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+"""Herringbone ring, planet, carrier, and output parts for the 20:1 reducer."""
+
+from __future__ import annotations
+
+import math
+
+import simplecadapi as scad
+
+try:
+    from .common import (
+        apply_tags,
+        make_axis_part_rpart,
+        make_axial_hole_cutters_rsolids,
+        make_z_rotation_rplacement,
+    )
+    from .dimensions import (
+        ADDENDUM_FACTOR,
+        BACKLASH,
+        CLEARANCE_FACTOR,
+        GEAR_HEIGHT,
+        HELIX_ANGLE,
+        INTERSTAGE_BEARING_CENTER_Z,
+        INTERSTAGE_SHAFT_RADIUS,
+        OUTPUT_BEARING_1_CENTER_Z,
+        OUTPUT_BEARING_2_CENTER_Z,
+        OUTPUT_FLANGE_BOTTOM_Z,
+        OUTPUT_FLANGE_RADIUS,
+        OUTPUT_FLANGE_TOP_Z,
+        OUTPUT_LINK_BOLT_ANGLES_DEGREES,
+        OUTPUT_LINK_BOLT_COUNT,
+        OUTPUT_LINK_HOLE_PCD,
+        OUTPUT_LINK_TAP_RADIUS,
+        OUTPUT_LINK_THREAD_DEPTH,
+        OUTPUT_REGISTER_HEIGHT,
+        OUTPUT_SHAFT_RADIUS,
+        PLANET_BEARING,
+        PLANET_COUNT,
+        PRESSURE_ANGLE,
+        RING_INSERT_OUTER_RADIUS,
+        RING_RIM_THICKNESS,
+        RING_SUPPORT_OVERLAP,
+        STAGE1_ARM_WIDTH,
+        STAGE1_CARRIER_BOTTOM_Z,
+        STAGE1_CARRIER_THICKNESS,
+        STAGE1_HUB_RADIUS,
+        STAGE1_PAD_RADIUS,
+        STAGE1_PIN_BOTTOM_Z,
+        STAGE1_PIN_RADIUS,
+        STAGE2_ARM_WIDTH,
+        STAGE2_CARRIER_BOTTOM_Z,
+        STAGE2_CARRIER_THICKNESS,
+        STAGE2_HUB_RADIUS,
+        STAGE2_PAD_RADIUS,
+        STAGE2_PIN_BOTTOM_Z,
+        STAGE2_PIN_RADIUS,
+        STAGE_1,
+        STAGE_2,
+        StageSpec,
+    )
+except ImportError:  # Support direct execution from this example directory.
+    from common import (
+        apply_tags,
+        make_axis_part_rpart,
+        make_axial_hole_cutters_rsolids,
+        make_z_rotation_rplacement,
+    )
+    from dimensions import (
+        ADDENDUM_FACTOR,
+        BACKLASH,
+        CLEARANCE_FACTOR,
+        GEAR_HEIGHT,
+        HELIX_ANGLE,
+        INTERSTAGE_BEARING_CENTER_Z,
+        INTERSTAGE_SHAFT_RADIUS,
+        OUTPUT_BEARING_1_CENTER_Z,
+        OUTPUT_BEARING_2_CENTER_Z,
+        OUTPUT_FLANGE_BOTTOM_Z,
+        OUTPUT_FLANGE_RADIUS,
+        OUTPUT_FLANGE_TOP_Z,
+        OUTPUT_LINK_BOLT_ANGLES_DEGREES,
+        OUTPUT_LINK_BOLT_COUNT,
+        OUTPUT_LINK_HOLE_PCD,
+        OUTPUT_LINK_TAP_RADIUS,
+        OUTPUT_LINK_THREAD_DEPTH,
+        OUTPUT_REGISTER_HEIGHT,
+        OUTPUT_SHAFT_RADIUS,
+        PLANET_BEARING,
+        PLANET_COUNT,
+        PRESSURE_ANGLE,
+        RING_INSERT_OUTER_RADIUS,
+        RING_RIM_THICKNESS,
+        RING_SUPPORT_OVERLAP,
+        STAGE1_ARM_WIDTH,
+        STAGE1_CARRIER_BOTTOM_Z,
+        STAGE1_CARRIER_THICKNESS,
+        STAGE1_HUB_RADIUS,
+        STAGE1_PAD_RADIUS,
+        STAGE1_PIN_BOTTOM_Z,
+        STAGE1_PIN_RADIUS,
+        STAGE2_ARM_WIDTH,
+        STAGE2_CARRIER_BOTTOM_Z,
+        STAGE2_CARRIER_THICKNESS,
+        STAGE2_HUB_RADIUS,
+        STAGE2_PAD_RADIUS,
+        STAGE2_PIN_BOTTOM_Z,
+        STAGE2_PIN_RADIUS,
+        STAGE_1,
+        STAGE_2,
+        StageSpec,
+    )
+
+
+def make_stage_ring_gear_rpart(
+    *,
+    stage: StageSpec,
+    material: scad.Material,
+) -> scad.Part:
+    """Create one herringbone ring insert with a full housing support rim."""
