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• Preface.
• 1. Introduction.-
• 2. Structural Synthesis and Architectures.-
• 3. Inverse Kinematics.-
• 4. Direct Kinematics.-
• 5. Velocity, Accuracy and Acceleration Analysis.-
• 6. Singular Configurations.-
• 7. Workspace.-
• 8. Static Analysis.-
• 9. Dynamics.-
• 10. Calibration.-
• 11. Design.-
• 12. Annex: System Solving.-
• 13. Annex: Interval Analysis.-
• 14. Conclusion.- Index. References.
• (source: Nielsen Book Data)

Parallel robots are closed-loop mechanisms presenting very good performances in terms of accuracy, velocity, rigidity and ability to manipulate large loads. They have been used in a large number of applications ranging from astronomy to flight simulators and are becoming increasingly popular in the field of machine-tool industry. This book presents a complete synthesis of the latest results on the possible mechanical architectures, analysis and synthesis of this type of mechanism. It is intended to be used by students (with over 150 exercises and numerous internet addresses), researchers (with over 650 references and anonymous ftp access to the code of some algorithms presented in this book) and engineers (for which practical results, mistakes to avoid, and applications are presented). Since the publication of the first edition (2000) there has been an impressive increase in terms of study and use of this kind of structure that are reported in this book. This second edition has been completely overhauled. The initial chapter on kinematics has been split into Inverse Kinematics and Direct Kinematics. A new chapter on calibration was added. The other chapters have also been rewritten to a large extent. The reference section has been updated to include around 45 per cent new works that appeared after the first edition.
(source: Nielsen Book Data)

• Preface.
• 1. Introduction.
• 2. Architectures.
• 3. Jacobian and inverse kinematics.
• 4. Direct kinematics.
• 5. Singular configurations.
• 6. Workspace.
• 7. Velocity and Acceleration.
• 8. Static analysis.
• 9. Dynamics.
• 10. Design.
• 11. Conclusion. WEB addresses. Index. References.
• (source: Nielsen Book Data)

Parallel robots are closed-loop mechanisms offering very good performance in terms of accuracy, rigidity and ability to manipulate large loads. Parallel robots have been used in a wide variety of applications ranging from astronomy to flight simulators and are becoming increasingly popular in the machine-tool industry. This book presents a synthesis of results on the possible mechanical architectures, analysis and synthesis of this type of mechanism. It is intended to be used by students (with over 100 exercises and numerous Internet addresses), researchers (with over 500 references and anonymous ftp access to the code of some algorithms presented in this book) and engineers (for whom practical results and applications are presented).
(source: Nielsen Book Data)

This volume gathers the latest advances, innovations and applications in the field of cable robots, as presented by leading international researchers and engineers at the 6th International Conference on Cable-Driven Parallel Robots (CableCon), held in Nantes, France on June 25-28, 2023. It covers the theory and applications of cable-driven parallel robots, including their classification, kinematics and singularity analysis, workspace, statics and dynamics, cable modeling and technologies, control and calibration, design methodologies, hardware development, experimental evaluation and prototypes, as well as application reports and new application concepts. The contributions, which were selected through a rigorous international peer-review process, share exciting ideas that will spur novel research directions and foster new multidisciplinary collaborations.

• Synthesis Approach.- Structural Analysis.- Type Synthesis of Single-Loop Kinematic Chains.- Classification of Parallel Mechanisms.- Virtual-Chain Approach for the Type Synthesis of Parallel Mechanisms.- Case Studies.- Three-DOF PPP= Parallel Mechanisms.- Three-DOF S= Parallel Mechanisms.- Three-DOF PPR= Parallel Mechanisms.- Four-DOF PPPR= Parallel Mechanisms.- Four-DOF SP= Parallel Mechanisms.- Five-DOF US= Parallel Mechanisms.- Five-DOF PPPU= Parallel Mechanisms.- Five-DOF PPS= Parallel Mechanisms.- Parallel Mechanisms with a Parallel Virtual Chain.- Conclusions.
• (source: Nielsen Book Data)

This unique monograph focuses on the systematic type synthesis of parallel mechanisms (PMs), a key issue in the creative design of a wide variety of innovative devices such as parallel manipulators, motion simulators, and haptic devices. Essential reading for researchers, developers, engineers and graduate students with interests in robotics, this book covers the classification of PMs as well as providing a large number of PMs ready to be used in practical applications.
(source: Nielsen Book Data)

