[Modern Robotics] 5. Velocity Kinematics and Statics

Preliminaries

Jacobian

Singularity

Manipulability ellipsoid

Force ellipsoid

5.1 Manipulator Jacobian

5.1.1 Space Jacobian

5.1.2 Body Jacobian

5.1.3 Visualizing the Space and Body Jacobian

5.1.4 Relationship between the Space and Body Jacobian

5.1.5 Alternative Notions of the Jacobian

analytic Jacobian

geometric Jacobian

5.1.6 Looking Ahead to Inverse Velocity Kinematics

5.2 Statics of Open Chains Using

5.3 Singularity Analysis

Case I: Two Collinear Revolute Joint Axes

Case II: Three Coplanar and Parallel Revolute Joint Axes

Case III: Four Revolute Joint Axes Intersecting at a Common Point

Case IV: Four Coplanar Revolute Joints

Case V: Six Revolute Joints Intersecting a Common Line

5.4 Manipulability

5.5 Summary