+
+    ring = scad.std.gear.make_herringbone_ring_gear_rsolid(
+        n_teeth=stage.ring_teeth,
+        module=stage.module,
+        pressure_angle=PRESSURE_ANGLE,
+        helix_angle=-HELIX_ANGLE,
+        gear_height=GEAR_HEIGHT,
+        rim_thickness=RING_RIM_THICKNESS,
+        backlash=BACKLASH,
+        addendum_factor=ADDENDUM_FACTOR,
+        clearance_factor=CLEARANCE_FACTOR,
+    )
+    support = scad.make_cylinder_rsolid(
+        radius=RING_INSERT_OUTER_RADIUS,
+        height=GEAR_HEIGHT,
+        bottom_face_center=(0.0, 0.0, 0.0),
+        axis=(0.0, 0.0, 1.0),
+    )
+    support_bore = scad.make_cylinder_rsolid(
+        radius=stage.ring_outer_radius - RING_SUPPORT_OVERLAP,
+        height=GEAR_HEIGHT + 2.0,
+        bottom_face_center=(0.0, 0.0, -1.0),
+        axis=(0.0, 0.0, 1.0),
+    )
+    support = scad.cut_rsolid(support, support_bore, skip_non_intersecting=False)
+    ring = scad.union_rsolid(ring, support, glue=False)
+    ring = apply_tags(
+        shape=ring,
+        tags=(f"role.{stage.stage_id}.fixed_ring_gear", "role.ring_gear_press_fit", "group.two_stage_reducer"),
+    )
+    print(
+        f"{stage.stage_id}_ring: teeth={stage.ring_teeth} pitch_r={stage.ring_pitch_radius:.3f} "
+        f"toothed_outer_r={stage.ring_outer_radius:.3f} insert_d={RING_INSERT_OUTER_RADIUS * 2.0:.2f}"
+    )
+    return make_axis_part_rpart(
+        part_id=f"{stage.stage_id}_fixed_ring",
+        body=ring,
+        name=f"{stage.label} replaceable fixed herringbone ring insert",
+        material=material,
+        connectors=(("axis", (0.0, 0.0, GEAR_HEIGHT / 2.0), "Fixed ring axis"),),
+    )
+
+
+def make_stage_planet_gear_rpart(
+    *,
+    stage: StageSpec,
+    material: scad.Material,
+) -> scad.Part:
+    """Create one reusable herringbone planet with a standard-bearing seat."""
