"""Map STEP arm stiffness to dynamic tool-tip tracking error.""" import argparse import hashlib import json import math import subprocess import sys from pathlib import Path ROOT = Path(__file__).resolve().parent def measure(step: Path, setup: dict) -> dict: import cadquery as cq import gmsh from OCP.BRepGProp import BRepGProp from OCP.GProp import GProp_GProps shape = cq.importers.importStep(str(step)).val() if shape.ShapeType() != "Solid" or not shape.isValid() or len(shape.Solids()) != 1: raise ValueError(f"Expected one valid solid: {step}") props = GProp_GProps() BRepGProp.VolumeProperties_s(shape.wrapped, props) if props.Mass() <= 0: raise ValueError("Beam volume must be positive") pad0 = cq.Solid.makeBox(10, 20, 10, cq.Vector(0, -10, -5)) pad1 = cq.Solid.makeBox(10, 20, 10, cq.Vector(110, -10, -5)) slabs = [cq.Solid.makeBox(10, 20, 14, cq.Vector(x, -10, -7)) for x in (0, 110)] envelope = cq.Solid.makeBox(120, 20, 14, cq.Vector(0, -10, -7)) pads = (pad0, pad1) pad_overlap = sum(pad.intersect(shape).Volume() for pad in pads) slab_overlap = sum(slab.intersect(shape).Volume() for slab in slabs) result = { "step_sha256": hashlib.sha256(step.read_bytes()).hexdigest(), "volume_mm3": props.Mass(), "mass_kg": props.Mass() * setup["material_density_kg_m3"] * 1e-9, "end_pad_missing_mm3": max(0.0, sum(p.Volume() for p in pads) - pad_overlap), "end_pad_excess_mm3": max(0.0, slab_overlap - pad_overlap), "envelope_excess_mm3": max(0.0, shape.Volume() - shape.intersect(envelope).Volume()), "meshes": {}, } gmsh.initialize() try: gmsh.option.setNumber("General.Terminal", 0) gmsh.model.add("robot_tool_arm") gmsh.model.occ.importShapes(str(step)) gmsh.model.occ.synchronize() if len(gmsh.model.getEntities(3)) != 1: raise ValueError("STEP import must produce one volume") for size in setup["mesh_sizes_mm"]: gmsh.model.mesh.clear() gmsh.option.setNumber("Mesh.CharacteristicLengthMin", size) gmsh.option.setNumber("Mesh.CharacteristicLengthMax", size) gmsh.option.setNumber("Mesh.Algorithm3D", 1) gmsh.model.mesh.generate(3) tags, coordinates, _ = gmsh.model.mesh.getNodes() nodes = {str(int(tag)): [coordinates[3 * i + axis] / 1000 for axis in range(3)] for i, tag in enumerate(tags)} types, _, element_nodes = gmsh.model.mesh.getElements(3) tets = [] for kind, connectivity in zip(types, element_nodes): if kind != 4: raise ValueError(f"Expected first-order tetrahedra, got {kind}") tets.extend([[int(value) for value in connectivity[i:i + 4]] for i in range(0, len(connectivity), 4)]) if not nodes or not tets: raise ValueError("Gmsh produced an empty mesh") result["meshes"][str(size)] = {"nodes": nodes, "tets": tets} finally: gmsh.finalize() return result def dynamics(meshes: dict, arm_mass_kg: float, setup: dict) -> dict: import pychrono as ch import pychrono.fea as fea results = {} for size, data in meshes.items(): system = ch.ChSystemSMC() system.SetGravitationalAcceleration(ch.ChVector3d(0, 0, 0)) system.SetSolver(ch.ChSolverSparseLU()) mesh = fea.ChMesh() material = fea.ChContinuumElastic() material.SetYoungModulus(setup["young_modulus_Pa"]) material.SetPoissonRatio(setup["poisson_ratio"]) material.SetDensity(setup["material_density_kg_m3"]) tip_ids = [key for key, point in data["nodes"].items() if abs(point[0] - 0.12) < 1e-8] fixed_ids = [key for key, point in data["nodes"].items() if abs(point[0]) < 1e-8] if len(tip_ids) < 4 or len(fixed_ids) < 4: raise ValueError("Mesh is missing a clamp or load face") nodes = {} for key, point in data["nodes"].items(): node = fea.ChNodeFEAxyz(ch.ChVector3d(*point)) if key in fixed_ids: node.SetFixed(True) if key in tip_ids: node.SetForce(ch.ChVector3d( 0, setup["lateral_test_force_N"] / len(tip_ids), 0)) mesh.AddNode(node) nodes[int(key)] = node for a, b, c, d in data["tets"]: element = fea.ChElementTetraCorot_4() element.SetNodes(nodes[a], nodes[b], nodes[c], nodes[d]) element.SetMaterial(material) mesh.AddElement(element) system.Add(mesh) system.DoStaticLinear() deflections = [nodes[int(key)].GetPos().y - data["nodes"][key][1] for key in tip_ids] mean_deflection = sum(deflections) / len(deflections) if not math.isfinite(mean_deflection) or mean_deflection <= 0: raise ValueError("Invalid lateral tool-arm deflection") stiffness = setup["lateral_test_force_N"] / mean_deflection effective_mass = (setup["tool_mass_kg"] + setup["modal_arm_mass_fraction"] * arm_mass_kg) damping = (2 * setup["damping_ratio"] * math.sqrt(stiffness * effective_mass)) tracking = {} for frequency in setup["acceleration_frequencies_Hz"]: tracking_system = ch.ChSystemSMC() tracking_system.SetGravitationalAcceleration(ch.ChVector3d(0, 0, 