schema_version: 1 name: gear-pair intent: 'Design the spur-gear pair and carrier plate exactly as specified in the attached specification: module 2, pressure angle 20 deg, zero profile shift, 20-tooth pinion (bore Ø6) at the origin and 40-tooth wheel (bore Ø8) at (60, 0), face width 8 (z 0..8), 0.10 mm total circular backlash, pinion tooth centred on +x and the wheel phased half a pitch so the pair meshes; carrier 110 x 50 x 5 under the gears with clearance holes on the axes. Three separate solids in one KCL file; the pair must turn through a full pitch without interference. Declare the three solids by contained points, the bores as cylinders, and the gears'' tooth counts and mesh as acceptance items.' units: length: mm angle: deg material: null density_kg_m3: null process: null release_status: reconstruction frame: origin: 'Intersection of the pinion axis and the common carrier-top / gear-bottom plane: (0,0,0).' axes: x: +x follows the line of centers from the pinion axis (0,0) toward the wheel axis (60,0). y: +y is perpendicular to +x in the carrier top plane, chosen so x cross y = +z; viewed from +z with +x to the right, +y is up. z: +z is upward along both gear axes, from the carrier into the gears; carrier occupies z=-5..0 and gears z=0..8. datums: - name: A description: Carrier top at z=0, coincident with both separate gear bottom faces; establishes axial seating. - name: B description: Pinion bore and its coaxial carrier-hole axis x=y=0, directed along +z; establishes the origin on A. - name: C description: Plane y=0 through both gear axes, with +x directed from datum B to the wheel; sets clocking. Pinion tooth center is +x, wheel tooth centers begin at +4.5 deg. envelope: min: - -25 - -41.921745526 - -5 max: - 101.921745526 - 41.921745526 - 8 tolerance: 0.05 parameters: - name: gearModule value: 2 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Module: "2 mm"' description: Common transverse module of both spur gears. - name: pressureAngle value: 20 unit: deg provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Pressure angle: "20 deg"' description: Common involute pressure angle at the pitch circles. - name: profileShift value: 0 unit: '' provenance: stated tolerance: 1.0e-06 source: 'sources/gear-pair-spec.md — table Profile shift: "0 (both gears)"' description: Common dimensionless profile-shift coefficient. - name: pinionTeeth value: 20 unit: '' provenance: stated tolerance: 1.0e-06 source: 'sources/gear-pair-spec.md — table Pinion: "20 teeth, bore Ø6, axis at (0, 0) parallel to z"' description: Integer pinion tooth count. - name: wheelTeeth value: 40 unit: '' provenance: stated tolerance: 1.0e-06 source: 'sources/gear-pair-spec.md — table Wheel: "40 teeth, bore Ø8, axis at (60, 0) parallel to z"' description: Integer wheel tooth count. - name: pinionBoreDiameter value: 6 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Pinion: "bore Ø6"; Carrier plate: "with Ø6 and Ø8 clearance holes on the two gear axes"' description: Shared diameter of pinion bore and its carrier hole; no extra fit allowance. - name: wheelBoreDiameter value: 8 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Wheel: "bore Ø8"; Carrier plate: "with Ø6 and Ø8 clearance holes on the two gear axes"' description: Shared diameter of wheel bore and its carrier hole; no extra fit allowance. - name: centerDistance value: 60 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Centre distance: "60 mm (= (20 + 40) x 2 / 2)"' description: Wheel x coordinate is pinionAxisX + centerDistance; nominal pitch radii sum to 60. - name: gearFaceWidth value: 8 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Face width: "8 mm, both gears from z = 0 to z = 8"' description: Both gears extrude upward from gearBaseZ; keep lower datum and carrier fixed. edit_test: delta: 2 expect: volume_delta: 12233.933119816 direction: increase tolerance_rel: 0.02 bbox_delta: - 0 - 0 - 2 sweep: values: - 6 - 8 - 10 infeasible_deltas: - -8 - name: addendumFactor value: 1 unit: '' provenance: stated tolerance: 1.0e-06 source: 'sources/gear-pair-spec.md — table Addendum / dedendum: "1.0 m / 1.25 m"' description: Tip radius is pitch radius + gearModule*(addendumFactor + profileShift). - name: dedendumFactor value: 1.25 unit: '' provenance: stated tolerance: 1.0e-06 source: 'sources/gear-pair-spec.md — table Addendum / dedendum: "1.0 m / 1.25 m"' description: Root radius is pitch radius - gearModule*(dedendumFactor - profileShift). - name: totalBacklash value: 0.1 unit: mm provenance: stated tolerance: 0.001 source: 'sources/gear-pair-spec.md — table Circular backlash: "0.10 mm total: thin each tooth by 0.05 mm at its pitch circle"' description: 'Split equally: each gear tooth loses totalBacklash/2 of circular pitch thickness.' edit_test: delta: 0.05 expect: volume_delta: -53.55 direction: decrease tolerance_rel: 0.02 bbox_delta: - -0.00080288 - -0.00160576 - 0 sweep: values: - 0.08 - 0.1 - 0.15 infeasible_deltas: - 6.5 - name: pinionPhase value: 0 unit: deg provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Tooth phase: "pinion has a tooth centred on +x"' description: Tooth-center angle measured counterclockwise from +x, viewed from +z. - name: pinionAxisX value: 0 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Pinion: "axis at (0, 0) parallel to z"' description: Pinion shaft axis x position in the stated source frame. - name: pinionAxisY value: 0 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Pinion: "axis at (0, 0) parallel to z"' description: Pinion shaft axis y position in the stated source frame. - name: wheelAxisY value: 0 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Wheel: "axis at (60, 0) parallel to z"' description: Wheel shaft axis y position in the stated source frame. - name: gearBaseZ value: 0 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Face width: "from z = 0 to z = 8"; Frame: "gear bottoms at z = 0, carrier top at z = 0"' description: Shared carrier-top / gear-bottom datum; carrier extends downward. - name: carrierLength value: 110 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Carrier plate: "110 x 50 x 5 mm"' description: Plate extent along +x from carrierMinX. - name: carrierWidth value: 50 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Carrier plate: "110 x 50 x 5 mm"' description: Plate extent along +y from carrierMinY. - name: carrierThickness value: 5 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Carrier plate: "110 x 50 x 5 mm"' description: Plate thickness below gearBaseZ. - name: carrierMinX value: -25 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Carrier plate: "corner at (-25, -25, -5) to (85, 25, 0)"' description: Plate minimum x; wheel intentionally overhangs the plate. - name: carrierMinY value: -25 unit: mm provenance: stated tolerance: 0.01 source: 'sources/gear-pair-spec.md — table Carrier plate: "corner at (-25, -25, -5) to (85, 25, 0)"' description: Plate minimum y. - name: wheelPhase value: 4.5 unit: deg provenance: derived tolerance: 0.01 formula: 180 / wheelTeeth description: Half a wheel pitch from a tooth center on +x; 180/wheelTeeth deg equals pi/wheelTeeth rad. With 40 teeth, a tooth space is centered on -x toward the pinion. features: - id: carrierPlate kind: extrude description: Rectangular carrier from (-25,-25,-5) to (85,25,0), with axis holes handled as separate features. parameters: - carrierLength - carrierWidth - carrierThickness - carrierMinX - carrierMinY - gearBaseZ - pinionBoreDiameter - wheelBoreDiameter verify: - method: solid points: - - 30 - 0 - -2.5 - method: section section: carrierMidsection - method: count section: carrierMidsection count: 1 - method: face face: carrierTop - method: face face: carrierBottom - method: face face: carrierLeft - method: face face: carrierRight - method: face face: carrierFront - method: face face: carrierBack - method: dimension dimension: carrierLength - method: dimension dimension: carrierWidth - method: dimension dimension: carrierThickness - id: pinionGear kind: pattern count: 20 description: 20-tooth involute spur pinion; exact source phase, pressure angle, profile shift, root/tip