+
+    planet = scad.std.gear.make_herringbone_gear_rsolid(
+        n_teeth=stage.planet_teeth,
+        module=stage.module,
+        pressure_angle=PRESSURE_ANGLE,
+        helix_angle=-HELIX_ANGLE,
+        gear_height=GEAR_HEIGHT,
+        addendum_factor=ADDENDUM_FACTOR,
+        clearance_factor=CLEARANCE_FACTOR,
+        backlash=BACKLASH,
+    )
+    bearing_seat_radius = PLANET_BEARING.outer_diameter / 2.0 + 0.05
+    bearing_seat = scad.make_cylinder_rsolid(
+        radius=bearing_seat_radius,
+        height=GEAR_HEIGHT + 2.0,
+        bottom_face_center=(0.0, 0.0, -1.0),
+        axis=(0.0, 0.0, 1.0),
+    )
+    planet = scad.cut_rsolid(planet, bearing_seat, skip_non_intersecting=False)
+    planet = apply_tags(
+        shape=planet,
+        tags=(f"role.{stage.stage_id}.planet_gear", "role.planet_bearing_seat", "group.two_stage_reducer"),
+    )
+    root_radius = stage.planet_pitch_radius - stage.module * (ADDENDUM_FACTOR + CLEARANCE_FACTOR)
+    print(
+        f"{stage.stage_id}_planet: teeth={stage.planet_teeth} pitch_r={stage.planet_pitch_radius:.3f} "
+        f"bearing_seat_r={bearing_seat_radius:.3f} root_ligament={root_radius - bearing_seat_radius:.3f}"
+    )
+    return make_axis_part_rpart(
+        part_id=f"{stage.stage_id}_reusable_planet",
+        body=planet,
+        name=f"{stage.label} reusable bearing-supported planet",
+        material=material,
+        connectors=(
+            ("axis", (0.0, 0.0, GEAR_HEIGHT / 2.0), "Planet spin axis"),
+            ("bearing_axis", (0.0, 0.0, GEAR_HEIGHT / 2.0), "Planet bearing outer-ring axis"),
+        ),
+    )
+
+
+def make_stage1_carrier_sun_rpart(*, material: scad.Material) -> scad.Part:
+    """Create the first carrier and integral second-stage sun/shaft."""
+
+    carrier = _make_carrier_body_rsolid(
+        stage=STAGE_1,
+        plate_bottom_z=STAGE1_CARRIER_BOTTOM_Z,
+        plate_thickness=STAGE1_CARRIER_THICKNESS,
+        pin_bottom_z=STAGE1_PIN_BOTTOM_Z,
+        pin_radius=STAGE1_PIN_RADIUS,
+        hub_radius=STAGE1_HUB_RADIUS,
+        arm_width=STAGE1_ARM_WIDTH,
+        pad_radius=STAGE1_PAD_RADIUS,
+    )
+    shaft = scad.make_cylinder_rsolid(
+        radius=INTERSTAGE_SHAFT_RADIUS,
+        height=STAGE_2.top_z - STAGE1_CARRIER_BOTTOM_Z + 0.1,
+        bottom_face_center=(0.0, 0.0, STAGE1_CARRIER_BOTTOM_Z - 0.05),
+        axis=(0.0, 0.0, 1.0),
+    )
+    stage2_sun = scad.std.gear.make_herringbone_gear_rsolid(
+        n_teeth=STAGE_2.sun_teeth,
+        module=STAGE_2.module,
+        pressure_angle=PRESSURE_ANGLE,
+        helix_angle=HELIX_ANGLE,
+        gear_height=GEAR_HEIGHT,
+        addendum_factor=ADDENDUM_FACTOR,
+        clearance_factor=CLEARANCE_FACTOR,
+        backlash=BACKLASH,
+    )
+    stage2_sun = scad.translate_shape(shape=stage2_sun, vector=(0.0, 0.0, STAGE_2.bottom_z))
+    carrier = scad.union_rsolid(carrier, shaft, stage2_sun, glue=False)
+    carrier = apply_tags(
+        shape=carrier,
+        tags=("role.stage1.planet_carrier", "role.stage2.sun_gear", "role.integral_interstage_drive", "group.two_stage_reducer"),
+    )
+    connectors = [
+        ("carrier_axis", (0.0, 0.0, INTERSTAGE_BEARING_CENTER_Z), "Stage 1 carrier bearing axis"),
+        (
+            "interstage_bearing_axis",
+            (0.0, 0.0, INTERSTAGE_BEARING_CENTER_Z),
+            "Interstage bearing inner-ring seat",
+        ),
+        ("stage2_sun_axis", (0.0, 0.0, STAGE_2.mid_z), "Integral stage 2 sun axis"),
+    ]
+    for index in range(PLANET_COUNT):
+        center = planet_center_xy(stage=STAGE_1, index=index)
+        connectors.extend(
+            (
+                (f"planet_{index + 1}_axis", (*center, STAGE_1.mid_z), f"Stage 1 planet {index + 1} axis"),
+                (f"planet_{index + 1}_bearing_axis", (*center, STAGE_1.mid_z), f"Stage 1 planet {index + 1} bearing pin"),
+            )
+        )
+    print(
+        f"stage1_carrier_sun: pins={PLANET_COUNT} shaft_d={INTERSTAGE_SHAFT_RADIUS * 2.0:.2f} "
+        f"stage2_sun_teeth={STAGE_2.sun_teeth}"
+    )
+    return make_axis_part_rpart(
+        part_id="stage1_carrier_integral_stage2_sun",
+        body=carrier,
+        name="Stage 1 carrier with integral stage-2 sun shaft",
+        material=material,
+        connectors=connectors,
+    )
+
+
+def make_output_carrier_flange_rpart(
+    *,
+    stage: StageSpec,
+    material: scad.Material,
+) -> scad.Part:
+    """Create the second carrier, 16 mm bearing land, and output flange."""