• Part I. Kinematics
• Efficient Kinematics of a 2-1 and 3-1 CDPR with Non-elastic Sagging Cables -- Kinematics of a 2-DOF Planar Suspended Cable-Driven Parallel Robot -- A New Performance Index for Underactuated Cable-Driven Parallel Robots -- CDPR Forward Kinematics with Error Covariance Bounds for Unconstrained End-Effector Attitude Parameterizations -- Neural Network-Based Inverse Kineto-Static Analysis of Cable-Driven Parallel Robot Considering Cable Mass and Elasticity -- Unsupervised Neural Network Based Forward Kinematics for Cable-Driven Parallel Robots with Elastic Cables -- Part II. Statics and Force Distribution -- Maximal Cable Tensions of a N-1 Cable-Driven Parallel Robot with Elastic or Ideal Cables -- Wrench Analysis of Kinematically Redundant Planar CDPRs -- Nonlinear Observer-Based Tension Distribution for Cable-Driven Parallel Robots -- A Practical Force Correction Method for Over-Constrained Cable-Driven Parallel Robots -- Force-Distribution Sensitivity to Cable-Tension Errors: A Preliminary Investigation -- Part III. Design -- Configuration Optimization of an Auto-Reconfigurable Cable-Driven Upper-Limb Rehabilitation Robot -- Design of a Docking System for Cable-Driven Parallel Robot to Allow Workspace Reconfiguration in Cluttered Environments --Multi Objective Optimization of a Cable-Driven Robot with Parallelogram Links -- Workspace Planning for In-Operation-Reconfiguration of Cable-Driven Parallel Robots -- Heuristic-Based Design Framework for the Cable Arrangement of Cable-Driven Parallel Robots -- Variable-Structure Cable-Driven Parallel Robots -- Part IV. Control -- An Emergency Strategy for Cable Failure in Reconfigurable Cable Robots -- Velocity Based Hybrid Position-Force Control of Cable Robots and Experimental Workspace Analysis -- Constrained Optimal Control of Cable-Driven Parallel Robots Based on SDRE -- Model-Based Control of a Planar 3-DoF Cable Robot Using Exact Linearization -- Motor Current Based Force Control of Simple Cable-Driven Parallel Robots -- Control Stability Workspace for a Cable-Driven Parallel Robot Controlled by Visual Servoing -- A Simple and Efficient Non-model Based Cable Tension Control -- Modeling and Observer-Based Control of a Planar Two-Cable Crane Manipulator -- Part V. Calibration and Performance Improvement -- Path Following Demonstration of a Hybrid Cable-Driven Parallel Robot -- Development of an Active End Effector for Cable Robot Calibration -- Accuracy Improvement for CDPRs Based on Direct Cable Length Measurement Sensors -- Development of Safety Concepts for Cable-Driven Parallel Robots -- Part VI. Applications -- Evaluation of a Cable-Driven Parallel Robot: Accuracy, Repeatability and Long-Term Running -- Under Constrained Cable-Driven Parallel Robot for Vertical Green Maintenance -- Real-World Development of a Cleaning CDPR for Primary Lamella Sedimentation Tanks -- Cable-Driven Robot to Simulate the Buoyancy Force for Improvingthe Performance of Underwater Robots.

This volume gathers the latest advances, innovations and applications in the field of cable robots, as presented by leading international researchers and engineers at the 5th International Conference on Cable-Driven Parallel Robots (CableCon 2021), held as virtual event on July 7-9, 2021. It covers the theory and applications of cable-driven parallel robots, including their classification, kinematics and singularity analysis, workspace, statics and dynamics, cable modeling and technologies, control and calibration, design methodologies, hardware development, experimental evaluation and prototypes, as well as application reports and new application concepts. The contributions, which were selected through a rigorous international peer-review process, share exciting ideas that will spur novel research directions and foster new multidisciplinary collaborations.
(source: Nielsen Book Data)