0)) tracking_system.SetSolver(ch.ChSolverSparseLU()) fixed = ch.ChBody() fixed.SetFixed(True) tracking_system.Add(fixed) tool = ch.ChBody() tool.SetMass(effective_mass) tool.SetInertiaXX(ch.ChVector3d(0.01, 0.01, 0.01)) tracking_system.Add(tool) guide = ch.ChLinkMateGeneric() guide.SetConstrainedCoords(True, False, True, True, True, True) guide.Initialize(tool, fixed, ch.ChFramed(ch.ChVector3d(0, 0, 0))) tracking_system.Add(guide) force = ch.ChForce() tool.AddForce(force) force.SetMode(ch.ChForce.FORCE) force.SetDir(ch.ChVector3d(0, 1, 0)) dt = setup["time_step_s"] steps = round(setup["duration_s"] / dt) if dt <= 0 or abs(steps * dt - setup["duration_s"]) > 1e-12: raise ValueError("Invalid tracking time grid") peak_error = 0.0 for index in range(steps): time = index * dt base_acceleration = (setup["base_acceleration_amplitude_m_s2"] * math.sin(2 * math.pi * frequency * time)) displacement = tool.GetPos().y velocity = tool.GetPosDt().y force.SetMforce(-effective_mass * base_acceleration - stiffness * displacement - damping * velocity) tracking_system.DoStepDynamics(dt) peak_error = max(peak_error, abs(tool.GetPos().y)) tracking[str(frequency)] = peak_error results[size] = { "mean_lateral_tip_deflection_m": mean_deflection, "lateral_stiffness_N_m": stiffness, "effective_tool_mass_kg": effective_mass, "tracking_error_m": tracking, "node_count": len(nodes), "tetrahedron_count": len(data["tets"]), "clamped_node_count": len(fixed_ids), "loaded_node_count": len(tip_ids), } return results def invoke(python: str, phase: str, payload: dict) -> dict: run = subprocess.run([python, str(Path(__file__).resolve()), "--phase", phase], input=json.dumps(payload), text=True, capture_output=True) if run.returncode: raise RuntimeError(f"{phase} failed:\n{run.stderr[-1600:]}") return json.loads(run.stdout) def main() -> None: parser = argparse.ArgumentParser() parser.add_argument("--cad-python", default=sys.executable) parser.add_argument("--physics-python", default=sys.executable) parser.add_argument("--phase", choices=("measure", "dynamics")) args = parser.parse_args() if args.phase: payload = json.load(sys.stdin) result = (measure(Path(payload["step"]), payload["setup"]) if args.phase == "measure" else dynamics(payload["meshes"], payload["arm_mass_kg"], payload["setup"])) print(json.dumps(result)) return setup = json.loads((ROOT / "setup.json").read_text()) results = {} for name in ("before", "after"): properties = invoke(args.cad_python, "measure", { "step": str(ROOT / f"{name}.step"), "setup": setup, }) meshes = properties.pop("meshes") results[name] = { "step_properties": properties, "simulation_result": invoke(args.physics_python, "dynamics", { "meshes": meshes, "arm_mass_kg": properties["mass_kg"], "setup": setup, }), } before = results["before"] after = results["after"] bp, ap = before["step_properties"], after["step_properties"] bs, gs = before["simulation_result"], after["simulation_result"] sizes = [str(size) for size in setup["mesh_sizes_mm"]] cases = [(size, str(frequency)) for size in sizes for frequency in setup["acceleration_frequencies_Hz"]] baseline = [bs[size]["tracking_error_m"][frequency] for size, frequency in cases] candidate = [gs[size]["tracking_error_m"][frequency] for size, frequency in cases] reductions = [1 - a / b for a, b in zip(candidate, baseline)] checks = { "tracking_error_reduced_all_cases": min(reductions) >= setup["required_relative_tracking_error_reduction"], "candidate_tracking_error_limit": max(candidate) <= setup["maximum_candidate_tracking_error_m"], "mesh_tracking_response_stable": all( abs(results["simulation_result"][sizes[1]]["tracking_error_m"][str(frequency)] / results["simulation_result"][sizes[0]]["tracking_error_m"][str(frequency)] - 1) <= setup["maximum_relative_mesh_tracking_error_change"] for results in (before, after) for frequency in setup["acceleration_frequencies_Hz"]), "mass_fixed": abs(ap["mass_kg"] / bp["mass_kg"] - 1) <= setup["maximum_relative_mass_change"], "end_pads_fixed": ap["end_pad_missing_mm3"] <= setup["maximum_end_pad_missing_mm3"] and ap["end_pad_excess_mm3"] <= setup["maximum_end_pad_excess_mm3"], "envelope_fixed": ap["envelope_excess_mm3"] <= setup["maximum_envelope_excess_mm3"], } after["comparison_to_before"] = { "relative_tracking_error_reductions": reductions, "checks": checks, "passed": all(checks.values()), } for name, result in results.items(): (ROOT / f"{name}.results.json").write_text(json.dumps(result, indent=2) + "\n") print(f"Tool-tip tracking error: {baseline} -> {candidate} m") print(f"Task passed: {all(checks.values())}") if not all(checks.values()): raise SystemExit(1) if __name__ == "__main__": main()