# Configurations and singularities

## Configurations

The same tool pose can be reached with the elbow up or down, the wrist flipped or not, the base facing the
target or turned 180° with the arm reaching backwards. Each combination is a **configuration**. A joint move
keeps the configuration it is in unless the target is in another; a Cartesian move cannot change configuration
at all, because that would mean passing through a pose where two configurations meet, which is a singularity.

Three choices with two answers each make eight configurations. The figure shows all eight for one tool pose:
PAROL6 with nothing on the flange, the tool centre point 250 mm in front of the base and 230 mm up, the tool
tilted 30° from vertical. The flange is in exactly the same place and orientation in every picture; only the
joints differ. The teal dot marks the centre of the flange and the arrow its axis, the same in every
picture.

- **Shoulder right or left**: the wrist centre in front of the joint 1 axis, or behind it with joint 1 turned
  about 180° and the arm reaching back over itself.
- **Elbow up or down**: the elbow above or below the line from the shoulder to the wrist centre.
- **Wrist flipped or not**: joint 5 positive or negative; joints 4 and 6 turn by 180° to keep the tool where it
  is.

![The eight configurations of PAROL6 for one tool pose: elbow up or down, shoulder right or left, wrist flipped or not; of these, only (a) is within the joint limits](https://docs.source-robotics.com/PAROL-docs/1.1/assets/theory/configurations_parol6.webp){ width="700" }
![The eight configurations of PAROL6 for one tool pose: elbow up or down, shoulder right or left, wrist flipped or not; of these, only (a) is within the joint limits](https://docs.source-robotics.com/PAROL-docs/1.1/assets/theory/configurations_parol6_dark.webp){ width="700" }

Mathematically all eight reach the pose. On the real robot, the joint limits rule most of them out: for this pose
only (a) is within every joint limit ([Joint limits and directions](https://docs.source-robotics.com/PAROL-docs/1.1/03-technical-data/joint-limits/)), and
several of the others would also hit the robot itself. The poses were solved and drawn from PAROL6's model in
[robot_descriptions](https://github.com/Source-Robotics/robot_descriptions), the same model the limits come from.

The practical rule: teach the poses of a program in the configuration you want, and make the move between two
configurations a joint move (`MoveJoint`, `move_j`), never a Cartesian one.

How the software chooses, when a target is given as a pose:

- **The Python API** solves every pose starting from the joints where the robot is, so it keeps the current
  configuration, in Cartesian moves and in joint moves to a pose alike.
- **The commander software** solves `MovePose` starting from the standby pose, so it takes the configuration
  nearest to standby, whichever the robot is in; its Cartesian moves keep the current one.

To be sure of the configuration, give the target as joint angles.

## Singularities

When the arm moves in Cartesian space, the software converts a tool velocity into six joint velocities every
cycle. In most poses that works. In some poses two joint axes line up, and a motion of the tool in a certain
direction would need infinite joint speed, or the joints can turn without the tool moving: a **singularity**. The
maths divides by something that goes to zero. Near it, small tool motions ask for huge joint speeds; at it, the
move is impossible.

The three singularities of a six-axis arm with a spherical wrist:

| | When | Looks like | You meet it |
|---|---|---|---|
| Wrist | Joint 5 at 0°: the axes of joints 4 and 6 in one line | The wrist straight; the standby pose is a wrist singularity | whenever the tool points the way the forearm does |
| Shoulder | The wrist centre on the joint 1 axis. The shoulder axis is 23.4 mm in front of it, so the arm leans back to get there: with joint 3 at 180°, at joint 2 = −133.1° | The wrist straight above the middle of the base | working close to the joint 1 axis, above the base |
| Elbow | Joint 3 at 256.2°: the upper arm and the line from the elbow to the wrist centre in one line, the wrist centre 362.3 mm from the shoulder axis | The arm fully stretched | at full reach |

![The wrist singularity: joint 5 at 0°, so the axes of joints 4 and 6 lie in one line](https://docs.source-robotics.com/PAROL-docs/1.1/assets/theory/singularity_wrist_parol6.webp){ width="571" }
![The wrist singularity: joint 5 at 0°, so the axes of joints 4 and 6 lie in one line](https://docs.source-robotics.com/PAROL-docs/1.1/assets/theory/singularity_wrist_parol6_dark.webp){ width="571" }

![The shoulder singularity: the wrist centre on the joint 1 axis, here with joint 2 at −133.1° and joint 3 at 180°](https://docs.source-robotics.com/PAROL-docs/1.1/assets/theory/singularity_shoulder_parol6.webp){ width="347" }
![The shoulder singularity: the wrist centre on the joint 1 axis, here with joint 2 at −133.1° and joint 3 at 180°](https://docs.source-robotics.com/PAROL-docs/1.1/assets/theory/singularity_shoulder_parol6_dark.webp){ width="347" }

![The elbow singularity: joint 3 at 256.2°, so joints 2 and 3 and the wrist centre lie in one line, the arm fully stretched](https://docs.source-robotics.com/PAROL-docs/1.1/assets/theory/singularity_elbow_parol6.webp){ width="517" }
![The elbow singularity: joint 3 at 256.2°, so joints 2 and 3 and the wrist centre lie in one line, the arm fully stretched](https://docs.source-robotics.com/PAROL-docs/1.1/assets/theory/singularity_elbow_parol6_dark.webp){ width="517" }

The angles are the ones the software shows, from PAROL6's model. The wrist centre is where the axes of joints 4,
5 and 6 meet. The elbow singularity is the outer edge of the workspace
([Workspace and reach](https://docs.source-robotics.com/PAROL-docs/1.1/theory/workspace-and-reach/)): singularities are part of its boundary, with the joint limits.

## What PAROL6 does

- **The commander software** stops a Cartesian move or jog when it reaches a singularity; the robot stays where
  it stopped. It does not deviate from the path to go around.
- **The Python API** refuses a Cartesian command whose path it cannot solve, before anything moves, and a jog
  that would enter a singular region stops.

Some industrial controllers can bend the path slightly to pass a singularity; PAROL6 keeps the path and stops
instead. The [demonstration video](https://www.youtube.com/watch?v=BJnZvwAE0PY) shows what singularities look
like on an industrial arm.

## Avoiding them

Singularities are a property of the geometry, so they are avoided by design, with trial and error:

- Keep the wrist bent: a few degrees of joint 5 away from 0° at the poses where you work.
- Place the parts so that the arm reaches them with a bent elbow, not at full stretch, and off the axis of
  joint 1.
- Mount the gripper at an angle, or on a plate that turns it, so that the working orientation needs a bent
  wrist.
- When a move keeps failing, make it a joint move, or add an intermediate pose.
- Run the program in the simulator: a stop or a refusal in the simulator is a singularity you can see.