This book discusses the dynamic analysis of rigid-flexible robots and multibody systems with serial as well as closed-loop architecture. The book presents a formulation of dynamic model of rigid-flexible robots based on the unique approach of de-coupling of natural orthogonal complements of velocity constraints. Based on this formulation, a computationally efficient and numerically stable forward dynamics algorithms for serial-chain and closed-loop robotic systems with rigid or flexible or rigid-flexible links is presented. The proposed algorithm is shown to be a numerically efficient for forward dynamics based on the investigation methodologies built on eigen value analytics. Precision and functionality of the simulation algorithms is presented/illustrated with application on different serial and closed-loop systems (both planar and spatial types). Some of the major robotic arms used to illustrate the proposed dynamic formulation and simulation algorithms are PUMA robot, Stanford robot arm, and Canadarm. It is envisaged that the book will be useful for researchers working on the development of rigid-flexible robots for use in defense, space, atomic energy, ocean exploration, and the manufacturing of biomedical equipment.
Author(s): Paramanand Vivekanand Nandihal, Ashish Mohan, Subir Kumar Saha
Series: Intelligent Systems, Control and Automation: Science and Engineering, 100
Publisher: Springer
Year: 2021
Language: English
Pages: 297
City: Singapore
Preface
Acknowledgements
Units and Notation
Contents
About the Authors
1 Introduction
1.1 Background
1.2 Dynamics of Multibody Systems
1.3 Dynamic Modeling
1.3.1 Dynamics of Rigid Systems
1.3.2 Dynamics of Flexible Systems
1.3.3 Dynamics of Closed-Loop Systems
1.4 Numerical Stability
1.5 Computational Efficiency
1.6 Experimental Work
1.7 Important Features of the Book
1.8 Organization of the Book
1.9 Summary
Bibliography
Part I Open-Loop Serial-Chain Systems
2 Dynamic Formulation Using the Decoupled Natural Orthogonal Complement (DeNOC)
2.1 Kinematics
2.1.1 Some Definitions
2.1.2 The DeNOC Matrices
2.2 Dynamic Modeling of Rigid Robots
2.3 Forward Dynamics Algorithm for Rigid Robots
2.3.1 Recursive Algorithm
2.3.2 Computational Complexity
2.4 Summary
Bibliography
3 Dynamics of Serial Rigid–Flexible Robots
3.1 Kinematics
3.1.1 Rotation Matrix
3.1.2 Kinematic Discretization
3.1.3 Definitions for Flexible Systems
3.1.4 The DeNOC Matrices for Rigid–Flexible Robots
3.2 Dynamic Modeling of Rigid–Flexible Robots
3.3 Geometric Stiffness
3.4 Forward Dynamics for Rigid–Flexible Robots
3.4.1 Recursive Algorithm
3.4.2 Computational Complexity
3.4.3 Comparison
3.5 Simulation Results
3.6 Shape Functions Evaluation
3.7 Single-Link Arm
3.7.1 Simulation Results
3.7.2 Number of Vibration Modes
3.8 Spinning Cantilever Beam
3.8.1 Numerical Simulation
3.9 Two-Link Planar Arm
3.9.1 Rigid Links
3.9.2 Rigid and Flexible Links
3.9.3 Both Links Flexible
3.10 Three-Link Planar Arm
3.10.1 Rigid Links
3.10.2 Canadarm with Two Flexible Links
3.11 Summary
References
4 Dynamics of Six-Link Spatial Robot Arms
4.1 PUMA Robot
4.2 Space Shuttle Remote Manipulator System Robot (SSRMS)
4.3 Stanford Arm
4.4 Summary
References
Part II Dynamic Modeling of Closed-Loop Systems
5 Dynamics of Closed-Loop Systems
5.1 Dynamics of Closed-Loop Systems
5.1.1 Forward Dynamics
5.1.2 Inverse Dynamics
5.2 Rigid–Flexible Planar Four-Bar Mechanism
5.2.1 RRR Planar Mechanism
5.2.2 RRF Planar Mechanism
5.2.3 RFF Planar Mechanism
5.2.4 FFF Planar Mechanism
5.3 Rigid–Flexible Five-Bar Mechanism
5.3.1 RRRR Mechanism
5.3.2 RFFR Mechanism
5.3.3 FFFF Mechanism
5.4 Rigid–Flexible 3-DOF Planar Parallel Manipulator
5.4.1 Equations of Motion of the Moving Platform
5.4.2 Kinematic Constraints
5.4.3 3RR Manipulator
5.4.4 3RF Manipulator
5.4.5 3FF Manipulator
5.5 Forced Simulation
5.5.1 Forced Simulation of 3-DOF Parallel Manipulator
5.6 Summary
References
6 Dynamics of Spatial Four-Bar Mechanism
6.1 Spatial Four-Bar Mechanism
6.2 Rigid–Flexible Spatial Four-Bar Mechanism
6.2.1 RRR Spatial Mechanism
6.2.2 RRF Spatial Mechanism
6.2.3 FRR Spatial Mechanism
6.2.4 FFF Spatial Mechanism
6.3 Summary
References
Part III Numerical Stability and Computational Efficiency of Dynamic Algorithm
7 Numerical Stability and Efficiency
7.1 Criteria for Numerical Stability
7.1.1 Zero Eigenvalue Phenomenon
7.1.2 Power Difference
7.1.3 Acceleration Plots
7.2 Stability and Efficiency for Rigid Robots
7.2.1 Zero Eigenvalue Phenomenon
7.2.2 Power Difference
7.2.3 Acceleration Plots
7.2.4 Computational Complexity
7.3 Stability and Efficiency for Rigid–Flexible Robots
7.3.1 Three-Link Planar Canadarm
7.3.2 Space Shuttle Remote Manipulator System (SSRMS)
7.4 Summary
References
Part IV Experimental Study of Flexible System
8 Experimental Results
8.1 Damping in Dynamic Model
8.2 Damping Coefficients
8.2.1 Joint Damping
8.2.2 Structural Damping
8.3 A Robotic Arm with Single Flexible Link
8.3.1 Calibration
8.3.2 Free Fall
8.3.3 Forced Response
8.4 A Robot Arm with Two Flexible Links
8.5 Summary
References
Appendix A Denavit and Hartenberg Parameters
Appendix B Derivation of Eq. (2.16)
Appendix C Computational Counts for Rigid Robots
Appendix D Derivation of Eq. (3.21a)
Appendix E Computational Counts for Flexible Robots
Appendix F Modeling of Four-Bar Mechanism in Recurdyn Software
F.1 Modeling of a 4-Bar Mechanism
F.1.1 Modeling of a Rigid Link
F.1.2 Modeling of a Joint
F.1.3 Modeling of a Flexible Link
F.2 Dynamic Analysis
Bibliography
