# Units and Pose Representation

## Public units

`URCtrl` standardizes its public units for convenient use in experimental scripts by researchers.

| Type | Representation | Unit |
|---|---|---|
| P coordinates | `[x, y, z, rx, ry, rz]` | mm, degree |
| J coordinates | `[j1, j2, j3, j4, j5, j6]` | degree |
| speed | `0 < value <= 100` | % |
| jspeed | `0 < value <= 100` | % |
| accel | `0 < value <= 100` | % |
| decel | `0 < value <= 100` | % |
| `move_path()` blend | float | m |

## Internal UR units

UR RTDE uses m / rad. `URCtrl` converts values at the boundary between the public interface and RTDE.

```text
Public interface
    mm / degree / %
        ↓
URCtrl
        ↓
RTDE
    m / rad / SI
```

## P coordinates

P coordinates contain the following six components:

```python
[x, y, z, rx, ry, rz]
```

`x, y, z` are expressed in mm.

`rx, ry, rz` form a rotation vector expressed in degrees.

## Rotation vector

UR orientations are not Euler angles.

`rx, ry, rz` form a rotation vector: three components obtained by multiplying the rotation axis by the rotation angle.

`URCtrl` exposes each rotation-vector component in degrees. These are **not** roll / pitch / yaw angles in degrees.

## J coordinates

J coordinates contain six joint angles:

```python
[j1, j2, j3, j4, j5, j6]
```

The public unit is degree.

## speed / accel

`speed`, `jspeed`, `accel`, and `decel` are all percentages.

Internally, they are converted to physical speeds and accelerations as follows:

```text
linear speed = UR_MAX_LINEAR_SPEED * speed / 100
joint speed  = UR_MAX_JOINT_SPEED  * jspeed / 100
linear accel = UR_MAX_LINEAR_ACCELERATION * accel / 100
joint accel  = UR_MAX_JOINT_ACCELERATION  * accel / 100
```

## Default values

| Setting | Default |
|---|---:|
| `UR_MAX_LINEAR_SPEED` | 0.25 m/s |
| `UR_MAX_LINEAR_ACCELERATION` | 1.2 m/s² |
| `UR_MAX_JOINT_SPEED` | 1.05 rad/s |
| `UR_MAX_JOINT_ACCELERATION` | 1.4 rad/s² |
| `UR_DEFAULT_BLEND_RADIUS` | 0.005 m |

These values can be overridden in the configuration.