• Introduction What Is a Robot? Robot Components Robot Degrees-of-Freedom Robot Classification The Aims and Scope of This Book Motion Representation Spatial Motion Representation Motion of a Rigid Body Homogeneous Transformations Problems Kinematics Introduction Loop Closure Method Kinematic Analysis of a Planar Manipulator Kinematic Analysis of Shoulder Manipulator Kinematic Analysis of Stewart-Gough Platform Problems Jacobians: Velocities and Static Forces Introduction Angular and Linear Velocities Jacobian Matrices of a Parallel Manipulator Velocity Loop Closure Singularity Analysis of Parallel Manipulators Jacobian Analysis of a Planar Manipulator Jacobian Analysis of Shoulder Manipulator Jacobian Analysis of the Stewart-Gough Platform Static Forces in Parallel Manipulators Stiffness Analysis of Parallel Manipulators Problems Dynamics Introduction Dynamics of Rigid Bodies: A Review Newton-Euler Formulation Virtual Work Formulation Lagrange Formulation Problems Motion Control Introduction Controller Topology Motion Control in Task Space Robust and Adaptive Control Motion Control in Joint Space Summary of Motion Control Techniques Redundancy Resolution Motion Control of a Planar Manipulator Motion Control of the Stewart-Gough Platform Problems Force Control Introduction Controller Topology Stiffness Control Direct Force Control Impedance Control Problems Appendix: Linear Algebra Vectors and Matrices Vector and Matrix Operations Eigenvalues and Singular Values Pseudo-Inverse Kronecker Product Appendix: Trajectory Planning Point-to-Point Motion Specified Path with Via Points Appendix: Nonlinear Control Review Dynamical Systems Stability Definitions Lyapunov Stability Krasovskii-Lasalle Theorem References Index.
• (source: Nielsen Book Data)

• Introduction. Motion Representation. Kinematics. Jacobians: Velocities and Static Forces. Dynamics. Motion Control. Force Control. Appendix A: Linear Algebra. Appendix B: Trajectory Planning. Appendix C: Nonlinear Control Review. References. Index.
• (source: Nielsen Book Data)

Parallel structures are more effective than serial ones for industrial automation applications that require high precision and stiffness, or a high load capacity relative to robot weight. Although many industrial applications have adopted parallel structures for their design, few textbooks introduce the analysis of such robots in terms of dynamics and control. Filling this gap, Parallel Robots: Mechanics and Control presents a systematic approach to analyze the kinematics, dynamics, and control of parallel robots. It brings together analysis and design tools for engineers and researchers who want to design and implement parallel structures in industry. Covers Kinematics, Dynamics, and Control in One Volume The book begins with the representation of motion of robots and the kinematic analysis of parallel manipulators. Moving beyond static positioning, it then examines a systematic approach to performing Jacobian analysis. A special feature of the book is its detailed coverage of the dynamics and control of parallel manipulators. The text examines dynamic analysis using the Newton-Euler method, the principle of virtual work, and the Lagrange formulations. Finally, the book elaborates on the control of parallel robots, considering both motion and force control. It introduces various model-free and model-based controllers and develops robust and adaptive control schemes. It also addresses redundancy resolution schemes in detail. Analysis and Design Tools to Help You Create Parallel Robots In each chapter, the author revisits the same case studies to show how the techniques may be applied. The case studies include a planar cable-driven parallel robot, part of a promising new generation of parallel structures that will allow for larger workspaces. The MATLAB (R) code used for analysis and simulation is available online. Combining the analysis of kinematics and dynamics with methods of designing controllers, this text offers a holistic introduction for anyone interested in designing and implementing parallel robots.
(source: Nielsen Book Data)
Parallel structures are more effective than serial ones for industrial automation applications that require high precision and stiffness, or a high load capacity relative to robot weight. Although many industrial applications have adopted parallel structures for their design, few textbooks introduce the analysis of such robots in terms of dynamics.
(source: Nielsen Book Data)

• Fully-parallel topologies with coupled Schönflies motions
• Overactuated topologies with coupled Schönflies motions
• Fully-parallel topologies with decoupled Schönflies motions
• Topologies with uncoupled Schönflies motions
• Maximally regular topologies with Schönflies motions.

This book represents the fifth part of a larger work dedicated to the structural synthesis of parallel robots. The originality of this work resides in the fact that it combines new formulae for mobility, connectivity, redundancy and overconstraints with evolutionary morphology in a unified structural synthesis approach that yields interesting and innovative solutions for parallel robotic manipulators. This is the first book on robotics that presents solutions for coupled, decoupled, uncoupled, fully-isotropic and maximally regular robotic manipulators with Schönflies motions systematically generated by using the structural synthesis approach proposed in Part 1. Overconstrained non-redundant/overactuated/redundantly actuated solutions with simple/complex limbs are proposed. Many solutions are presented here for the first time in the literature. The author had to make a difficult and challenging choice between protecting these solutions through patents and releasing them directly into the public domain. The second option was adopted by publishing them in various recent scientific publications and above all in this book. In this way, the author hopes to contribute to a rapid and widespread implementation of these solutions in future industrial products.

