null-space motion
Null-space motion is when a robot rearranges its joints internally while the working end — the hand or tool — stays perfectly still in place and pointing the same way. Picture your own arm holding a coffee cup steady on a table: you can swing your elbow up, out, or down without the cup budging. The elbow is moving freely, yet the cup's position never changes. That elbow shuffle, in which the body shifts but the goal point holds, is null-space motion.
This is only possible when a robot has more joints than it strictly needs to place its end where you want — extra freedom, often called redundancy. With spare joints, many different body postures all land the hand in the same spot, so the robot can drift among those postures without disturbing the task. The name comes from the math: these are exactly the joint motions that produce zero movement at the end-effector, a set mathematicians call the null space of the arm's Jacobian.
Far from being a useless wiggle, null-space motion is genuinely useful. While the hand keeps doing its job, the freed-up joints can quietly take care of secondary goals — dodging an obstacle, steering clear of an awkward locked posture, staying within joint limits, or keeping the arm comfortable and balanced. It is how a redundant robot does two things at once: hold the main task fixed with one hand, so to speak, while tidying up everything else with the rest of its body.
A seven-jointed arm holds its gripper fixed over a bolt while its elbow slowly rises to slip past a low beam overhead — the gripper never moves, but the arm reshapes itself to avoid the obstacle.
The task point stays locked while the body uses its spare freedom to dodge.
Null-space motion exists only in redundant robots — those with more joints than the task strictly requires; a robot with just enough joints has no spare freedom to move this way.