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The Resource Dynamics of Parallel Robots : From Rigid Bodies to Flexible Elements

Dynamics of Parallel Robots : From Rigid Bodies to Flexible Elements

Label
Dynamics of Parallel Robots : From Rigid Bodies to Flexible Elements
Title
Dynamics of Parallel Robots
Title remainder
From Rigid Bodies to Flexible Elements
Creator
Contributor
Subject
Language
eng
Summary
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
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Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Mechanisms and Machine Science Ser.
Series volume
v.35
Dynamics of Parallel Robots : From Rigid Bodies to Flexible Elements
Label
Dynamics of Parallel Robots : From Rigid Bodies to Flexible Elements
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=2120669
Publication
Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • "Preface" -- "Contents" -- "Symbols and Abbreviations" -- "Part I Prerequisites " -- "1 Generalities on Parallel Robots" -- "1.1 Introduction" -- "1.2 General Definitions" -- "1.3 Types of PKM Architectures" -- "1.3.1 Planar Motions of the Platform" -- "1.3.2 Spatial Motions of the Platform" -- "1.3.3 Redundant PKM" -- "1.3.4 Other Types of PKM" -- "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" -- "2.2.1 Transformation Matrix of a Pure Translation" -- "2.2.2 Transformation Matrices of a Rotation About the Principle Axes x, y and z" -- "2.3 Properties of Homogeneous Transformation Matrices" -- "2.4 Parameterization of the General Matrices of Rotation" -- "2.4.1 Rotation About One General Axis u" -- "2.4.2 Quaternions" -- "2.4.3 Euler Angles" -- "2.4.4 Roll-Pitch-Yaw Angles" -- "2.4.5 Tilt-and-Torsion Angles" -- "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 Description of Multibody Systems" -- "4.1 Kinematic Pairs and Joint Variables" -- "4.2 Modified Denavit-Hartenberg Parameters" -- "4.2.1 Parameterizing Tree-Structure Open Kinematic Chains" -- "4.2.2 Parameterizing Kinematic Chains Including Closed Loops" -- "4.2.3 Computation of the Homogeneous Transformation Matrix Representing the Location of the Frame mathcalFk with Respect to the Frame mathcalFi" -- "5 Geometric, Velocity and Acceleration Analysis of Open Kinematic Chains"
  • "5.1 Geometric Analysis of Open Kinematic Chains" -- "5.1.1 Direct Geometric Model of Open Kinematic Chains" -- "5.1.2 Inverse Geometric Model of Open Kinematic Chains" -- "5.2 Velocity Analysis of Open Kinematic Chains" -- "5.2.1 Forward Kinematic Models" -- "5.2.2 Inverse Kinematic Models" -- "5.2.3 Inverse Kinematic Models Degeneracy/Notions of Singularity" -- "5.2.4 Recursive Computation of Velocities and Kinematic Jacobian Matrix for Open Kinematic Chains" -- "5.3 Acceleration Analysis of Open Kinematic Chains" -- "6 Dynamics Principles" -- "6.1 The Lagrange Formulation" -- "6.1.1 Introduction to the Lagrange Formulation" -- "6.1.2 Computation of Kinetic Energy" -- "6.1.3 Computation of Potential Energy" -- "6.1.4 Lagrange Equations with Constraints" -- "6.1.5 Dynamic Model Properties" -- "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" -- "7.1.1 General Methodology" -- "7.1.2 Examples" -- "7.2 Forward Geometric Model" -- "7.2.1 General Methodology" -- "7.2.2 Examples" -- "7.2.3 Assembly Mode Selection and Numerical Methods for Solving the FGM" -- "7.3 Velocity Analysis" -- "7.3.1 Computation of the Kinematic Constraint Relations" -- "7.3.2 Kinematic Models" -- "7.3.3 Computation of the Passive Joint Velocities" -- "7.3.4 Examples" -- "7.4 Acceleration Analysis" -- "7.4.1 Kinematic Constraint Relations of the Second Order" -- "7.4.2 Forward and Inverse Second-Order Kinematic Models" -- "7.4.3 Computation of the Passive Joint Accelerations" -- "7.4.4 Examples" -- "7.5 Singularity Analysis" -- "7.5.1 Input-Output Singularities" -- "7.5.2 Serial Singularities" -- "7.5.3 Other Types of Singularities"