radii, and equally split circular backlash. Tooth count and motion use acceptance.gears/meshes; feature count probes only count section regions. parameters: - gearModule - pressureAngle - profileShift - gearFaceWidth - gearBaseZ - addendumFactor - dedendumFactor - totalBacklash - pinionAxisX - pinionAxisY - pinionPhase - pinionTeeth - pinionBoreDiameter verify: - method: section section: gearMidsection - method: face face: pinionBottom - method: face face: pinionTop - method: dimension dimension: pinionFaceWidth - method: solid points: - - 21.5 - 0 - 4 - method: void points: - - -21.235299323 - -3.363340998 - 4 - id: wheelGear kind: pattern count: 40 description: 40-tooth involute spur wheel; exact source phase, pressure angle, profile shift, root/tip radii, and equally split circular backlash. Tooth count and motion use acceptance.gears/meshes; feature count probes only count section regions. parameters: - gearModule - pressureAngle - profileShift - gearFaceWidth - gearBaseZ - addendumFactor - dedendumFactor - totalBacklash - pinionAxisX - centerDistance - wheelAxisY - wheelPhase - wheelTeeth - wheelBoreDiameter verify: - method: section section: gearMidsection - method: face face: wheelBottom - method: face face: wheelTop - method: dimension dimension: wheelFaceWidth - method: solid points: - - 101.37206935 - 3.256052473 - 4 - method: void points: - - 101.5 - 0 - 4 - id: pinionBore kind: hole description: Through hole in pinion; the axis point is strictly within this body's axial extent, distinguishing touching coaxial holes. parameters: - pinionBoreDiameter - pinionAxisX - pinionAxisY - gearBaseZ - gearFaceWidth verify: - method: cylinder cylinder: pinionBore - method: void points: - - 0 - 0 - 4 - method: section section: gearMidsection - id: wheelBore kind: hole description: Through hole in wheel; the axis point is strictly within this body's axial extent, distinguishing touching coaxial holes. parameters: - wheelBoreDiameter - pinionAxisX - wheelAxisY - gearBaseZ - gearFaceWidth - centerDistance verify: - method: cylinder cylinder: wheelBore - method: void points: - - 60 - 0 - 4 - method: section section: gearMidsection - id: carrierPinionHole kind: hole description: Through hole in carrier; the axis point is strictly within this body's axial extent, distinguishing touching coaxial holes. parameters: - pinionBoreDiameter - pinionAxisX - pinionAxisY - gearBaseZ - carrierThickness verify: - method: cylinder cylinder: carrierPinionHole - method: void points: - - 0 - 0 - -2.5 - method: section section: carrierMidsection - id: carrierWheelHole kind: hole description: Through hole in carrier; the axis point is strictly within this body's axial extent, distinguishing touching coaxial holes. parameters: - wheelBoreDiameter - pinionAxisX - wheelAxisY - gearBaseZ - carrierThickness - centerDistance verify: - method: cylinder cylinder: carrierWheelHole - method: void points: - - 60 - 0 - -2.5 - method: section section: carrierMidsection - id: assemblyAndMesh kind: other description: Exactly three separate solids in one KCL file; gear bottoms contact carrier top at z=0, 60 mm shaft spacing, no fusion. Tooth counts, ratio, full-pitch motion, and flank-gap band are acceptance.gears, acceptance.meshes, acceptance.solids, and acceptance.clearances. parameters: - centerDistance - gearFaceWidth - gearBaseZ - carrierThickness - pinionPhase - wheelPhase - totalBacklash verify: - method: bbox - method: solid points: - - 0 - 10 - 4 - - 60 - 10 - 4 - - 30 - 0 - -2.5 - method: dimension dimension: pinionSeat - method: dimension dimension: wheelSeat - method: dimension dimension: assemblySpanX - method: dimension dimension: assemblySpanY - method: dimension dimension: assemblySpanZ - id: analyticToothWitnesses kind: profile description: Analytically derived witnesses for addendum, dedendum, tooth phase, pressure-angle flanks, zero shift and circular-backlash thinning. Sparse point checks do not replace the source whole-profile deviation requirement. parameters: - gearModule - pressureAngle - profileShift - addendumFactor - dedendumFactor - pinionTeeth - wheelTeeth - totalBacklash - pinionPhase - wheelPhase verify: - method: solid points: - - -17.037623875 - -2.698494522 - 4 - - 97.25 - 0 - 4 note: Material 0.25 mm inside the stated root circles, along tooth-space centerlines. - method: void points: - - -17.531468046 - -2.776711754 - 4 - - 97.75 - 0 - 4 note: Void 0.25 mm outside the stated root circles, along tooth-space centerlines; probes avoid the unspecified root-transition corners. - method: solid points: - - 21.75 - 0 - 4 - - 101.621298683 - 3.275667247 - 4 note: Material 0.25 mm inside each stated tip radius on a tooth centerline. - method: void points: - - -22.25 - 0 - 4 - - 102.11975735 - 3.314896795 - 4 note: Void 0.25 mm beyond each stated tip circle, away from the other body. - method: solid points: - - -19.94144516 - 1.529302109 - 4 - - -19.94144516 - -1.529302109 - 4 - - 58.389639 - 39.967571073 - 4 - - 55.338229184 - 39.727419912 - 4 note: Both flanks of a remote tooth on each gear, at the pitch radius, bracketed by +/-0.015 mm tangential offsets from the analytic flank. Tooth thickness is pi*gearModule/2 - totalBacklash/2 = 3.091592654 mm. Pinion tooth center 180 deg; wheel tooth center 94.5 deg. These reject an unthinned standard tooth; they do not directly measure circular backlash to 0.001 mm. - method: solid points: - - -19.22913108 - 1.579005686 - 4 - - -19.22913108 - -1.579005686 - 4 - - -21.68822364 - 0.714811393 - 4 - - -21.68822364 - -0.714811393 - 4 - - 58.873566574 - 38.071044208 - 4 - - 55.156941727 - 37.778539489 - 4 - - 57.481917782 - 41.623902531 - 4 - - 55.975667522 - 41.505358065 - 4 note: Both flanks at r=baseRadius+0.5 and r=tipRadius-0.3, bracketed by +/-0.12 mm tangential offsets. Derived from the 20 deg involute with zero profile shift. These sparse witnesses supplement, but cannot replace, the evaluator-only whole-profile p95 <= 0.10 mm comparison. - method: void points: - - -19.939128773 - 1.559212545 - 4 - - -19.939128773 - -1.559212545 - 4 - - 58.419615128 - 39.968767602 - 4 - - 55.308434933 - 39.723912411 - 4 note: Both flanks of a remote tooth on each gear, at the pitch radius, bracketed by +/-0.015 mm tangential offsets from the analytic flank. Tooth thickness is pi*gearModule/2 - totalBacklash/2 = 3.091592654 mm. Pinion tooth center 180 deg; wheel tooth center 94.5 deg. These reject an unthinned standard tooth; they do not directly measure circular backlash to 0.001 mm. - method: void points: - - -19.208002349 - 1.818072275 - 4 - - -19.208002349 - -1.818072275 - 4 - - -21.678991598 - 0.95463254 - 4 - - -21.678991598 - -0.95463254 - 4 - - 59.113482367 - 38.077386279 - 4 - - 54.918987578 - 37.747272379 - 4 - - 57.721520193 - 41.637705626 - 4 - - 55.736855734 - 41.481509145 - 4 note: Both flanks at r=baseRadius+0.5 and r=tipRadius-0.3, bracketed by +/-0.12 mm tangential offsets. Derived from the 20 deg involute with zero profile shift. These sparse witnesses supplement, but cannot replace, the evaluator-only whole-profile p95 <= 0.10 mm comparison. interfaces: - name: carrierSeatingDatum description: Carrier seating plane and plan dimensions remain fixed when gear face width or backlash changes. must_not_change: true checks: - carrierTop - carrierLength - carrierWidth - name: pinionAxisAndSeat description: Pinion alignment is pinned by the Ø6 carrier cylinder axis and pinion bottom-face centroid at (0,0); axial gear length may follow gearFaceWidth. must_not_change: true checks: - carrierPinionHole - pinionBottom - name: wheelAxisAndSeat description: Wheel alignment is pinned by the Ø8 carrier cylinder axis and wheel bottom-face centroid at (60,0); axial gear length may follow gearFaceWidth. must_not_change: true checks: - carrierWheelHole - wheelBottom - name: gearSectionTopology description: At z=4 the assembly retains two gear regions and two bores through the declared face-width and backlash sweeps; small analytic area changes remain inside the section band. must_not_change: true checks: - gearMidsection acceptance: bbox_tolerance: 0.05 volume: expected: 76043.033397564 