+
+    carrier = _make_carrier_body_rsolid(
+        stage=stage,
+        plate_bottom_z=STAGE2_CARRIER_BOTTOM_Z,
+        plate_thickness=STAGE2_CARRIER_THICKNESS,
+        pin_bottom_z=STAGE2_PIN_BOTTOM_Z,
+        pin_radius=STAGE2_PIN_RADIUS,
+        hub_radius=STAGE2_HUB_RADIUS,
+        arm_width=STAGE2_ARM_WIDTH,
+        pad_radius=STAGE2_PAD_RADIUS,
+    )
+    shaft = scad.make_cylinder_rsolid(
+        radius=OUTPUT_SHAFT_RADIUS,
+        height=(
+            OUTPUT_FLANGE_TOP_Z
+            + OUTPUT_REGISTER_HEIGHT
+            - STAGE2_CARRIER_BOTTOM_Z
+            + 0.05
+        ),
+        bottom_face_center=(0.0, 0.0, STAGE2_CARRIER_BOTTOM_Z - 0.05),
+        axis=(0.0, 0.0, 1.0),
+    )
+    flange = scad.make_cylinder_rsolid(
+        radius=OUTPUT_FLANGE_RADIUS,
+        height=OUTPUT_FLANGE_TOP_Z - OUTPUT_FLANGE_BOTTOM_Z,
+        bottom_face_center=(0.0, 0.0, OUTPUT_FLANGE_BOTTOM_Z),
+        axis=(0.0, 0.0, 1.0),
+    )
+    output = scad.union_rsolid(carrier, shaft, flange, glue=False)
+    output = scad.cut_rsolid(
+        output,
+        make_axial_hole_cutters_rsolids(
+            count=OUTPUT_LINK_BOLT_COUNT,
+            pcd=OUTPUT_LINK_HOLE_PCD,
+            hole_radius=OUTPUT_LINK_TAP_RADIUS,
+            bottom_z=OUTPUT_FLANGE_TOP_Z - OUTPUT_LINK_THREAD_DEPTH,
+            height=OUTPUT_LINK_THREAD_DEPTH + 1.0,
+            angle_offset=OUTPUT_LINK_BOLT_ANGLES_DEGREES[0],
+        ),
+        skip_non_intersecting=False,
+    )
+    output = apply_tags(
+        shape=output,
+        tags=("role.stage2.output_carrier", "role.output_bearing_land", "role.output_link_flange", "group.two_stage_reducer"),
+    )
+    connectors = [
+        ("carrier_axis", (0.0, 0.0, STAGE2_CARRIER_BOTTOM_Z + STAGE2_CARRIER_THICKNESS / 2.0), "Stage 2 output carrier axis"),
+        ("bearing_1_axis", (0.0, 0.0, OUTPUT_BEARING_1_CENTER_Z), "Rear output bearing inner-ring seat"),
+        ("bearing_2_axis", (0.0, 0.0, OUTPUT_BEARING_2_CENTER_Z), "Front output bearing inner-ring seat"),
+        ("output_link_axis", (0.0, 0.0, OUTPUT_FLANGE_TOP_Z), "Six-hole driven-link flange"),
+    ]
+    for index in range(PLANET_COUNT):
+        center = planet_center_xy(stage=stage, index=index)
+        connectors.extend(
+            (
+                (f"planet_{index + 1}_axis", (*center, stage.mid_z), f"Stage 2 planet {index + 1} axis"),
+                (f"planet_{index + 1}_bearing_axis", (*center, stage.mid_z), f"Stage 2 planet {index + 1} bearing pin"),
+            )
+        )
+    radial_ligament = OUTPUT_FLANGE_RADIUS - (OUTPUT_LINK_HOLE_PCD / 2.0 + OUTPUT_LINK_TAP_RADIUS)
+    print(
+        f"output_carrier_flange: shaft_d={OUTPUT_SHAFT_RADIUS * 2.0:.2f} "
+        f"pilot_h={OUTPUT_REGISTER_HEIGHT:.1f} tapped_holes={OUTPUT_LINK_BOLT_COUNT} "
+        f"pcd={OUTPUT_LINK_HOLE_PCD:.1f} thread_depth={OUTPUT_LINK_THREAD_DEPTH:.1f} "
+        f"radial_ligament={radial_ligament:.2f}"
+    )
+    return make_axis_part_rpart(
+        part_id="stage2_output_carrier_flange",
+        body=output,
+        name="Stage 2 carrier with paired-bearing shaft and output flange",
+        material=material,
+        connectors=connectors,
+    )
+
+
+def make_planet_rplacement(*, stage: StageSpec, index: int) -> scad.Placement:
+    """Place and visually phase one planet at its pitch center."""
