# External Involute Spur Gear Working Mesh Tooth Profile Geometry

> External Involute Spur Gear Working Mesh Tooth Profile Geometry is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

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.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B008/external-involute-spur-gear-working-mesh-tooth-profile-geometry?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/external-involute-spur-gear-working-mesh-tooth-profile-geometry-8bef263e
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_gbQFIR4xF6mpDMNI2lOVb

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability external-involute-spur-gear-working-mesh-tooth-profile-geometry-8bef263e -d '<json body>'
```

Example prompt: 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?

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Compute exact declared involute profiles and the geometric working mesh relationship.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/external-involute-spur-gear-working-mesh-tooth-profile-geometry-8bef263e/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)