## Book Chapter: Chapter 5

Velocity Kinematics and Statics

#### Chapter 5 Autoplay

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.

#### Velocity Kinematics and Statics

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.

#### 5.1.1. Space Jacobian

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

#### 5.1.2. Body Jacobian

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).

#### 5.2. Statics of Open Chains

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

#### 5.3. Singularities

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.

#### 5.4. Manipulability

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.