• Part 1. Motion Planning
• Global Planning of Dynamically Feasible Trajectories for Three-DOF Spatial Cable-Suspended Parallel Robots / Clément Gosselin
• Experimental Validation of a Trajectory Planning Approach Avoiding Cable Slackness and Excessive Tension in Underconstrained Translational Planar Cable-Driven Robots / Alberto Trevisani
• Time-Energy Optimal Trajectory Planning of Cable-Suspended Manipulators / Mahdi Bamdad
• Navigating the Wrench-Feasible C-Space of Cable-Driven Hexapods / Oriol Bohigas, Montserrat Manubens and Lluís Ros.

• Part 2. Force Distribution
• A Tension Distribution Method with Improved Computational Efficiency / Johann Lamaury and Marc Gouttefarde
• Optimal Force Distribution Based on Slack Rope Model in the Incompletely Constrained Cable-Driven Parallel Mechanism of FAST Telescope / Hui Li, Xinyu Zhang, Rui Yao, Jinghai Sun and Gaofeng Pan, et al.
• Investigation of the Influence of Elastic Cables on the Force Distribution of a Parallel Cable-Driven Robot / Werner Kraus, Philipp Miermeister and Andreas Pott.

• Part 3. Application and Protoypes
• IPAnema: A family of Cable-Driven Parallel Robots for Industrial Applications / Andreas Pott, Hendrick Mütherich, Werner Kraus, Valentine Schmidt and Philipp Miermeister, et al.
• A Reconfigurable Robot for Cable-Driven Parallel Robotic Research and Industrial Scenario Proofing / Jean-Baptiste Izard, Marc Gouttefarde, Micaël Michelin, Olivier Tempier and Cedric Baradat
• Integration of a Parallel Cable-Driven Robot on an Existing Building Façade / Jean-Baptiste Izard, Marc Gouttefarde, Cedric Baradat, David Culla and Damien Sallé.

• Part 4. Design and Components
• Use of Passively Guided Deflection Units and Energy-Storing Elements to Increase the Application Range of Wire Robots / Joachim von Zitzewitz, Lisa Fehlberg, Tobias Bruckmann and Heike Vallery
• Use of High Strength Fibre Ropes in Multi-Rope Kinematic Robot Systems / Jens C. Weis, Björn Ernst and Karl -Heinz Wehking
• Workspace Improvement of Two-Link Cable-Driven Mechanisms with Spring Cable / Amir Taghavi, Saeed Behzadipour, Navid Khalilinasab and Hassen Zohoor
• The Constant-Orientation Dimensional Synthesis of Planar Cable-Driven Parallel Mechanisms Through Convex Relaxations / Kaveh Azizian and Philippe Cardou.

• Part 5. Kinematics and Interval Methods
• Feasible Kinematic Sensitivity in Cable Robots Based on Interval Analysis / Seyed Ahmad Khalilpour, Azadeh Zarif Loloei, Hamid D. Taghirad and Mehdi Tale Masouleh
• Solving the Direct Geometrico-Static Problem of 3-3 Cable-Driven Parallel Robots by Interval Analysis: Preliminary Results / Alessandro Berti, Jean-Pierre Merlet and Marco Carricato
• Direct Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with 4 Cables / Marco Carricato and Ghasem Abbasnejad
• Implementing Extended Kinematics of a Cable-Driven Parallel Robot in Real-Time / Valentin Schmidt and Andreas Pott.

• Part 6. Calibration und Identification
• An Identification Methodology for 6-DoF Cable-Driven Parallel Robots Parameters Application to the INCA 6D Robot / Ryad Chellal, Edouard Laroche, Loïc Cuvillon and Jacques Gangloff
• Differential Kinematics for Calibration, System Investigation, and Force Based Forward Kinematics of Cable-Driven Parallel Robots / Philipp Miermeister, Werner Kraus and Andreas Pott.

• Part 8. Dynamics Modelling
• Geometric Stiffness Analysis of Wire Robots: A Mechanical Approach / Dragoljub Surdilovic, Jelena Radojicic and Jörg Krüger
• Stiffness Analysis of a Planar 2-DoF Cable-Suspended Mechanism While Considering Cable Mass / Marc Arsenault
• A Modeling Method of the Cable Driven Parallel Manipulator for FAST / Rui Yao, Hui Li and Xinyu Zhang
• Cable Vibration Analysis for Large Workspace Cable-Driven Parallel Manipulators / Jingli Du, Wen Ding and Hong Bao.

