{"uid":"cap_gbQFIR4xF6mpDMNI2lOVb","slug":"external-involute-spur-gear-working-mesh-tooth-profile-geometry-8bef263e","name":"External Involute Spur Gear Working Mesh Tooth Profile Geometry","description":"Compute exact declared involute profiles and the geometric working mesh relationship.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B008/external-involute-spur-gear-working-mesh-tooth-profile-geometry?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["involuteGear"],"properties":{"involuteGear":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["module_mm","teeth","profile_shifts","reference_pressure_angle_degrees","center_distance_mm","radius_samples"],"properties":{"teeth":{"type":"array","items":{"type":"integer","maximum":1000,"minimum":6},"maxItems":2,"minItems":2},"module_mm":{"type":"number","maximum":100,"minimum":0.01},"profile_shifts":{"type":"array","items":{"type":"number","maximum":1,"minimum":-0.5},"maxItems":2,"minItems":2},"radius_samples":{"type":"array","items":{"type":"array","items":{"type":"number","maximum":1000000,"minimum":0},"maxItems":16,"minItems":1},"maxItems":2,"minItems":2},"center_distance_mm":{"type":"number","maximum":1000000,"minimum":0.01},"reference_pressure_angle_degrees":{"type":"number","maximum":40,"minimum":5}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_qmh2nSHT2U3L_yoswnqPF","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes exact declared involute tooth profiles and the geometric working mesh relationship for a pair of external spur gears given module, tooth counts, profile shifts, pressure angle, center distance, and radius sample arrays.","exampleAgentPrompt":"Can you compute the exact involute tooth profiles and working mesh geometry for a pair of external spur gears — module 2 mm, 20 and 40 teeth, profile shifts of 0.2 and -0.1, reference pressure angle 20 degrees, center distance 62 mm, and sample radii from 10 to 20 mm on each gear across 8 points?","exampleUseCases":[{"title":"CAD validation of custom gear pair","prompt":"I'm designing a profile-shifted spur gear pair for a gearbox — module 1.5 mm, 18 and 36 teeth, profile shifts of 0.3 and 0.0, 20-degree reference pressure angle, center distance 41.5 mm. Can you compute the exact involute tooth profiles and working mesh geometry with 10 radius samples per gear so I can validate my CAD model?"},{"title":"Contact ratio check for tight center distance","prompt":"We're squeezing a gear pair into a compact housing with a center distance of 85 mm — module 2.5, 24 and 42 teeth, no profile shift on either gear, 20-degree pressure angle. Can you calculate the working mesh geometry and involute profiles with 8 radius samples each so I can confirm the contact ratio is acceptable?"},{"title":"Gear mesh analysis for manufacturing tolerance study","prompt":"For a tolerance study, I need the declared involute profiles and full working mesh relationship for a 3 mm module gear pair, 16 and 48 teeth, profile shifts of 0.5 and -0.3, 25-degree reference pressure angle, center distance 97 mm, with 12 sample radii on each gear spanning from their base circles to tip circles."}],"resultDescription":"Returns the exact computed involute tooth profile coordinate sets for each gear (sampled at the requested radii), plus the geometric working mesh parameters including working pressure angle, working pitch radii, base circle radii, center distance verification, and contact ratio for the gear pair.","failureModes":["Invalid module or tooth count outside allowed range (6–1000 teeth, 0.01–100 mm module)","Profile shift outside allowed range (−0.5 to 1.0) causes rejection","Center distance geometrically inconsistent with the specified gear parameters (e.g. less than sum of base radii)","Radius sample points outside valid involute range (below base circle or above tip) may produce partial or empty profile points","Mismatched array lengths for teeth, profile_shifts, or radius_samples (must each have exactly 2 entries)","Pressure angle outside 5–40 degree range rejected"],"whenToPreferThis":"Use this endpoint when you need mathematically exact involute spur gear tooth profile coordinates and working mesh geometry — particularly when profile shifts, non-standard center distances, or precise contact ratio verification are required. It is preferable over general CAD tools when you need raw numeric geometry for downstream analysis, tolerance validation, or programmatic gear design without manual CAD interaction.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:39:17.946Z","isFirstParty":false,"canonicalSlug":"external-involute-spur-gear-working-mesh-tooth-profile-geometry-8bef263e"}