{"openapi":"3.1.0","info":{"title":"Worm Gear API","version":"1.0.0","description":"Worm-gear engineering maths as an API, computed locally and deterministically — the ratio, lead-angle and efficiency numbers a machine designer or millwright sizes a worm drive with. The ratio endpoint gives the reduction = wheel teeth ÷ worm starts, so a single-start worm on a 40-tooth wheel is a big 40:1 reduction in one compact stage — the high ratio in a small package is the whole appeal of a worm drive. The geometry endpoint gives the lead (= starts × axial pitch, with axial pitch = π × module) and the lead angle = atan(lead ÷ (π × worm pitch diameter)), and tests for self-locking: a small lead angle (roughly under 5–6° for typical steel-on-bronze) means the wheel cannot back-drive the worm — invaluable for hoists and holding loads, at the cost of efficiency. The efficiency endpoint gives the mesh efficiency when the worm drives = tan(lead angle) ÷ tan(lead angle + friction angle), which is low for the small lead angles that give big ratios — often 50–70 %, which is why worm gears run warm and need good lubrication — while high-lead multi-start worms reach 90 %+; when the lead angle drops to the friction angle the drive becomes self-locking. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-design and gearbox tools, machine-building and CAD utilities, and engineering calculators. Pure local computation — no key, no third-party service, instant. Confirm self-locking dynamically — vibration can unlock a marginal pair. 3 compute endpoints. For spur gears use a spur-gear API; for a general ratio a gear-ratio API.","contact":{"name":"PremiumApi","url":"https://www.oanor.com/by/premiumapi"}},"servers":[{"url":"https://api.oanor.com/wormgear-api","description":"oanor gateway"}],"tags":[{"name":"Worm"},{"name":"Meta"}],"components":{"securitySchemes":{"oanorKey":{"type":"apiKey","in":"header","name":"x-oanor-key","description":"Get your key at https://www.oanor.com/developer/keys"}}},"security":[{"oanorKey":[]}],"paths":{"/v1/efficiency":{"get":{"operationId":"get_v1_efficiency","tags":["Worm"],"summary":"Mesh efficiency (worm driving)","description":"","parameters":[{"name":"lead_angle_deg","in":"query","required":true,"description":"Lead angle (degrees)","schema":{"type":"string"},"example":"3.814"},{"name":"friction_coeff","in":"query","required":false,"description":"Friction coefficient (default 0.05)","schema":{"type":"string"},"example":"0.05"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Worm-drive efficiency (worm driving the wheel) = tan(lead angle) ÷ tan(lead angle + friction angle), where the friction angle = atan(μ). It is low for the small lead angles that give big ratios — often 50–70 % — which is why worm gears run warm and need good lubrication; multi-start, high-lead worms reach 90 %+. When the lead angle ≤ the friction angle the back-driving efficiency goes to zero: the drive is self-locking.","inputs":{"friction_coeff":0.05,"lead_angle_deg":3.814},"self_locking":false,"efficiency_driving":0.5695,"friction_angle_deg":2.862,"efficiency_driving_pct":56.95},"meta":{"timestamp":"2026-06-07T08:18:08.050Z","request_id":"26e68854-7608-4049-855f-59ec4f986e47"},"status":"ok","message":"Efficiency","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/geometry":{"get":{"operationId":"get_v1_geometry","tags":["Worm"],"summary":"Lead angle and self-locking test","description":"","parameters":[{"name":"worm_starts","in":"query","required":true,"description":"Worm starts (threads)","schema":{"type":"string"},"example":"1"},{"name":"module_mm","in":"query","required":true,"description":"Axial module (mm)","schema":{"type":"string"},"example":"2"},{"name":"worm_pitch_diameter_mm","in":"query","required":true,"description":"Worm pitch diameter (mm)","schema":{"type":"string"},"example":"30"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"The lead = starts × axial pitch (π × module), and the lead angle = atan(lead ÷ (π × worm pitch diameter)). A small lead angle (roughly under 5–6° for typical steel-on-bronze) makes the drive self-locking — the wheel cannot back-drive the worm, useful for hoists and holding loads, but it caps efficiency. Bigger lead angles (multi-start, thin worm) drive more freely and efficiently but lose the self-locking. Confirm self-locking dynamically; vibration can unlock a marginal pair.","inputs":{"module_mm":2,"worm_starts":1,"worm_pitch_diameter_mm":30},"lead_mm":6.283,"self_locking":true,"axial_pitch_mm":6.283,"lead_angle_deg":3.814},"meta":{"timestamp":"2026-06-07T08:18:08.119Z","request_id":"10470bbd-2d28-4686-8cf6-9d835c3b884a"},"status":"ok","message":"Worm geometry","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/ratio":{"get":{"operationId":"get_v1_ratio","tags":["Worm"],"summary":"Gear ratio from starts and teeth","description":"","parameters":[{"name":"worm_starts","in":"query","required":true,"description":"Worm starts (threads)","schema":{"type":"string"},"example":"1"},{"name":"gear_teeth","in":"query","required":true,"description":"Wheel teeth","schema":{"type":"string"},"example":"40"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"A worm drive's ratio = wheel teeth ÷ worm starts (threads), and the worm turns the wheel one tooth per worm turn for a single start — so a single-start worm on a 40-tooth wheel is a big 40:1 reduction in one compact stage. More starts cut the ratio but raise the lead angle and efficiency. Drive is almost always worm-in, wheel-out: the high ratio and often self-locking action are the whole point.","inputs":{"gear_teeth":40,"worm_starts":1},"gear_ratio":40,"ratio_label":"40:1"},"meta":{"timestamp":"2026-06-07T08:18:08.193Z","request_id":"4a36ea86-d93b-4c83-a036-44620cbd14ac"},"status":"ok","message":"Gear ratio","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/meta":{"get":{"operationId":"get_v1_meta","tags":["Meta"],"summary":"Spec","description":"","parameters":[],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"notes":"Metric (mm, °, %). ratio = teeth/starts; lead = starts·π·module; lead angle = atan(lead/(π·d)); efficiency = tan λ / tan(λ+φ), φ = atan μ; self-locking when λ ≤ φ. For spur gears use a spur-gear API; for a general ratio a gear-ratio API.","service":"wormgear-api","endpoints":{"GET /v1/meta":"This document.","GET /v1/ratio":"Gear ratio from worm starts and wheel teeth.","GET /v1/geometry":"Lead, lead angle and self-locking from the worm geometry.","GET /v1/efficiency":"Mesh efficiency (worm driving) from lead angle and friction."},"description":"Worm-gear maths: gear ratio, lead angle and self-locking test, and mesh efficiency."},"meta":{"timestamp":"2026-06-07T08:18:08.289Z","request_id":"f7ab9973-e609-4207-907d-6e77a27f5edc"},"status":"ok","message":"Meta","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}}},"x-oanor-pricing":[{"slug":"free","name":"Free","price_cents_month":0,"monthly_call_quota":4600,"rps_limit":2,"hard_limit":true},{"slug":"starter","name":"Starter","price_cents_month":1270,"monthly_call_quota":51000,"rps_limit":6,"hard_limit":true},{"slug":"pro","name":"Pro","price_cents_month":3920,"monthly_call_quota":217000,"rps_limit":15,"hard_limit":true},{"slug":"mega","name":"Mega","price_cents_month":12100,"monthly_call_quota":1120000,"rps_limit":40,"hard_limit":true}],"x-oanor-marketplace-url":"https://www.oanor.com/api/wormgear-api"}