The Resource Dynamics of parallel robots : from rigid bodies to flexible elements, Seb́astien Briot, Wisama Khalil
Dynamics of parallel robots : from rigid bodies to flexible elements, Seb́astien Briot, Wisama Khalil
 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 treestructure 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 treestructure 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
 Language
 eng
 Extent
 xvii, 350 pages
 Contents

 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 DenavitHartenberg 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 NewtonEuler equations
 6.3 The principle of virtual powers
 6.4 Computation of actuator input efforts under a wrench exerted on the endeffector
 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 treestructure robots
 8.3 Dynamic model of the free moving platform
 8.4 Inverse and direct dynamic models of nonredundant 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 fivebar 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 NewtonEuler equations of a flexible link
 10.2.3 Matrix form of the generalized NewtonEuler model for a flexible clampedfree 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 Pointtopoint 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 clampedfree 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
 Isbn
 9783319197876
 Label
 Dynamics of parallel robots : from rigid bodies to flexible elements
 Title
 Dynamics of parallel robots
 Title remainder
 from rigid bodies to flexible elements
 Statement of responsibility
 Seb́astien Briot, Wisama Khalil
 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 treestructure 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 treestructure 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
 Cataloging source
 BTCTA
 Dewey number
 629.8/92
 Index
 no index present
 Literary form
 non fiction
 Series statement
 Mechanisms and machine science
 Series volume
 volume 35
 Label
 Dynamics of parallel robots : from rigid bodies to flexible elements, Seb́astien Briot, Wisama Khalil
 Bibliography note
 Includes bibliographical references and index
 http://library.link/vocab/branchCode

 zbnus
 glg
 Carrier category
 online resource
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 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 DenavitHartenberg 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 NewtonEuler equations  6.3 The principle of virtual powers  6.4 Computation of actuator input efforts under a wrench exerted on the endeffector  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 treestructure robots  8.3 Dynamic model of the free moving platform  8.4 Inverse and direct dynamic models of nonredundant 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 fivebar 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 NewtonEuler equations of a flexible link  10.2.3 Matrix form of the generalized NewtonEuler model for a flexible clampedfree 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 Pointtopoint 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 clampedfree 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
 Control code
 ocn908374476
 Extent
 xvii, 350 pages
 Isbn
 9783319197876
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 http://library.link/vocab/recordID
 .b33206004
 System control number

 (OCoLC)908374476
 ci33206004
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