• Part 8. Control
• Experimental Performance of Robust PID Controller on a Planar Cable Robot / Mohammad A. Khosravi and Hamid D. Taghirad
• A Preliminary Study for H Control of Parallel Cable-Driven Manipulators / Edouard Laroche, Ryad Chellal, Loïc Cuvillon and Jacques Gangloff
• Trajectory Tracking for a Three-Cable Suspension Manipulator by Nonlinear Feedforward and Linear Feedback Control / Christoph Woernle.

This publication presents the outcome of the "First International Conference on Cable-Driven Parallel Robots" in 2012. This is the first conference to bring together the cable robot community and dedicate a forum for the international experts of this field. It contains the Know-how, ideas and experiences of active researchers developing cable-driven robots. The book presents the state of the art, including summarizing contributions and latest research results and, where relevant, the future outlook. The book covers the essential topics for cable-driven robots: classification and definition, kinematics, workspace analysis, cable modeling, control and calibration, design methodology, hardware/prototype development, experimental evaluation, application reports and new application concepts

• Introduction.- Classification and Architecture.- Geometric and Static Foundations.- Kinematic Codes.- Workspace.- Dynamics.- Kinematics with Nonstandard Cable Models.- Design.- Practice.
• (source: Nielsen Book Data)

Cable-driven parallel robots are a new kind of lightweight manipulators with excellent scalability in terms of size, payload, and dynamics capacities. For the first time, a comprehensive compendium is presented of the field of cable-driven parallel robots. A thorough theory of cable robots is setup leading the reader from first principles to the latest results in research. The main topics covered in the book are classification, terminology, and fields of application for cable-driven parallel robots. The geometric foundation of the standard cable model is introduced followed by statics, force distribution, and stiffness. Inverse and forward kinematics are addressed by elaborating efficient algorithms. Furthermore, the workspace is introduced and different algorithms are detailed. The book contains the dynamic equations as well as simulation models with applicable parameters. Advanced cable models are described taking into account pulleys, elastic cables, and sagging cables. For practitioner, a descriptive design method is stated including methodology, parameter synthesis, construction design, component selection, and calibration. Rich examples are presented by means of simulation results from sample robots as well as experimental validation on reference demonstrators. The book contains a representative overview of reference demonstrator system. Tables with physical parameters for geometry, cable properties, and robot parameterizations support case studies and are valuable references for building custom cable robots. For scientist, the book provides the starting point to address new scientific challenges as open problems are named and a commented review of the literature on cable robot with more than 500 references are given.
(source: Nielsen Book Data)

• From the content:The forward kinematics of cable-driven parallel robots with sagging cables.- An Elastic Cable Model for Cable-Driven Parallel Robots Including Hysteresis Effects.- On the Improvement of Cable Collision Detection Algorithms.- Experimental determination of the accuracy of a three-dof cable-suspended parallel robot performing dynamic trajectories.
• (source: Nielsen Book Data)

This volume presents the outcome of the second forum to cable-driven parallel robots, bringing the cable robot community together. It shows the new ideas of the active researchers developing cable-driven robots. The book presents the state of the art, including both summarizing contributions as well as latest research and future options. The book cover all topics which are essential for cable-driven robots: Classification Kinematics, Workspace and Singularity Analysis Statics and Dynamics Cable Modeling Control and Calibration Design Methodology Hardware Development Experimental Evaluation Prototypes, Application Reports and new Application concepts.
(source: Nielsen Book Data)

• Introduction
• Kinematic Geometry of the PnP Robots
• Differential Kinematics of the Robots
• Kinematic Performance Criteria
• Elastostatics and Stiffness
• Rigid Multibody Dynamics
• Robot Elastodynamics
• Design optimization of parallel PnP Robots.

