Autoplay of the YouTube playlist for all videos in this chapter.  This description box will not be updated with information about each video as the videos advance.

This video introduces the Jacobian of a robot, and how it is used to relate joint velocities to end-effector velocities and endpoint forces to joint forces and torques. The notions of singularities, manipulability, the manipulability ellipsoid, and the force ellipsoid are also introduced.

This video introduces the space Jacobian, the Jacobian relating joint velocities to the end-effector twist expressed in the space frame.

This video introduces the body Jacobian, the Jacobian relating joint velocities to the end-effector twist expressed in the body frame (a frame at the end-effector).

This video derives the relationship between the end-effector wrench and joint forces and torques using the Jacobian.

This video discusses robot singularities and Jacobians where the number of joints is not equal to the number of components of the end-effector twist or velocity, resulting in “tall” (“kinematically deficient”) and “fat” Jacobians.

This video describes the visualization of a robot’s ease of moving in different directions in terms of a manipulability ellipsoid, as well as scalar measures of the manipulability. Analogous ideas are presented describing the robot’s ability to apply wrenches as its end-effector.