初始提交：机械臂 CadQuery 建模源码、设计文档与 3D 查看器
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# -*- coding: utf-8 -*-
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"""Structural check of the printed arm, using section properties measured from the SOLIDS.
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Nothing here is hand-waved from a sketch dimension: for each critical cut plane the part is
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boolean-cut and the freshly created planar face is taken and integrated with
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BRepGProp.SurfaceProperties_s, so area, centroid and the second moments are the real
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section of the real printed part (including whatever the lightening windows left behind).
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Why the allowables are so low: a printed part is not the material datasheet. Bending
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across layers, an un-filleted internal corner (Kt ~ 2.5 measured on square corners), and
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PLA creep under permanent static load together cut 35-50 MPa down to single digits, which
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is exactly the failure mode to design against. See docs/strength.md.
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Run: python strength.py -> docs/strength.md (+ console table)
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"""
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import io
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import json
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import math
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import os
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import sys
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sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
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try:
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sys.stdout.reconfigure(encoding="utf-8")
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except Exception:
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pass
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import cadquery as cq
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from armcore import OUT, DOCS, solids_of, bb, mesh_of
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from OCP.BRepAlgoAPI import BRepAlgoAPI_Common
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from OCP.BRepGProp import BRepGProp
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from OCP.GProp import GProp_GProps
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from OCP.BRepPrimAPI import BRepPrimAPI_MakeBox
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from OCP.gp import gp_Pnt, gp_Dir, gp_Ax2, gp_Vec
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import human_layout as HL
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RHO = {"PLA": 1.24e-3, "motor_g": 210.0} # g/mm3 for printed, g per module
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# a slicer does not print solid: 3 perimeters + 30% infill lands near this fraction of
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# the CAD envelope, and using the solid mass would blame the part for plastic that is not there
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INFILL = float(os.environ.get("ARMINFILL", "0.38"))
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# allowable bending stress across the print layers, after notch + creep derating
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ALLOW = {"PLA": 12.0, "PETG": 20.0, "PA_CF": 30.0} # MPa
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MAT = os.environ.get("ARMMAT", "PLA")
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PAYLOAD = float(os.environ.get("ARMPAY", "0.5")) # kg held at the fingertip
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DYN = float(os.environ.get("ARMDYN", "2.0")) # dynamic factor on the moving mass
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G981 = 9.81
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GRIP_T = 12.0 # N*mm per motor is far too small to matter; the grip force
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# case is carried separately below as a normal force at the pad
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_cache = {}
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def load(name):
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if name not in _cache:
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_cache[name] = cq.importers.importStep("%s/parts_step/%s.step" % (OUT, name)).val()
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return _cache[name]
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def volume(sh):
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p = GProp_GProps()
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BRepGProp.VolumeProperties_s(sh.wrapped, p)
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return p.Mass()
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def _caps_at(sh, n, o, t):
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"""The section faces of (solid ∩ thin slab), taken on the +normal side of the slab.
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Two things this replaces. (1) 'Zero extent along the normal' on a HALF-SPACE cut also
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matches the part's own horizontal faces (top chord, gusset crowns) sitting anywhere above
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the plane - that over-read the shoulder fork by 2.4x (480 mm2 true vs 1155 reported).
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(2) The half-space Common outright fails on the filleted fork at z=600 (returns an empty
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shape) while a thin slab of the same solid cuts fine.
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A slab is also self-checking: its volume / t must equal the integrated area.
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"""
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c0 = sum(n[k] * o[k] for k in range(3))
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lo, hi = [], []
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for k in range(3):
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if n[k] > 0:
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lo.append(o[k] - t / 2.0); hi.append(o[k] + t / 2.0)
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elif n[k] < 0:
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lo.append(o[k] - t / 2.0); hi.append(o[k] + t / 2.0)
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else:
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lo.append(o[k] - 400.0); hi.append(o[k] + 400.0)
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box = BRepPrimAPI_MakeBox(gp_Pnt(*lo), gp_Pnt(*hi)).Shape()
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cut = BRepAlgoAPI_Common(sh.wrapped, box)
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cut.Build()
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if not cut.IsDone():
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return []
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off = c0 + t / 2.0
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out = []
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for f in cq.Shape(cut.Shape()).Faces():
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if f.geomType() != "PLANE" or f.Area() <= 1e-6:
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continue
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cx, cy, cz = f.Center().toTuple()
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if abs(n[0] * cx + n[1] * cy + n[2] * cz - off) > 1e-4:
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continue
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out.append(f)
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return out
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def section_props(sh, normal, origin, bend=2, size=400.0):
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"""Cut the solid with a thin slab and integrate the section face.
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Returns (area mm2, Ixx mm4, Iyy mm4, cmax mm, bbox) about the face centroid, with the
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in-plane axes taken as (u, v) where u x v = normal.