This book discusses the parametric modeling, performance evaluation, design optimization and comparative study of the high-speed, parallel pick-and-place robots. It collects the modeling methodology, evaluation criteria and design guidelines for parallel PnP robots to provide a systematic analysis method for robotic developers. Furthermore, it gathers the research results previously scattered in many prestigious international journals and conference proceedings and methodically edits them and presents them in a unified form. The book is of interest to researchers, R&D engineers and graduate students in industrial parallel robotics who wish to learn the core principles, methods, algorithms, and applications.
(source: Nielsen Book Data)

• Review of Recent Advances on Reactionless Mechanisms and Parallel Robots.- Design of Reactionless Mechanisms without Counter-Rotations.- Design of Reactionless Linkages and Robots Equipped with Balancing Assur Groups.
• Design of Reactionless Planar Parallel Manipulators with Inertia Flywheel or With Base-Mounted Counter-Rotations.- Design of Reactionless Mechanisms with Counter-Rotary Counter-Masses.- Shaking Force and Shaking Moment Balancing of Six- and Eight-Bar Planar Mechanisms.- Synthesizing of Parallel Robots using Adjusting Kinematic Parameters Method.-Balancing of a 3 DOFs Parallel Manipulator.- Dynamic Balancing with Respect to a Given Trajectory.-Dynamic Balancing and Flexible Task Execution for Dynamic Bipedal Walking Machines.- Design of Reactionless Mechanisms Based on Constrained Optimization Procedure.- Optimization of Dynamically Balanced 4-Bar Linkages.- Balancing of Planar Mechanisms Having Imperfect Joints Using Neural Network-Genetic Algorithm (NN-GA) Approach.- Minimization of Shaking Force and Moment on a Four-Bar Mechanism Using Genetic Algorithm.- Optimal Balancing of the Robotic Manipulators.- Dynamics and Control of Planar, Translation and Spherical Parallel Manipulators.- Dynamic Modelling and Control of Balanced Parallel Mechanisms.-Controlled Biped Balanced Locomotion and Climbing.- D ynamic Balancing of Mobile Robots in Simulation and Real Environments.- Balancing Conditions of Planar and Spatial Mechanisms in the Algebraic Form.- Static Balancing of Articulated Wheeled Vehicles by Parallelogram- and Spring-based Compensation.
• (source: Nielsen Book Data)

This book covers the state-of-the-art technologies in dynamic balancing of mechanisms with minimum increase of mass and inertia. The synthesis of parallel robots based on the Decomposition and Integration concept is also covered in detail. The latest advances are described, including different balancing principles, design of reactionless mechanisms with minimum increase of mass and inertia, and synthesizing parallel robots. This is an ideal book for mechanical engineering students and researchers who are interested in the dynamic balancing of mechanisms and synthesizing of parallel robots. This book also: * Broadens reader understanding of the synthesis of parallel robots based on the Decomposition and Integration concept * Reinforces basic principles with detailed coverage of different balancing principles, including input torque balancing mechanisms * Reviews exhaustively the key recent research into the design of reactionless mechanisms with minimum increase of mass and inertia, such as the design of reactionless mechanisms with auxiliary parallelograms, the design of reactionless mechanisms with flywheels, and the design of reactionless mechanisms by symmetrical structure design.
(source: Nielsen Book Data)

• Synthesis Approach.- Structural Analysis.- Type Synthesis of Single-Loop Kinematic Chains.- Classification of Parallel Mechanisms.- Virtual-Chain Approach for the Type Synthesis of Parallel Mechanisms.- Case Studies.- Three-DOF PPP= Parallel Mechanisms.- Three-DOF S= Parallel Mechanisms.- Three-DOF PPR= Parallel Mechanisms.- Four-DOF PPPR= Parallel Mechanisms.- Four-DOF SP= Parallel Mechanisms.- Five-DOF US= Parallel Mechanisms.- Five-DOF PPPU= Parallel Mechanisms.- Five-DOF PPS= Parallel Mechanisms.- Parallel Mechanisms with a Parallel Virtual Chain.- Conclusions.
• (source: Nielsen Book Data)

This unique monograph focuses on the systematic type synthesis of parallel mechanisms (PMs), a key issue in the creative design of a wide variety of innovative devices such as parallel manipulators, motion simulators, and haptic devices. Essential reading for researchers, developers, engineers and graduate students with interests in robotics, this book covers the classification of PMs as well as providing a large number of PMs ready to be used in practical applications.
(source: Nielsen Book Data)

• Preface; Acknowledgements; List of abbreviations and notations; 1 Introduction; 1.1 Terminology; 1.1 Links, joints and kinematic chains; 1.2 Serial, parallel and hybrid robots; 1.2 Methodology of structural synthesis; 1.2.1 New formulae for mobility, connectivity, redundancy and overconstraint of parallel robots; 1.2.2 Evolutionary morphology approach; 1.2.3 Types of parallel robots with respect to motion coupling; 2 Parallel mechanisms with cylindrical motion of the moving platform; 2.1 T1R1-type parallel mechanisms with coupled cylindrical motion; 2.1.1 Overconstrained solutions.