tolerance_rel: 0.01 provenance: derived note: Analytic radial-root construction estimate, not a reference-model measurement. For each gear, Rp=m*N/2, Rb=Rp*cos(alpha), Ra=Rp+m, Rf=Rp-1.25*m, h0=(pi*m/2-totalBacklash/2)/(2*Rp)+tan(alpha)-alpha, T=sqrt((Ra/Rb)^2-1), F(T)=T^3/3-((1+T^2)*atan(T)-T)/2, A=pi*Rf^2+N*(h0*(Ra^2-Rf^2)-2*Rb^2*F(T))-pi*D^2/4. Angles in these formulas are radians. Sharp radial root-to-base extensions and circular tip/root arcs provide the provisional estimate; the unspecified root transition is recorded in open_questions. Total V=gearFaceWidth*(A_pinion+A_wheel)+carrierThickness*(carrierLength*carrierWidth-pi*(pinionBoreDiameter^2+wheelBoreDiameter^2)/4). surface_area: expected: 31468.596211209 tolerance_rel: 0.03 provenance: derived note: Analytic radial-root construction estimate, not a reference-model measurement. For each gear, Rp=m*N/2, Rb=Rp*cos(alpha), Ra=Rp+m, Rf=Rp-1.25*m, h0=(pi*m/2-totalBacklash/2)/(2*Rp)+tan(alpha)-alpha, T=sqrt((Ra/Rb)^2-1), F(T)=T^3/3-((1+T^2)*atan(T)-T)/2, A=pi*Rf^2+N*(h0*(Ra^2-Rf^2)-2*Rb^2*F(T))-pi*D^2/4. Angles in these formulas are radians. Sharp radial root-to-base extensions and circular tip/root arcs provide the provisional estimate; the unspecified root transition is recorded in open_questions. Gear outer perimeter P=N*(2*(Rb-Rf)+Rb*T^2+2*Ra*(h0-T+atan(T))+Rf*(2*pi/N-2*h0)). Gear surface=2*A+gearFaceWidth*(P+pi*D). Carrier surface=2*A_carrier+carrierThickness*(2*(carrierLength+carrierWidth)+pi*(pinionBoreDiameter+wheelBoreDiameter)). Sum all three bodies; touching faces are counted once per body, not removed as if fused. center_of_mass: expected: - 41.729506395 - 0 - 1.682924417 tolerance: 0.15 provenance: derived note: Geometric centroid with uniform unit density, not a material/mass claim. Vp=9547.100925818, Vw=39388.631553445, Vc=27107.300918301 mm3 using the radial-root estimate above. Carrier xc=(110*50*30-pi*3^2*0-pi*4^2*60)/(110*50-pi*(3^2+4^2))=29.878310559 mm. COM=((Vp*0+Vw*60+Vc*xc)/(Vp+Vw+Vc),0,((Vp+Vw)*4+Vc*(-2.5))/(Vp+Vw+Vc)). solid_count: 3 sections: - id: gearMidsection plane: z at: 4 expect: area: 6116.966559908 area_tolerance_rel: 0.02 loops: 2 holes: 2 description: Two disjoint annular toothed regions; each has one central bore. Area uses the analytic radial-root estimate. Tooth counts are checked separately in acceptance.gears; loops do not count teeth. - id: carrierMidsection plane: z at: -2.5 expect: area: 5421.46018366 area_tolerance_rel: 0.002 loops: 1 holes: 2 description: One rectangular plate region with two through-hole loops; area=110*50-pi*(3^2+4^2). faces: - name: carrierTop plane: z at: 0 normal: + area: 5421.46018366 area_tolerance_rel: 0.002 tolerance: 0.02 center: - 29.878310559 - 0 mode: one - name: carrierBottom plane: z at: -5 normal: '-' area: 5421.46018366 area_tolerance_rel: 0.002 tolerance: 0.02 center: - 29.878310559 - 0 mode: one - name: carrierLeft plane: x at: -25 normal: '-' area: 250 area_tolerance_rel: 0.002 tolerance: 0.02 center: - 0 - -2.5 mode: one - name: carrierRight plane: x at: 85 normal: + area: 250 area_tolerance_rel: 0.002 tolerance: 0.02 center: - 0 - -2.5 mode: one - name: carrierFront plane: y at: -25 normal: '-' area: 550 area_tolerance_rel: 0.002 tolerance: 0.02 center: - 30 - -2.5 mode: one - name: carrierBack plane: y at: 25 normal: + area: 550 area_tolerance_rel: 0.002 tolerance: 0.02 center: - 30 - -2.5 mode: one - name: pinionBottom plane: z at: 0 normal: '-' area: 1193.387615727 area_tolerance_rel: 0.02 tolerance: 0.02 center: - 0 - 0 mode: one - name: pinionTop plane: z at: 8 normal: + area: 1193.387615727 area_tolerance_rel: 0.02 tolerance: 0.02 center: - 0 - 0 mode: one - name: wheelBottom plane: z at: 0 normal: '-' area: 4923.578944181 area_tolerance_rel: 0.02 tolerance: 0.02 center: - 60 - 0 mode: one - name: wheelTop plane: z at: 8 normal: + area: 4923.578944181 area_tolerance_rel: 0.02 tolerance: 0.02 center: - 60 - 0 mode: one cylinders: - name: pinionBore point: - 0 - 0 - 4 direction: - 0 - 0 - 1 kind: hole diameter: 6 radius_tolerance: 0.005 axis_tolerance: 0.01 