Yoshikawa manipulability is computed from which matrix?

• A. The inverse of the Jacobian.
• B. The inertia matrix.
• C. The Jacobian.
• D. The end-effector pose.

Answer: (C)

Yoshikawa manipulability measures how freely the end-effector can move in all directions from the current joint configuration, and this depends on the Jacobian—the matrix that maps joint velocities to end-effector velocities. The standard scalar measure is the square root of the determinant of J J^T (often written as sqrt(det(J J^T))). A larger value means directions of motion are well-supported by the joint motion, while a zero value signals a singular configuration where motion is constrained in some directions. The inertia matrix relates to dynamics, not the instantaneous kinematic capability; the end-effector pose is the result of motion, not the velocity mapping used for manipulability; and the inverse Jacobian is used to compute joint rates from end-effector rates, not to define the manipulability measure itself.