x = 3 - pi/2 and 97 + pi/2 from y = 3 to 57" % (reach, a3), base=S3)
|
||||
# A bracket: a flange, a lip on that flange's far edge, and a hole through the base.
|
||||
H1, H2 = 30.0, 10.0
|
||||
leg1 = H1 - s90 - s90
|
||||
leg2 = H2 - s90
|
||||
A14 = WS * (DS - s90) + WS * ba90 + WS * leg1 + WS * ba90 + WS * leg2 - PI * 25
|
||||
case(T12, "014-bracket", "a bracket: a 30 mm flange on the front edge, a 10 mm lip turned out on its far edge, a d10 hole through the base",
|
||||
[C("sheet.flange", type="edge", edges=[[WS / 2, 0, TS]], height=H1, angle=90),
|
||||
C("sheet.flange", type="edge", edges=[[WS / 2, 0, H1]], height=H2, angle=90),
|
||||
H(position=[WS / 2, 35, TS], diameter=10)],
|
||||
{"body_count": 1, "volume_mm3": TS * A14, "bbox": {"min": [0, -(H2 - TS), 0], "max": [WS, DS, H1]}},
|
||||
SMETH + "The flange (as 002, H 30) stands on y = 0 up to z = 30. The lip is picked on that flange's far edge on its outer face (y = 0), the panel's bottom face, so it "
|
||||
"bends down there, turning out over y < 0; its outer virtual sharp is on the edge (z = 30, y = 2, the flange's top-face plane), so the flange's panel is cut back s0 = 3 "
|
||||
"more (30 - 3 - 3 = 24) and the lip's outer face is the plane z = 30, its panel 10 - 3 = 7, reaching y = 2 - 10 = -8. The hole (d10 at (50, 35)) is a cut-out of the "
|
||||
"flat. V = 2 (100 57 + 100 pi + 100 24 + 100 pi + 100 7 - 25 pi). Bbox: x 0..100, y -8..60, z 0..30", base=S1)
|
||||
|
||||
# manifest: tiers in order, cases in authoring order until --record sorts them by time
|
||||
WHAT = {
|
||||
T1: "primitives with closed-form volumes", T2: "booleans in the degeneracy classes, and cuts that end in a single line",
|
||||
T3: "extrudes and revolves of line-and-arc profiles", T4: "spline profiles, sweeps and lofts", T5: "holes and tapped holes",
|
||||
T6: "modelled threads", T7: "constant, variable and corner fillets", T8: "chamfers", T9: "shells and offsets",
|
||||
T10: "patterns and mirrors", T11: "parts combining every tier"}
|
||||
T10: "patterns and mirrors", T11: "parts combining every tier", T12: "sheet metal: flanges, closed corners, reliefs, hems, folds and the flat pattern"}
|
||||
mpath = os.path.join(ROOT, "ladder.json")
|
||||
order = [T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11]
|
||||
order = [T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12]
|
||||
try:
|
||||
with open(mpath) as f:
|
||||
listed = {t["tier"]: t["cases"] for t in json.load(f)["tiers"]}
|
||||
|
||||
Reference in New Issue
Block a user