length: 8 length_tolerance: 0.02 t_range: - -4.0 - 4.0 description: Through hole in pinion; the axis point is strictly within this body's axial extent, distinguishing touching coaxial holes. - name: wheelBore point: - 60 - 0 - 4 direction: - 0 - 0 - 1 kind: hole diameter: 8 radius_tolerance: 0.005 axis_tolerance: 0.01 length: 8 length_tolerance: 0.02 t_range: - -4.0 - 4.0 description: Through hole in wheel; the axis point is strictly within this body's axial extent, distinguishing touching coaxial holes. - name: carrierPinionHole point: - 0 - 0 - -2.5 direction: - 0 - 0 - 1 kind: hole diameter: 6 radius_tolerance: 0.005 axis_tolerance: 0.01 length: 5 length_tolerance: 0.02 t_range: - -2.5 - 2.5 description: Through hole in carrier; the axis point is strictly within this body's axial extent, distinguishing touching coaxial holes. - name: carrierWheelHole point: - 60 - 0 - -2.5 direction: - 0 - 0 - 1 kind: hole diameter: 8 radius_tolerance: 0.005 axis_tolerance: 0.01 length: 5 length_tolerance: 0.02 t_range: - -2.5 - 2.5 description: Through hole in carrier; the axis point is strictly within this body's axial extent, distinguishing touching coaxial holes. planes: [] dimensions: - name: carrierLength axis: x expected: 110 tolerance: 0.02 description: '' between: - carrierLeft - carrierRight - name: carrierWidth axis: y expected: 50 tolerance: 0.02 description: '' between: - carrierFront - carrierBack - name: carrierThickness axis: z expected: 5 tolerance: 0.02 description: '' between: - carrierBottom - carrierTop - name: pinionFaceWidth axis: z expected: 8 tolerance: 0.02 description: '' between: - pinionBottom - pinionTop - name: wheelFaceWidth axis: z expected: 8 tolerance: 0.02 description: '' between: - wheelBottom - wheelTop - name: pinionSeat axis: z expected: 0 tolerance: 0.01 description: Coincident seating planes; carrier and gear remain separate solids. between: - carrierTop - pinionBottom - name: wheelSeat axis: z expected: 0 tolerance: 0.01 description: Coincident seating planes; carrier and gear remain separate solids. between: - carrierTop - wheelBottom - name: assemblySpanX axis: x expected: 126.921745526 tolerance: 0.05 description: Full assembly envelope at the specified initial tooth phase; includes wheel overhang. - name: assemblySpanY axis: y expected: 83.843491052 tolerance: 0.05 description: Full assembly envelope at the specified initial tooth phase; includes wheel overhang. - name: assemblySpanZ axis: z expected: 13 tolerance: 0.05 description: Full assembly envelope at the specified initial tooth phase; includes wheel overhang. solids: - name: pinion contains_point: - 0 - 10 - 4 volume: expected: 9547.100925818 tolerance_rel: 0.02 provenance: derived note: gearFaceWidth*A_pinion; analytic radial-root estimate defined in acceptance.volume.note. description: 20-tooth gear only, z=0..8, with its own Ø6 through bore. - name: wheel contains_point: - 60 - 10 - 4 volume: expected: 39388.631553445 tolerance_rel: 0.02 provenance: derived note: gearFaceWidth*A_wheel; analytic radial-root estimate defined in acceptance.volume.note. description: 40-tooth gear only, z=0..8, with its own Ø8 through bore. - name: carrier contains_point: - 30 - 0 - -2.5 volume: expected: 27107.300918301 tolerance_rel: 0.002 provenance: derived note: carrierThickness*(carrierLength*carrierWidth-pi*(pinionBoreDiameter^2+wheelBoreDiameter^2)/4). description: 110 x 50 x 5 plate with two axis holes; z=-5..0, touching both gears without fusion. hardware: [] clearances: - name: pinionCarrierContact a: pinion b: carrier min_gap: 0 max_gap: 0 interference_tolerance: 0.001 description: Touching at z=0, separate material bodies; zero nominal overlap volume. The 0.001 mm3 threshold is only numerical Boolean tolerance. - name: wheelCarrierContact a: wheel b: carrier min_gap: 0 max_gap: 0 interference_tolerance: 0.001 description: Touching at z=0, separate material bodies; zero nominal overlap volume. The wheel overhang is intentional. - name: initialGearClearance a: pinion b: wheel min_gap: 0 max_gap: 0.15 interference_tolerance: 