# Node KinematicMotorNode

Defined in `mime.nodes.actuation._chain.KinematicMotorNode`.

Algorithm `MIME-NODE-105`.

A kinematic motor: a rotor turned by a prescribed angle, or at a prescribed speed integrated over each step, about an axis of the frame it mounts on.

## Governing equations

$$
\phi_{n+1} = a \quad \text{(an angle prescribed)}, \qquad \phi_{n+1} = \phi_{n} + \omega \, \mathrm{d}t \quad \text{(a speed prescribed)}; \quad \mathbf{P}_{s} = \mathbf{M}_{j} \circ \mathbf{O}, \quad \mathbf{P}_{r} = \mathbf{P}_{s} \circ \mathrm{Rot}(\mathbf{e}, \phi_{n+1}); \quad \boldsymbol{\Omega}_{s} = \boldsymbol{\omega}_{j}, \quad \boldsymbol{\Omega}_{r} = \boldsymbol{\omega}_{j} + \dot{\phi} \, R(\mathbf{P}_{s}) \mathbf{e}
$$

## Discretisation

A prescribed speed is integrated by the rectangle rule over the step, exact for a speed held through it.

## Assumptions

- An ideal source of the prescribed motion: no cogging, imbalance or thermal terms (MIME-ANO-102)
- Its motion is prescribed: it takes no load, and its reaction is not applied

## Limitations

none declared

## Declared regimes (not evidenced here)

none declared

## References

[@Sola2017]

## Symbols

| Symbol | Kind | Name | Units | Implemented by |
|---|---|---|---|---|
| $\phi$ | state | `angle` | 1 (units declared, not checked) | `mime.nodes.actuation._chain.KinematicMotorNode.advance` |
| $a$ | input | `angle` | 1 | `mime.nodes.actuation._chain.KinematicMotorNode.advance` |
| $\omega$ | input | `velocity` | Hz | `mime.nodes.actuation._chain.KinematicMotorNode.advance` |
| $\mathbf{P}$ | state | `frame_poses` | m; 1 | `mime.nodes.actuation._chain.KinematicMotorNode.advance` |
| $\boldsymbol{\Omega}$ | state | `frame_angular_velocities` | rad/s | `mime.nodes.actuation._chain.KinematicMotorNode.rates` |
| $\boldsymbol{\omega}$ | input | `mount_rates` | rad/s | `mime.nodes.actuation._chain.MountedNode.base_rate` |
| $\mathbf{M}$ | input | `mount_poses` | m; 1 | `mime.nodes.actuation._chain.MountedNode.base` |
| $\mathbf{O}$ | parameter | `placement` | m; 1 | `mime.nodes.actuation._chain.MountedNode.base` |
| $\mathbf{e}$ | parameter | `axis` | 1 | `mime.nodes.actuation._chain.KinematicMotorNode.poses` |

A row marked *units declared, not checked* has the units its author wrote: the code declares none there, so the node walk cannot compare them with anything.

## Built by

- [`motor`](../entries/dynamics/motor.md) 0.2.0, rung `kinematic`