twist (spatial velocity)

A twist is a compact way to describe everything about how a rigid body is moving at one instant, packed into a single six-number bundle. Three of the numbers describe how fast and about which axis the body is spinning (its angular velocity), and the other three describe how fast and in which direction a chosen reference point on the body is sliding along a straight line (its linear velocity). Bundling both together makes sense because real objects usually move and turn at the same time — think of a thrown football that flies forward while it spirals.

Why keep them as one object instead of two separate ideas? Because translation and rotation are deeply intertwined when something moves. If a robot's whole arm is rotating, then a tool clamped near the far end is not only spinning, it is also being swept sideways through space — its straight-line speed depends on the turning and on how far out it sits. A twist captures this entire coupled picture honestly in one go, so the linear and angular parts are never accidentally treated as if they were independent. (This is also why the linear part is tied to a specific reference point: the same motion gives a different linear velocity at a different point on the body.)

Twists are the velocity counterpart to pose. A pose answers "where and how is the body placed right now?"; a twist answers "and how is that placement changing this very moment?" Engineers lean on them constantly when they want a robot to move its hand along a smooth path at a controlled speed, because a twist is the single quantity that says, all at once, how the linear and angular motion should blend together.