• 2.1.2 Non overconstrained solutions2.2 T1R1-type parallel mechanisms with decoupled cylindrical motion; 2.2.1 Overconstrained solutions; 2.2.2 Non overconstrained solutions; 2.3 T1R1-type parallel mechanisms with uncoupled cylindrical motion; 2.3.1 Overconstrained solutions; 2.3.2 Non overconstrained solutions; 2.4 Maximally regular parallel mechanisms with cylindrical motion; 2.4.1 Overconstrained solutions; 2.4.2 Non overconstrained solutions; 3 Other T1R1-type parallel mechanisms; 3.1 T1R1-type parallel mechanisms with coupled motions; 3.1.1 Overconstrained solutions.

• 3.1.2 Non overconstrained solutions3.2 T1R1-type parallel mechanisms with decoupled motions; 3.2.1 Overconstrained solutions; 3.2.2 Non overconstrained solutions; 3.3 T1R1-type parallel mechanisms with uncoupled motions; 3.3.1 Overconstrained solutions; 3.3.2 Non overconstrained solutions; 3.4 Maximally regular T1R1-type parallel mechanisms; 3.4.1 Overconstrained solutions; 3.4.2 Non overconstrained solutions; 4 Parallel wrists with two degrees of freedom; 4.1 R2-type parallel wrists with coupled motions; 4.1.1 Overconstrained solutions; 4.1.2 Non overconstrained solutions.

• 4.2 R2-type parallel wrists with decoupled motions4.2.1 Overconstrained solutions; 4.2.2 Non overconstrained solutions; 4.3 R2-type parallel wrists with uncoupled motions; 4.3.1 Overconstrained solutions; 4.3.2 Non overconstrained solutions; 4.4 Maximally regular R2-type parallel wrists; 4.4.1 Overconstrained solutions; 4.4.2 Non overconstrained solutions; 5 T2R1-type overconstrained spatial parallel manipulators; 5.1 Overconstrained solutions with coupled motions; 5.1.1 Fully-parallel solutions; 5.1.2 Non fully-parallel solutions; 5.2 Overconstrained solutions with decoupled motions.

• 5.2.1 Fully-parallel solutions5.2.2 Non fully-parallel solutions; 5.3 Overconstrained solutions with uncoupled motions; 5.3.1 Fully-parallel solutions; 5.3.2 Non fully-parallel solutions; 5.4 Overconstrained maximally regular solutions; 5.4.1 Fully-parallel solutions; 5.4.2 Non fully-parallel solutions; 6 Non overconstrained T2R1-type spatial parallel manipulators; 6.1 Non overconstrained solutions with coupled motions; 6.1.1 Fully-parallel solutions; 6.1.2 Non fully-parallel solutions; 6.2 Non overconstrained solutions with decoupled motions; 6.2.1 Fully-parallel solutions.

This book represents the fourth part of a larger work dedicated to the structural synthesis of parallel robots. Part 1 (Gogu 2008a) presented the methodology of structural synthesis and the systematisation of structural solutions of simple and complex limbs with two to six degrees of connectivity systematically generated by the structural synthesis approach. Part 2 (Gogu 2009a) presented structural solutions of translational parallel robotic manipulators with two and three degrees of mobility. Part 3 (Gogu 2010a) focussed on structural solutions of parallel robotic manipulators with planar mot.

