Parallel Robots. Mechanics and Control H AMID D. TAG HI RAD. CRC Press. Taylor & Francis Group. Taylor & Francis Croup, Boca Raton London NewYoric

Transcription

1 Parallel Robots Mechanics and Control H AMID D TAG HI RAD CRC Press Taylor & Francis Group Boca Raton London NewYoric CRC Press Is an Imprint of the Taylor & Francis Croup, an informs business

2 Contents Preface xi 1 Introduction 1 11 What Is a Robot? 1 12 Robot Components 3 13 Robot Degrees-of-Freedom 6 14 Robot Classification Serial Robots Parallel Robots The Stewart-Gough Platform The Delta Robot Cable-Driven Parallel Robots The Aims and Scope of This Book 21 2 Motion Representation Spatial Motion Representation Position of a Point Orientation of a Rigid Body Rotation Matrix Rotation Matrix Properties Screw Axis Representation Euler Angles Motion of a Rigid Body Homogeneous 231 Homogeneous 232 Homogeneous Transformations 44 Coordinates 44 Transformation Matrix Screw Displacement Transformation Arithmetics Consecutive Transformations Inverse Transformation 52 Problems 53 3 Kinematics Introduction Loop Closure Method Kinematic Analysis of a Planar Manipulator Mechanism Description Geometry of the Manipulator Inverse Kinematics Forward Kinematics Simulations,66

3 yi Contents 34 Kinematic Analysis of Shoulder Manipulator Mechanism Description Geometry of the Manipulator Inverse Kinematics Forward Kinematics Simulations Kinematic Analysis of Stewart-Gough Platform Mechanism Description Geometry of the Manipulator Inverse Kinematics Forward Kinematics Background Literature Analytical Solution Numerical Solution Simulations Analytical Solution Numerical Solution 91 Problems 95 : Jacobians: Velocities and Static Forces Ill 41 Introduction Ill 42 Angular and Linear Velocities Angular Velocity of a Rigid Body Angular Velocity and Rotation Matrix Rate Angular Velocity and Euler Angles Rate Linear Velocity of a Point Screw Coordinates Jacobian Matrices of a Parallel Manipulator Velocity Loop Closure Singularity Analysis of Parallel Manipulators Inverse Kinematic Singularity Forward Kinematic Singularity Combined Singularity Jacobian Analysis of a Planar Manipulator Velocity Loop Closure Singularity Analysis Sensitivity Analysis Jacobian Analysis of Shoulder Manipulator 471 Velocity Loop Closure Jacobian of the Actuated Limbs Jacobian of the Passive Limb Singularity Analysis Jacobian Analysis of the Stewart-Gough Platform Velocity Loop Closure Singularity Analysis Background Literature A 3-6 Stewart-Gough Platform Static Forces in Parallel Manipulators Free-Body Diagram Approach 139

4 Contents vii 492 Virtual Work Approach Static Forces of a Planar Manipulator Static Forces of Shoulder Manipulator Static Forces of the Stewart-Gough Platform Stiffness Analysis of Parallel Manipulators Stiffness and Compliance Matrices Transformation Ellipsoid Stiffness Analysis of a Planar Manipulator Stiffness Analysis of Shoulder Manipulator Stiffness Analysis of the Stewart-Gough Platform 155 Problems Dynamics Introduction Dynamics of Rigid Bodies: A Review Acceleration of Rigid Bodies Angular Acceleration of a Rigid Body Linear Acceleration of a Point Mass Properties Center of Mass Moments of Inertia Principal Axes Inertia Matrix Transformations Momentum and Kinetic Energy Linear Momentum Angular Momentum Kinetic Energy Newton-Euler Laws Variable-Mass Systems Newton-Euler Formulation Dynamic Formulation of a Planar Manipulator: Constant Mass Treatment Acceleration Analysis Dynamic Formulation of the Limbs Dynamic Formulation of the Moving Platform Forward Dynamics Simulations Inverse Dynamics Simulation Dynamic Formulation of a Planar Manipulator: Variable-Mass Treatment Acceleration Analysis Dynamic Analysis of the Limbs Dynamic Formulation of the Stewart-Gough Platform Acceleration Analysis Dynamic Formulation of the Limbs Dynamic Formulation of the Moving Platform Closed-Form Dynamics Closed-Form Dynamics of the Limbs Closed-Form Dynamics of the Moving Platform 209

