Jacobian
Also: kinematic Jacobian
A matrix relating small joint changes or rates to task-space changes or rates.
For robot kinematics, V = J(q)q̇; rank and conditioning reveal lost motion directions and force amplification.
- Formula
V = J(q)q̇
Example Near a straight two-link arm, sideways joint motion may produce little extension change.
Common misconception A Jacobian is local and configuration-dependent, not one fixed transform for the whole workspace.