• Part I Prerequisites
• 1 Generalities on parallel robots
• 1.1 Introduction
• 1.2 General definitions
• 1.3 Types of PKM architectures
• 1.4 Why a book dedicated to the dynamics of parallel robots?
• 2 Homogeneous transformation matrix
• 2.1 Homogeneous coordinates and homogeneous transformation matrix
• 2.2 Elementary transformation matrices
• 2.3 Properties of homogeneous transformation matrices
• 2.4 Parameterization of the general matrices of rotation
• 3 Representation of velocities and forces / acceleration of a body
• 3.1 Definition of a screw
• 3.2 Kinematic screw (or twist)
• 3.3 Representation of forces and moments (wrench)
• 3.4 Condition of reciprocity
• 3.5 Transformation matrix between twists
• 3.6 Transformation matrix between wrenches
• 3.7 Acceleration of a body
• 4 Kinematic parameterizing of multibody systems
• 4.1 Kinematic pairs and joint variables
• 4.2 Modified Denavit-Hartenberg parameters
• 5 Geometric, velocity and acceleration analysis of open kinematic chains
• 5.1 Geometric analysis of open kinematic chains
• 5.2 Velocity analysis of open kinematic chains
• 5.3 Acceleration analysis of open kinematic chains
• 6 Dynamics principles
• 6.1 The Lagrange formulation
• 6.2 The Newton-Euler equations
• 6.3 The principle of virtual powers
• 6.4 Computation of actuator input efforts under a wrench exerted on the end-effector
• Part II Dynamics of rigid parallel robots
• 7 Kinematics of parallel robots
• 7.1 Inverse geometric model
• 7.2 Forward geometric model
• 7.3 Velocity analysis
• 7.4 Acceleration analysis
• 7.5 Singularity analysis
• 8 Dynamic modeling of parallel robots
• 8.1 Introduction
• 8.2 Dynamics of tree-structure robots
• 8.3 Dynamic model of the free moving platform
• 8.4 Inverse and direct dynamic models of non-redundant parallel robots
• 8.5 Inverse and direct dynamic models of parallel robots with actuation redundancy
• 8.6 Other models
• 8.7 Computation of the base dynamic parameters
• 9 Analysis of the degeneracy conditions for the dynamic model of parallel robots
• 9.1 Introduction
• 9.2 Analysis of the degeneracy conditions of the IDM of PKM
• 9.3 Avoiding infinite input efforts while crossing Type 2 or LPJTS singularities thanks to an optimal trajectory planning
• 9.4 Example 1: the five-bar mechanism crossing a Type 2 singularity
• 9.5 Example 2: the Tripterion crossing a LPJTS singularity
• 9.6 Discussion
• Part III Dynamics of flexible parallel robots
• 10 Elastodynamic modeling of parallel robots
• 10.1 Introduction
• 10.2 Generalized Newton-Euler equations of a flexible link
• 10.2.3 Matrix form of the generalized Newton-Euler model for a flexible clamped-free body
• 10.3 Dynamic model of virtual flexible systems
• 10.4 Dynamic model of a flexible parallel robot
• 10.5 Including the actuator elasticity
• 10.6 Practical implementation of the algorithm
• 10.7 Case Study: the DualEMPS
• 11 Computation of natural frequencies
• 11.1 Introduction
• 11.2 Stiffness and inertia matrices of the virtual system
• 11.3 Stiffness and inertia matrices of the PKM
• 11.4 Including the actuator elasticity
• 11.5 Practical implementation of the algorithm
• 11.6 Case Studies
• 11.7 Conclusion
• Appendices
• A Calculation of the number of degrees of freedom of robots with closed chains
• A.1 Introduction
• A.2 Moroskine's Method
• A.3 Gogu's Method
• A.4 Examples
• B Lagrange equations with multipliers
• C Computation of wrenches reciprocal to a system of twists
• C.1 Definitions
• C.2 Condition of reciprocity
• C.3 Computation of wrenches reciprocal to a system of twists constrained in a plane
• C.4 Computation of wrenches reciprocal to other types of twist systems
• D Point-to-point trajectory generation
• E Calculation of the terms facc1, facc2 and facc3 in Chapter 10
• E.1 Calculation of the term facc1
• E.2 Calculation of the term facc2
• E.3 Calculation of the term facc3
• F Dynamics equations for a clamped-free flexible beam
• F.1 Shape functions for a free flexible beam
• F.2 Stiffness matrix for a free flexible beam
• F.3 Evaluation of the inertia matrix of a free flexible 3D Bernoulli beam for qe j = 0
• References
• Index.

This book starts with a short recapitulation on basic concepts, common to any types of robots (serial, tree structure, parallel, etc.), that are also necessary for computation of the dynamic models of parallel robots. Then, as dynamics requires the use of geometry and kinematics, the general equations of geometric and kinematic models of parallel robots are given. After, it is explained that parallel robot dynamic models can be obtained by decomposing the real robot into two virtual systems: a tree-structure robot (equivalent to the robot legs for which all joints would be actuated) plus a free body corresponding to the platform. Thus, the dynamics of rigid tree-structure robots is analyzed and algorithms to obtain their dynamic models in the most compact form are given. The dynamic model of the real rigid parallel robot is obtained by closing the loops through the use of the Lagrange multipliers. The problem of the dynamic model degeneracy near singularities is treated and optimal trajectory planning for crossing singularities is proposed. Lastly, the approach is extended to flexible parallel robots and the algorithms for computing their symbolic model in the most compact form are given. All theoretical developments are validated through experiments.