5 viii Contents 5343 Closed-Form Dynamics of the Stewart-Gough Manipulator Forward Dynamics Simulations Inverse Dynamics Simulation Virtual Work Formulation 541 D'Alembert's Principle Principle of Virtual Work 543 Dynamic Formulation of a Planar Manipulator: Constant Mass Treatment 544 Formulation Verification 545 Dynamic Formulation of a Planar Manipulator: Variable Mass Treatment 546 Dynamic Formulation of the Stewart-Gough Platform Lagrange Formulation Generalized Coordinates Lagrange Equations of the Second Kind Lagrange Equations of the First Kind Dynamic Formulation Properties Mass Matrix Properties Linearity in Parameters 5543 Coriolis and Centrifugal Vector Properties Dynamic Formulation of a Planar Manipulator Dynamic Formulation of the Limbs Dynamic Formulation of the Moving Platform Dynamic Formulation of the Whole Manipulator Dynamic Analysis of the Stewart-Gough Platform Dynamic Formulation of the Limbs Dynamic Formulation of the Moving Platform Problems 5563 Dynamic Formulation of the Whole Manipulator Motion Control 61 Introduction 62 Controller Topology Motion Control in Task Space Decentralized PD Control 632 Feed Forward Control 633 Inverse Dynamics Control 634 Partial Linearization IDC 64 Robust and Adaptive Control 641 Robust Inverse Dynamics Control 642 Adaptive Inverse Dynamics Control ' Motion Control in Joint Space Dynamic Formulation in the Joint Space Decentralized PD Control Feed Forward Control Inverse Dynamics Control Summary of Motion Control Techniques Dynamic Formulations 662 Decentralized PD Control

6 Contents ix Feed Forward Control 664 Inverse Dynamics Control Partial Linearization IDC Robust Inverse Dynamics Control Adaptive Inverse Dynamics Control Redundancy Resolution 671 Introduction Problem Formulation Lagrange and Karush-Kuhn-Tucker Multipliers Iterative Solutions Numerical Methods 6742 An Iterative-Analytical Method Motion Control of a Planar Manipulator 681 Decentralized PD Control Feed Forward Control 683 Inverse Dynamics Control ; Partial Linearization IDC Robust Inverse Dynamics Control Adaptive Inverse Dynamics Control Motion Control in Joint Space 69 Motion Control of the Stewart-Gough Platform Decentralized PD Control Feed Forward Control Inverse Dynamics Control Partial Linearization IDC Robust Inverse Dynamics Control Motion Control in Joint Space Decentralized PD Control Feed Forward Control Inverse Dynamics Control 376 Problems Force Control Introduction Controller Topology Cascade Control Force Feedback in Outer Loop Force Feedback in Inner Loop Stiffness Control Single-Degree-of-Freedom Stiffness Control General Stiffness Control Stiffness Control of a Planar Manipulator Stiffness Control of the Stewart-Gough Platform Direct Force Control Force Control of a Planar Manipulator Force Control of the Stewart-Gough Platform Impedance Control Impedance 752 Impedance Control Concept

7 x Contents 753 Impedance Control Structure Impedance Control of a Planar Manipulator Impedance Control of the Stewart-Gough Platform 456 Problems 464 Appendix A: Linear Algebra 477 Al Vectors and Matrices 477 A2 Vector and Matrix Operations 478 A3 Eigenvalues and Singular Values 480 A4 Pseudo-Inverse 482 A41 Pseudo-Inverse Properties 483 A42 Linear Inverse Problems 484 A 5 Kronecker Product 485 Appendix B: Trajectory Planning 487 B l Point-to-Point Motion 487 Bll Cubic Polynomials 487 Bl2 Quintic Polynomials 488 B13 Linear Segments with Parabolic Blends 489 B14 Minimum Time Trajectory 490 B2 Specified Path with Via Points 491 Appendix C: Nonlinear Control Review 493 C l Dynamical Systems 493 C2 Stability Definitions 494 C3 Lyapunov Stability 495 C4 Krasovskii-Lasalle Theorem 498 References 501 Index 511