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E-raamat: Dynamics of Parallel Robots: From Rigid Bodies to Flexible Elements

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  • Formaat: PDF+DRM
  • Sari: Mechanisms and Machine Science 35
  • Ilmumisaeg: 22-Jun-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319197883
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Dynamics of Parallel Robots: From Rigid Bodies to Flexible ElementsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Mechanisms and Machine Science 35
  • Ilmumisaeg: 22-Jun-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319197883
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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.

Arvustused

The present book, based on results published by many authors as well as by the two authors of the book over the last fifteen years, treats some special problems on the dynamics of parallel robots from rigid bodies to flexible elements . the intended audience for it consists of researchers, scientists and engineers, as well as master and PhD students interested in the theory and applications of parallel robots. (Clementina Mladenova, zbMATH 1369.68001, 2017)

Part I Prerequisites
1 Generalities on Parallel Robots
3(16)
1.1 Introduction
3(3)
1.2 General Definitions
6(3)
1.3 Types of PKM Architectures
9(6)
1.3.1 Planar Motions of the Platform
9(1)
1.3.2 Spatial Motions of the Platform
10(3)
1.3.3 Redundant PKM
13(1)
1.3.4 Other Types of PKM
14(1)
1.4 Why a Book Dedicated to the Dynamics of Parallel Robots?
15(4)
2 Homogeneous Transformation Matrix
19(14)
2.1 Homogeneous Coordinates and Homogeneous Transformation Matrix
19(2)
2.2 Elementary Transformation Matrices
21(1)
2.2.1 Transformation Matrix of a Pure Translation
21(1)
2.2.2 Transformation Matrices of a Rotation About the Principle Axes x, y and z
21(1)
2.3 Properties of Homogeneous Transformation Matrices
22(2)
2.4 Parameterization of the General Matrices of Rotation
24(9)
2.4.1 Rotation About One General Axis u
24(2)
2.4.2 Quaternions
26(1)
2.4.3 Euler Angles
27(2)
2.4.4 Roll-Pitch-Yaw Angles
29(2)
2.4.5 Tilt-and-Torsion Angles
31(2)
3 Representation of Velocities and Forces/Acceleration of a Body
33(6)
3.1 Definition of a Screw
33(1)
3.2 Kinematic Screw (or Twist)
33(1)
3.3 Representation of Forces and Moments (wrench)
34(1)
3.4 Condition of Reciprocity
34(1)
3.5 Transformation Matrix Between Twists
35(1)
3.6 Transformation Matrix Between Wrenches
36(1)
3.7 Acceleration of a Body
36(3)
4 Kinematic Description of Multibody Systems
39(12)
4.1 Kinematic Pairs and Joint Variables
39(1)
4.2 Modified Denavit-Hartenberg Parameters
40(11)
4.2.1 Parameterizing Tree-Structure Open Kinematic Chains
41(3)
4.2.2 Parameterizing Kinematic Chains Including Closed Loops
44(3)
4.2.3 Computation of the Homogeneous Transformation Matrix Representing the Location of the Frame Fk with Respect to the Frame Fi
47(4)
5 Geometric, Velocity and Acceleration Analysis of Open Kinematic Chains
51(10)
5.1 Geometric Analysis of Open Kinematic Chains
51(1)
5.1.1 Direct Geometric Model of Open Kinematic Chains
51(1)
5.1.2 Inverse Geometric Model of Open Kinematic Chains
52(1)
5.2 Velocity Analysis of Open Kinematic Chains
52(6)
5.2.1 Forward Kinematic Models
52(3)
5.2.2 Inverse Kinematic Models
55(1)
5.2.3 Inverse Kinematic Models Degeneracy/Notions of Singularity
56(1)
5.2.4 Recursive Computation of Velocities and Kinematic Jacobian Matrix for Open Kinematic Chains
57(1)
5.3 Acceleration Analysis of Open Kinematic Chains
58(3)
6 Dynamics Principles
61(14)
6.1 The Lagrange Formulation
61(6)
6.1.1 Introduction to the Lagrange Formulation
61(1)
6.1.2 Computation of Kinetic Energy
62(2)
6.1.3 Computation of Potential Energy
64(1)
6.1.4 Lagrange Equations with Constraints
65(1)
6.1.5 Dynamic Model Properties
66(1)
6.2 The Newton-Euler Equations
67(1)
6.3 The Principle of Virtual Powers
68(2)
6.4 Computation of Actuator Input Efforts Under a Wrench Exerted on the End-Effector
70(5)
Part II Dynamics of Rigid Parallel Robots
7 Kinematics of Parallel Robots
75(64)
7.1 Inverse Geometric Model
75(17)
7.1.1 General Methodology
75(5)
7.1.2 Examples
80(12)
7.2 Forward Geometric Model
92(13)
7.2.1 General Methodology
92(2)
7.2.2 Examples
94(7)
7.2.3 Assembly Mode Selection and Numerical Methods for Solving the FGM
101(4)
7.3 Velocity Analysis
105(16)
7.3.1 Computation of the Kinematic Constraint Relations
105(2)
7.3.2 Kinematic Models
107(4)
7.3.3 Computation of the Passive Joint Velocities
111(2)
7.3.4 Examples
113(8)
7.4 Acceleration Analysis
121(7)
7.4.1 Kinematic Constraint Relations of the Second Order
