velocity-force duality

The reciprocal relationship in robotics where the Jacobian maps velocities forward, while its transpose maps forces backward. A position where velocities are amplified (low mechanical advantage) is also where forces are reduced; conversely, singular configurations are where forces are amplified.

So where the robot is good at moving quickly (mechanical advantage for velocity), it’s bad at exerting large forces — and vice versa. Near singular configurations the gearbox breaks: certain directions can require huge joint speeds for small hand motion or produce enormous forces from small torques, which makes control unstable or unsafe.

Bottom line: motion and force are two sides of the same mapping — being favorable for one usually means being unfavorable for the other.