0.001 description: Initial-pose no-interference and maximum flank-gap check; full-pitch motion is separately required below. passages: [] thickness: [] probes: - name: bodyMaterial state: solid points: - - 0 - 10 - 4 - - 60 - 10 - 4 - - 30 - 0 - -2.5 description: Interior witnesses for the three material bodies, away from holes, teeth, and contact faces. - name: boresThroughGears state: void points: - - 0 - 0 - 0.5 - - 0 - 0 - 4 - - 0 - 0 - 7.5 - - 60 - 0 - 0.5 - - 60 - 0 - 4 - - 60 - 0 - 7.5 description: The two axes must remain void through the gear thickness. - name: boresThroughCarrier state: void points: - - 0 - 0 - -4.5 - - 0 - 0 - -2.5 - - 0 - 0 - -0.5 - - 60 - 0 - -4.5 - - 60 - 0 - -2.5 - - 60 - 0 - -0.5 description: The two coaxial carrier holes must remain void through the plate. - name: pinionToothPhase state: solid points: - - 21.5 - 0 - 4 description: A pinion tooth is centered on +x; radius 21.5 is inside its addendum. - name: pinionSpacePhase state: void points: - - -21.235299323 - -3.363340998 - 4 description: A pinion tooth space is centered at 189 deg, safely away from the other gear. - name: wheelToothPhase state: solid points: - - 101.37206935 - 3.256052473 - 4 description: A wheel tooth is centered at +4.5 deg. - name: wheelSpacePhase state: void points: - - 101.5 - 0 - 4 description: A wheel tooth space is centered on +x; the even 40-tooth pattern also places a space on -x toward the pinion. A void probe on -x would be occupied by the pinion and is intentionally avoided. - name: rootMaterial state: solid points: - - -17.037623875 - -2.698494522 - 4 - - 97.25 - 0 - 4 description: Material 0.25 mm inside the stated root circles, along tooth-space centerlines. - name: rootSpaces state: void points: - - -17.531468046 - -2.776711754 - 4 - - 97.75 - 0 - 4 description: Void 0.25 mm outside the stated root circles, along tooth-space centerlines; probes avoid the unspecified root-transition corners. - name: tipMaterial state: solid points: - - 21.75 - 0 - 4 - - 101.621298683 - 3.275667247 - 4 description: Material 0.25 mm inside each stated tip radius on a tooth centerline. - name: beyondTips state: void points: - - -22.25 - 0 - 4 - - 102.11975735 - 3.314896795 - 4 description: Void 0.25 mm beyond each stated tip circle, away from the other body. - name: pitchThicknessSolid state: solid points: - - -19.94144516 - 1.529302109 - 4 - - -19.94144516 - -1.529302109 - 4 - - 58.389639 - 39.967571073 - 4 - - 55.338229184 - 39.727419912 - 4 description: Both flanks of a remote tooth on each gear, at the pitch radius, bracketed by +/-0.015 mm tangential offsets from the analytic flank. Tooth thickness is pi*gearModule/2 - totalBacklash/2 = 3.091592654 mm. Pinion tooth center 180 deg; wheel tooth center 94.5 deg. These reject an unthinned standard tooth; they do not directly measure circular backlash to 0.001 mm. - name: involuteFlankSolid state: solid points: - - -19.22913108 - 1.579005686 - 4 - - -19.22913108 - -1.579005686 - 4 - - -21.68822364 - 0.714811393 - 4 - - -21.68822364 - -0.714811393 - 4 - - 58.873566574 - 38.071044208 - 4 - - 55.156941727 - 37.778539489 - 4 - - 57.481917782 - 41.623902531 - 4 - - 55.975667522 - 41.505358065 - 4 description: Both flanks at r=baseRadius+0.5 and r=tipRadius-0.3, bracketed by +/-0.12 mm tangential offsets. Derived from the 20 deg involute with zero profile shift. These sparse witnesses supplement, but cannot replace, the evaluator-only whole-profile p95 <= 0.10 mm comparison. - name: pitchThicknessVoid state: void points: - - -19.939128773 - 1.559212545 - 4 - - -19.939128773 - -1.559212545 - 4 - - 58.419615128 - 39.968767602 - 4 - - 55.308434933 - 39.723912411 - 4 description: Both flanks of a remote tooth on each gear, at the pitch radius, bracketed by +/-0.015 mm tangential offsets from the analytic flank. Tooth thickness is pi*gearModule/2 - totalBacklash/2 = 3.091592654 mm. Pinion tooth center 180 deg; wheel tooth center 94.5 deg. These reject an unthinned standard tooth; they do not directly measure circular backlash to 0.001 mm. - name: involuteFlankVoid state: void points: - - -19.208002349 - 1.818072275 - 4 - - -19.208002349 - -1.818072275 - 4 - - -21.678991598 - 0.95463254 - 4 - - -21.678991598 - -0.95463254 - 4 - - 59.113482367 - 38.077386279 - 4 - - 54.918987578 - 37.747272379 - 4 - - 57.721520193 - 41.637705626 - 4 - - 55.736855734 - 41.481509145 - 4 description: Both flanks at r=baseRadius+0.5 and r=tipRadius-0.3, bracketed by +/-0.12 mm tangential offsets. Derived from the 20 deg involute with zero profile shift. These sparse witnesses supplement, but cannot replace, the evaluator-only whole-profile p95 <= 0.10 mm comparison. cylinder_counts: - name: sixMillimeterHoles diameter: 6 radius_tolerance: 0.005 kind: hole direction: - 0 - 0 - 1 expected: 2 description: Pinion bore plus the separate carrier hole on the same axis. - name: eightMillimeterHoles diameter: 8 radius_tolerance: 0.005 kind: hole direction: - 0 - 0 - 1 expected: 2 description: Wheel bore plus the separate carrier hole on the same axis. gears: - name: pinionTeeth solid: pinion point: - 0 - 0 - 0 direction: - 0 - 0 - 1 at: 4 module: 2 teeth: 20 description: 'Mid-thickness tooth count. Source profile: pressure angle 20 deg, zero shift, pitch/base/tip/root radii 20/18.793852416/22/17.5 mm; tooth center at 0 deg. Analytic probes check the profile and 0.05 mm tooth thinning. Whole-profile p95 <= 0.10 mm remains an evaluator-only check.' - name: wheelTeeth solid: wheel point: - 60 - 0 - 0 direction: - 0 - 0 - 1 at: 4 module: 2 teeth: 40 description: 'Mid-thickness tooth count. Source profile: pressure angle 20 deg, zero shift, pitch/base/tip/root radii 40/37.587704831/42/37.5 mm; tooth pattern rotated +4.5 deg. Analytic probes check the profile and 0.05 mm tooth thinning. Whole-profile p95 <= 0.10 mm remains an evaluator-only check.' meshes: - name: fullPitchMesh a: pinion b: wheel axis_a: - - 0 - 0 - 0 - - 0 - 0 - 1 axis_b: - - 60 - 0 - 0 - - 0 - 0 - 1 ratio: 0.5 pitch_deg: 18 steps: 72 backlash_max: 0.15 description: Turn pinion theta=0..18 deg and wheel -theta/2=0..-9 deg from the specified initial phase. Axes 60 mm apart. Zero interference throughout and flank gap <=0.15 mm. Initial circular backlash is 0.10 mm total, achieved by thinning each tooth 0.05 mm at its own pitch circle; this is distinct from the maximum closest-flank gap. The inspector samples 73 poses at 0.25 deg plus local refinement and uses its fixed 0.001 mm3 Boolean interference tolerance. Sampling is evidence, not a proof of the continuous sweep. deviation: null blockout: volume_min: 79362.75412533 volume_max: 87716.728243786 export_volume_tolerance_rel: 0.002 references: - path: sources/gear-pair-spec.md kind: text role: authoritative sha256: 0acea6d35513df93499f95e7242721b64488c45819f6e58ebd09ed627fb09d87 units: mm and deg revision: Unversioned supplied specification; revision identified by SHA-256. note: Only supplied source. No images, coordinate tables, reference mesh, or ingested reference model; evaluator-only involutes are not part of this bundle. open_questions: - 'Which below-base-circle root transition is intended: radial extension, generated trochoid, or a specified fillet? The root radii are stated, but the transition is not; gear volume, area, and surface estimates provisionally use sharp radial extensions, with no invented fillet radius.' - What material, density, manufacturing process, and production fit tolerances are intended? These are unspecified; material, density_kg_m3, and process remain null, and the stated Ø6/Ø8 carrier holes receive no added clearance allowance. - How will the evaluator-only involute p95 <= 0.10 mm requirement be reported? No reference geometry is supplied and PartContract has no reference-free per-gear profile-deviation field; analytic probes cannot establish that percentile, so acceptance.deviation remains null. - What evidence will certify zero interference between the sampled sweep poses? The required continuous full-pitch motion is retained, but the available inspector uses discrete poses with local refinement and a fixed 0.001 mm3 Boolean tolerance.