Composition of Rotations
2.5 Parameterizations of Rotations
2.6 Rigid Motions
2.7 Chapter Summary
Problems
Notes and References
Notes
Chapter 3 Forward Kinematics
3.1 Kinematic Chains
3.2 The Denavit–Hartenberg Convention
3.3 Examples
3.4 Chapter Summary
Problems
Notes and References
Chapter 4 Velocity Kinematics
4.1 Angular Velocity: The Fixed Axis Case
4.2 Skew-Symmetric Matrices
4.3 Angular Velocity: The General Case
4.4 Addition of Angular Velocities
4.5 Linear Velocity of a Point Attached to a Moving Frame
4.6 Derivation of the Jacobian
4.7 The Tool Velocity
4.8 The Analytical Jacobian
4.9 Singularities
4.10 Static Force/Torque Relationships
4.11 Inverse Velocity and Acceleration
4.12 Manipulability
4.13 Chapter Summary
Problems
Notes and References
Notes
Chapter 5 Inverse Kinematics
5.1 The General Inverse Kinematics Problem
5.2 Kinematic Decoupling
5.3 Inverse Position: A Geometric Approach
5.4 Inverse Orientation
5.5 Numerical Inverse Kinematics
5.6 Chapter Summary
Problems
Notes and References
5
Part II Dynamics and Motion Planning
Chapter 6 Dynamics
6.1 The Euler–Lagrange Equations
6.2 Kinetic and Potential Energy
6.3 Equations of Motion
6.4 Some Common Configurations
6.5 Properties of Robot Dynamic Equations
6.6 Newton–Euler Formulation
6.7 Chapter Summary
Problems
Notes and References
Chapter 7 Path and Trajectory Planning
7.1 The Configuration Space
7.2 Path Planning for 
6 Part III Control of Manipulators Chapter 8 Independent Joint Control 8.1 Introduction 8.2 Actuator Dynamics 8.3 Load Dynamics 8.4 Independent Joint Model 8.5 PID Control 8.6 Feedforward Control 8.7 Drive-Train Dynamics 8.8 State Space Design 8.9 Chapter Summary Problems Notes and References Notes Chapter 9 Nonlinear and Multivariable Control 9.1 Introduction 9.2 PD Control Revisited 9.3 Inverse Dynamics 9.4 Passivity-Based Control 9.5 Torque Optimization 9.6 Chapter Summary Problems