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"""
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n = [float(x) for x in normal]
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o = [float(x) for x in origin]
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caps = []
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for t in (0.2, 0.05, 1.0):
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for nudge in (0.0, 0.05, -0.05, 0.25, -0.25):
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oo = [o[k] + nudge * n[k] for k in range(3)]
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caps = _caps_at(sh, n, oo, t)
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if caps:
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break
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if caps:
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break
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if not caps:
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return None
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plane_ax = [k for k in (0, 1, 2) if abs(n[k]) < 0.5]
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p_ax, q_ax = plane_ax
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bend_ax = bend if bend in plane_ax else q_ax
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far_ax = p_ax if bend_ax == q_ax else q_ax
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A = Sv = Suu = Svv = S = 0.0
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for f in caps:
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verts, tris = mesh_of(f, 0.02)
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fa = fu = fv = fuu = fvv = 0.0
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for t in tris:
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(u1, v1), (u2, v2), (u3, v3) = [(verts[k][p_ax], verts[k][q_ax]) for k in t]
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ar = ((u2 - u1) * (v3 - v1) - (u3 - u1) * (v2 - v1)) / 2.0
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fa += ar # SIGNED: inner wires (holes) cancel
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fu += ar * (u1 + u2 + u3) / 3.0
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fv += ar * (v1 + v2 + v3) / 3.0
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fvv += ar * (v1**2 + v2**2 + v3**2 + v1*v2 + v2*v3 + v3*v1) / 6.0
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fuu += ar * (u1**2 + u2**2 + u3**2 + u1*u2 + u2*u3 + u3*u1) / 6.0
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if fa < 0: # face normal opposed to the cut normal
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fa, fu, fv, fvv, fuu = -fa, -fu, -fv, -fvv, -fuu
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A += fa; S += fu; Sv += fv; Svv += fvv; Suu += fuu
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if A <= 1e-9:
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return None
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uc, vc = S / A, Sv / A
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best = max(caps, key=lambda f: f.Area()) # only for the bounding box below
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allb = [f.BoundingBox() for f in caps]
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lo = [min(getattr(b, ("xmin", "ymin", "zmin")[k]) for b in allb) for k in range(3)]
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hi = [max(getattr(b, ("xmax", "ymax", "zmax")[k]) for b in allb) for k in range(3)]
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cmax = max(hi[far_ax] - uc if far_ax == p_ax else hi[far_ax] - vc,
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uc - lo[far_ax] if far_ax == p_ax else vc - lo[far_ax]) / 1.0
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# distance from the neutral axis to the extreme fibre, measured in the bending direction
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ext = (hi[far_ax] - lo[far_ax])
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cen = uc if far_ax == p_ax else vc
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cmax = max(hi[far_ax] - cen, cen - lo[far_ax])
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I = (Svv - A * vc * vc) if far_ax == q_ax else (Suu - A * uc * uc)
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return dict(A=A, I=I, c=cmax, bend=bend_ax, centroid=(uc, vc))
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def arm_masses():
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"""Everything distal to each joint, in grams, from the model itself."""
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meta = json.load(io.open(OUT.replace("/out", "/web") + "/mesh_arm.json", encoding="utf-8"))
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TREE = ["root", "J1", "J2", "J3", "J4", "J5", "J6"]
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tot = {}
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for p in meta["parts"]:
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sh = load(p["name"])
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v = volume(sh) / 1000.0
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g = (v * RHO["PLA"] * 1000.0 * INFILL) if p["printed"] else RHO["motor_g"]
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tot[p["name"]] = (g, p["grp"])
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out = {}
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for k, jid in enumerate(TREE[1:], 1):
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down = set(TREE[k:])
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out[jid] = sum(g for g, grp in tot.values() if grp in down)
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out["all"] = sum(g for g, _ in tot.values())
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return out, tot
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# critical cuts: (label, part, plane normal, plane origin, which load case owns it)
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def cuts():
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"""(label, part, cut-plane normal, point, joint whose load it carries, bend axis)
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bend axis: 0=X (roll of the shoulder/forearm), 1=Y (every pitch joint), 2=Z."""
