# Sprocket

> Component kind `sprocket` (category `mech`, DSL name `sprocket`, API v1)

Toothed wheel that engages a chain without slipping. Pairs with another sprocket via `mech.chain`; the ratio is driven by tooth counts (not diameters, unlike pulleys).

## Parameters

- **`teeth`** — Tooth count. Must be ≥ 6 for a usable chain engagement. Drives the chain ratio: ω_to = ω_from · (teeth_from / teeth_to).
- **`pitch`** — Chain pitch — center-to-center distance between two adjacent roller pins (mm). Both sprockets on a chain must share the same pitch.
- **`width`** — Face width along the spin axis (mm).
- **`boreDiameter`** — Central bore diameter (mm), for mounting on a shaft.

## Parameters schema

| Parameter | Type | Default | Constraints |
| --- | --- | --- | --- |
| `teeth` | Number | 18 | min: 6 |
| `pitch` | Number | 8 | min: 1 |
| `width` | Number | 6 | min: 1 |
| `boreDiameter` | Number | 8 |  |
| `color` | String | — |  |

## Ports

| Port | Type | Description |
| --- | --- | --- |
| `axis` | `rotational` | Spin axis (rotational). Receives ω from the coupling or chain propagation. |

## Kinematics

Passive — ω is set by the chain or coupling attached to the axis port. Theta integrates from ω each tick.

## Example

```
sprocket "S1" {
  teeth: 18
  pitch: 8
  at: position(0, 0, 0)
}
```