+
+    center = planet_center_xy(stage=stage, index=index)
+    carrier_angle = 360.0 * index / PLANET_COUNT
+    spin = carrier_angle + 180.0 - 180.0 / stage.planet_teeth
+    print(
+        f"{stage.stage_id}_planet_{index + 1}_placement: center="
+        f"({center[0]:.3f},{center[1]:.3f},{stage.bottom_z:.3f}) spin={spin:.2f}"
+    )
+    return make_z_rotation_rplacement(
+        origin=(center[0], center[1], stage.bottom_z),
+        angle_degrees=spin,
+    )
+
+
+def planet_center_xy(*, stage: StageSpec, index: int) -> tuple[float, float]:
+    """Return one equally spaced planet pitch center."""
+
+    angle = math.radians(360.0 * index / PLANET_COUNT)
+    return (
+        stage.planet_center_radius * math.cos(angle),
+        stage.planet_center_radius * math.sin(angle),
+    )
+
+
+def _make_carrier_body_rsolid(
+    *,
+    stage: StageSpec,
+    plate_bottom_z: float,
+    plate_thickness: float,
+    pin_bottom_z: float,
+    pin_radius: float,
+    hub_radius: float,
+    arm_width: float,
+    pad_radius: float,
+) -> scad.Solid:
+    hub = scad.make_cylinder_rsolid(
+        radius=hub_radius,
+        height=plate_thickness,
+        bottom_face_center=(0.0, 0.0, plate_bottom_z),
+        axis=(0.0, 0.0, 1.0),
+    )
+    solids = [hub]
+    pin_height = plate_bottom_z + plate_thickness - pin_bottom_z
+    arm_inner_radius = hub_radius - 1.25
+    arm_outer_radius = stage.planet_center_radius + pad_radius - 0.25
+    arm_length = arm_outer_radius - arm_inner_radius
+    arm_center_radius = (arm_inner_radius + arm_outer_radius) / 2.0
+    for index in range(PLANET_COUNT):
+        angle = 360.0 * index / PLANET_COUNT
+        center = planet_center_xy(stage=stage, index=index)
+        arm = scad.make_box_rsolid(
+            width=arm_length,
+            height=arm_width,
+            depth=plate_thickness,
+            bottom_face_center=(arm_center_radius, 0.0, plate_bottom_z),
+        )
+        solids.append(
+            scad.rotate_shape(
+                shape=arm,
+                angle=angle,
+                axis=(0.0, 0.0, 1.0),
+                origin=(0.0, 0.0, 0.0),
+            )
+        )
+        solids.append(
+            scad.make_cylinder_rsolid(
+                radius=pad_radius,
+                height=plate_thickness,
+                bottom_face_center=(center[0], center[1], plate_bottom_z),
+                axis=(0.0, 0.0, 1.0),
+            )
+        )
+        solids.append(
+            scad.make_cylinder_rsolid(
+                radius=pin_radius,
+                height=pin_height,
+                bottom_face_center=(center[0], center[1], pin_bottom_z),
+                axis=(0.0, 0.0, 1.0),
+            )
+        )
+    carrier = scad.union_rsolid(solids, glue=False)
+    print(
+        f"{stage.stage_id}_carrier_body: arm_length={arm_length:.3f} "
+        f"hub_embed={hub_radius - arm_inner_radius:.3f} pin_height={pin_height:.3f}"
+    )
+    return carrier