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Y = HL.Y_AXIS
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return [
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("吊臂根座 @z=480", "P03_肩吊臂", (0, 0, 1), (0.0, 55.0, 480.0), "J1", 1),
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("吊臂颊板 @z=560", "P03_肩吊臂", (0, 0, 1), (0.0, 100.0, 560.0), "J1", 1),
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("肩叉腹板 @z=560", "P04_肩叉", (0, 0, 1), (HL.X_ARM, Y, 560.0), "J2", 1),
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("肩叉腹板 @z=600", "P04_肩叉", (0, 0, 1), (HL.X_ARM, Y, 600.0), "J2", 1),
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("大臂旋转座横梁 @z=480", "P05_大臂旋转座", (0, 0, 1), (HL.X_ARM, Y, 480.0), "J2", 1),
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("大臂旋转座套筒 @z=440", "P05_大臂旋转座", (0, 0, 1), (HL.X_ARM, Y, 440.0), "J3", 1),
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("大臂骨架中段 @z=350", "P06_大臂骨架", (0, 0, 1), (HL.X_ARM, Y, 350.0), "J3", 1),
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("大臂骨架抱箍 @z=325", "P06_大臂骨架", (0, 0, 1), (HL.X_ARM, Y, 325.0), "J4", 1),
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("小臂骨架中段 @z=245", "P07_小臂骨架", (0, 0, 1), (HL.X_ARM, Y, 245.0), "J4", 1),
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("小臂骨架抱箍 @z=195", "P07_小臂骨架", (0, 0, 1), (HL.X_ARM, Y, 195.0), "J5", 1),
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("腕偏转座根部 @z=150", "P08_腕偏转座", (0, 0, 1), (HL.X_ARM, Y, 150.0), "J5", 1),
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("工具法兰 @z=55", "P09_工具法兰", (0, 0, 1), (HL.X_ARM, Y, 55.0), "J6", 0),
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]
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MOMENT = { # worst reachable bending moment per joint, N*mm
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# computed in main() from the reachable pose + masses
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}
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def main():
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masses, per = arm_masses()
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# Moment arms DERIVED from the swept travel (docs/travel.json), not hand-typed: they were
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# stale (J4 said 24 deg while the arm now sweeps 360, and J1 was missing entirely), which
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# silently under-loaded those sections. A continuous or >90 deg axis is capped at 90 deg
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# because that is where a gravity load sits furthest off the axis.
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TRV = json.load(io.open(DOCS + "/travel.json", encoding="utf-8"))
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dev = {t["axis"]: min(max(abs(t["hi"]), abs(t["lo"])), 90.0) for t in TRV}
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# distance from each joint axis out to the fingertip load, mm
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dist = {"J1": 564.0, "J2": 444.0, "J3": 380.0, "J4": 264.0, "J5": 129.0, "J6": 60.0}
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reach = {k: dist[k] * math.sin(math.radians(dev.get(k, 90.0))) for k in dist}
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from concurrent.futures import ThreadPoolExecutor
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def compute_cut(c_item):
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lab, part, n, o, jid, bend = c_item
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sh = load(part)
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sp = section_props(sh, n, o, bend)
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if not sp:
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return (lab, part, None, jid)
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m_g = masses[jid] * DYN + PAYLOAD * 1000.0 * DYN
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F = m_g * G981 / 1000.0 # N
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# the section carries everything distal to its own joint, at that joint's worst
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# reachable moment arm, plus the grip reaction on the finger root
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M = F * reach[jid] # N*mm
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if jid == "J6":
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M = max(M, GRIP_T * 60.0)
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I = sp["I"] # already the real bend axis, not min(Iu,Iv)
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sigma = M * sp["c"] / max(I, 1e-6)
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tau = 1.5 * F / sp["A"]
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return (lab, part, dict(sp, M=M, F=F, sigma=sigma, tau=tau,
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SF=ALLOW[MAT] / sigma if sigma > 0 else 99.0), jid)
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with ThreadPoolExecutor(max_workers=min(13, os.cpu_count() or 4)) as executor:
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rows = list(executor.map(compute_cut, cuts()))
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print("材料 %s 许用弯曲 %g MPa（跨层、含缺口与蠕变折减） 末端负载 %g kg 动载系数 %g\n"
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% (MAT, ALLOW[MAT], PAYLOAD, DYN))
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print("打印件按 %d%% 实体率计质量（壁+填充），电机按 %.0f g/台" % (INFILL * 100, RHO["motor_g"]))
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print("%-26s %-10s %7s %9s %6s %8s %7s %5s %9s" %
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("截面", "零件", "面积mm2", "Imin mm4", "c mm", "M N*mm", "sigma", "SF", "需Z mm3"))
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bad = []
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for lab, part, d, jid in rows:
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if not d:
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print("%-26s %-10s 剖切失败" % (lab, part))
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continue
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Zreq = d["M"] / ALLOW[MAT] * 1.5 # section modulus x1.5 SF
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print("%-26s %-10s %7.0f %9.0f %6.1f %8.0f %7.1f %5.2f %9.0f%s" %
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(lab, part, d["A"], d["I"], d["c"], d["M"], d["sigma"], d["SF"], Zreq,
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" <<< 不足" if d["SF"] < 1.5 else ""))
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if d["SF"] < 1.5:
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bad.append((lab, part, d))
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print("\n各关节以下质量(g, 含电机): " + " ".join("%s=%.0f" % (k, v) for k, v in masses.items() if k != "all"))
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print("整机质量(含 6 电机) %.0f g" % masses["all"])
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io.open(DOCS + "/strength.json", "w", encoding="utf-8").write(
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json.dumps([dict(截面=a, 零件=b, 关节=d, **(c or {})) for a, b, c, d in rows],
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ensure_ascii=False, indent=1, default=float))
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return bad
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if __name__ == "__main__":
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b = main()
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print("\n不合格截面 %d 处" % len(b))
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os._exit(0)
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