  • "7.5.4 Finding Robot Singular Configurations" -- "7.5.5 Finding Robot Serial Singular Configurations" -- "7.5.6 Examples" -- "8 Dynamic Modeling of Parallel Robots" -- "8.1 Introduction" -- "8.2 Dynamics of Tree-Structure Robots" -- "8.2.1 Newton-Euler Formulation for Computation of the Inverse Dynamic Model" -- "8.2.2 Considering the Inertia of Actuators" -- "8.2.3 Considering Friction" -- "8.2.4 Computing the Vector of Coriolis, Centrifugal, Gravity Effects, Friction and External Wrenches" -- "8.2.5 Computing the Inertia Matrix" -- "8.2.6 Automatic Computation of the IDM, Inertia Matrix and Vector of Coriolis, Centrifugal/Gravity/Friction Effects" -- "8.3 Dynamic Model of the Free Moving Platform" -- "8.4 Inverse and Direct Dynamic Models of Non-redundant Parallel Robots" -- "8.4.1 Inverse Dynamic Model" -- "8.4.2 Direct Dynamic Model" -- "8.4.3 Examples" -- "8.5 Inverse and Direct Dynamic Models of Parallel Robots with Actuation Redundancy" -- "8.5.1 Inverse Dynamic Model" -- "8.5.2 Direct Dynamic Model" -- "8.5.3 Example: The DualV" -- "8.6 Other Models" -- "8.6.1 Computation of the Ground Reactions of PKM" -- "8.6.2 Energy Models of PKM" -- "8.7 Computation of the Base Dynamic Parameters" -- "8.7.1 Expressing the Dynamic Model Linearly as a Function of the Standard Dynamic Parameters" -- "8.7.2 Linearity of the Energy w.r.t. the Inertial Parameters" -- "8.7.3 Linearity of the IDM w.r.t. the Dynamic Parameters" -- "8.7.4 Numerical Method Based on a QR Decomposition" -- "8.7.5 Examples" -- "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" -- "9.2.1 Degeneracy Conditions of the IDM Due to the Matrix Ar" -- "9.2.2 Degeneracy Conditions of the IDM Due to the Matrix Jtd"
  • "9.3 Avoiding Infinite Input Efforts While Crossing Type 2 or LPJTS Singularities Thanks to an Optimal Trajectory Planning" -- "9.3.1 Optimal Trajectory Planning Through Type 2 Singularities" -- "9.3.2 Optimal Trajectory Planning Through LPJTS Singularities" -- "9.4 Example 1: The Five-Bar Mechanism Crossing a Type 2 Singularity" -- "9.4.1 Trajectory Planning Through the Type 2 Singularities" -- "9.4.2 Simulations and Experimental Results" -- "9.5 Example 2: The Tripterion Crossing a LPJTS Singularity" -- "9.5.1 Geometric Description of the Tripteron" -- "9.5.2 Kinematics of the Tripteron" -- "9.5.3 Full IDM of the Tripteron" -- "9.5.4 Trajectory Planning Through the LPJTS Singularities" -- "9.5.5 Simulations and Experimental Results" -- "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" -- "10.2.1 Geometry and First-Order Kinematics of a Clamped-Free Flexible Body" -- "10.2.2 Computation of the Elastodynamic Model of the Flexible Free Body Using the PVP" -- "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" -- "10.3.1 Application of the PVP" -- "10.3.2 Recursive Computation of Velocities and Jacobian Matrices" -- "10.3.3 Recursive Computation of the Accelerations" -- "10.3.4 Elastodynamic Model of the Virtual System" -- "10.4 Dynamic Model of a Flexible Parallel Robot" -- "10.4.1 Determination of the Joint and Platform Velocities as a Function of the Generalized Velocities of the Parallel Robot" -- "10.4.2 Determination of Joint and Platform Accelerations as a Function of the Generalized Accelerations of the Parallel Robot" -- "10.4.3 Elastodynamic Model of the Actual 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" -- "11.2.1 Kinetic Energy and Elastic Potential Energy of the Body mathcalBij" -- "11.2.2 Kinetic Energy and Elastic Potential Energy of the Virtual Tree Structure" -- "11.2.3 Kinetic Energy of the Free Moving Platform" -- "11.2.4 Introducing the Actuator Inertia Effects" -- "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" -- "11.6.1 Natural Frequencies of DualEMPS" -- "11.6.2 Natural Frequencies of the NaVARo" -- "11.7 Conclusion" -- "Errata to: Dynamics of Parallel Robots" -- "Appendix A Calculation of the Number of Degreesof Freedom of Robots with Closed Chains " -- "Appendix B Lagrange Equations with Multipliers " -- "Appendix C Computation of Wrenches Reciprocalto a System of Twists " -- "Appendix D Point-to-Point Trajectory Generation " -- "Appendix E Calculation of the Terms facc1, facc2 and facc3in Chapter 10 " -- "Appendix F Dynamics Equations for a Clamped-FreeFlexible Beam " -- "References"
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Extent
1 online resource (356 pages)
Form of item
online
Isbn
9783319197883
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
unknown sound
Specific material designation
remote

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