121(1)
7.4.2 Forward and Inverse Second-Order Kinematic Models
122(3)
7.4.3 Computation of the Passive Joint Accelerations
125(2)
7.4.4 Examples
127(1)
7.5 Singularity Analysis
128(11)
7.5.1 Input-Output Singularities
128(2)
7.5.2 Serial Singularities
130(2)
7.5.3 Other Types of Singularities
132(1)
7.5.4 Finding Robot Singular Configurations
133(3)
7.5.5 Finding Robot Serial Singular Configurations
136(1)
7.5.6 Examples
137(2)
8 Dynamic Modeling of Parallel Robots
139(62)
8.1 Introduction
139(4)
8.2 Dynamics of Tree-Structure Robots
143(10)
8.2.1 Newton-Euler Formulation for Computation of the Inverse Dynamic Model
143(4)
8.2.2 Considering the Inertia of Actuators
147(1)
8.2.3 Considering Friction
147(2)
8.2.4 Computing the Vector of Coriolis, Centrifugal, Gravity Effects, Friction and External Wrenches
149(1)
8.2.5 Computing the Inertia Matrix
149(3)
8.2.6 Automatic Computation of the IDM, Inertia Matrix and Vector of Coriolis, Centrifugal/Gravity/Friction Effects
152(1)
8.3 Dynamic Model of the Free Moving Platform
153(1)
8.4 Inverse and Direct Dynamic Models of Non-redundant Parallel Robots
153(19)
8.4.1 Inverse Dynamic Model
154(5)
8.4.2 Direct Dynamic Model
159(3)
8.4.3 Examples
162(10)
8.5 Inverse and Direct Dynamic Models of Parallel Robots with Actuation Redundancy
172(11)
8.5.1 Inverse Dynamic Model
172(3)
8.5.2 Direct Dynamic Model
175(3)
8.5.3 Example: The DualV
178(5)
8.6 Other Models
183(6)
8.6.1 Computation of the Ground Reactions of PKM
183(4)
8.6.2 Energy Models of PKM
187(2)
8.7 Computation of the Base Dynamic Parameters
189(12)
8.7.1 Expressing the Dynamic Model Linearly as a Function of the Standard Dynamic Parameters
190(1)
8.7.2 Linearity of the Energy w.r.t. the Inertial Parameters
190(3)
8.7.3 Linearity of the IDM w.r.t. the Dynamic Parameters
193(2)
8.7.4 Numerical Method Based on a QR Decomposition
195(3)
8.7.5 Examples
198(3)
9 Analysis of the Degeneracy Conditions for the Dynamic Model of Parallel Robots
201(36)
9.1 Introduction
201(2)
9.2 Analysis of the Degeneracy Conditions of the IDM of PKM
203(2)
9.2.1 Degeneracy Conditions of the IDM Due to the Matrix Ar
204(1)
9.2.2 Degeneracy Conditions of the IDM Due to the Matrix Jtd
204(1)
9.3 Avoiding Infinite Input Efforts While Crossing Type 2 or LPJTS Singularities Thanks to an Optimal Trajectory Planning
205(6)
9.3.1 Optimal Trajectory Planning Through Type 2 Singularities
205(2)
9.3.2 Optimal Trajectory Planning Through LPJTS Singularities
207(4)
9.4 Example 1: The Five-Bar Mechanism Crossing a Type 2 Singularity
211(5)
9.4.1 Trajectory Planning Through the Type 2 Singularities
211(2)
9.4.2 Simulations and Experimental Results
213(3)
9.5 Example 2: The Tripterion Crossing a LPJTS Singularity
216(16)
9.5.1 Geometric Description of the Tripteron
216(2)
9.5.2 Kinematics of the Tripteron
218(5)
9.5.3 Full IDM of the Tripteron
223(1)
9.5.4 Trajectory Planning Through the LPJTS Singularities
224(2)
9.5.5 Simulations and Experimental Results
226(6)
9.6 Discussion
232(5)
Part III Dynamics of Flexible Parallel Robots
10 Elastodynamic Modeling of Parallel Robots
237(42)
10.1 Introduction
237(3)
10.2 Generalized Newton-Euler Equations of a Flexible Link
240(14)
10.2.1 Geometry and First-Order Kinematics of a Clamped-Free Flexible Body
240(2)
10.2.2 Computation of the Elastodynamic Model of the Flexible Free Body Using the PVP
242(10)
10.2.3 Matrix Form of the Generalized Newton-Euler Model for a Flexible Clamped-Free Body
252(2)
10.3 Dynamic Model of Virtual Flexible Systems
254(7)
10.3.1 Application of the PVP
254(1)
10.3.2 Recursive Computation of Velocities and Jacobian Matrices
255(2)
10.3.3 Recursive Computation of the Accelerations
257(3)
10.3.4 Elastodynamic Model of the Virtual System
260(1)
10.4 Dynamic Model of a Flexible Parallel Robot
261(5)
10.4.1 Determination of the Joint and Platform Velocities as a Function of the Generalized Velocities q of the Parallel Robot
261(3)
10.4.2 Determination of Joint and Platform Accelerations as a Function of the Generalized Accelerations q of the Parallel Robot
264(1)
10.4.3 Elastodynamic Model of the Actual Parallel Robot
265(1)
10.5 Including the Actuator Elasticity
266(1)
10.6 Practical Implementation of the Algorithm
267(2)
10.7 Case Study: The DualEMPS
269(10)
11 Computation of Natural Frequencies
279(20)
11.1 Introduction
279(1)
11.2 Stiffness and Inertia Matrices of the Virtual System
280(5)
11.2.1 Kinetic Energy and Elastic Potential Energy of the Body Bij
281(1)
11.2.2 Kinetic Energy and Elastic Potential Energy of the Virtual Tree Structure
282(1)
11.2.3 Kinetic Energy of the Free Moving Platform
283(1)
11.2.4 Introducing the Actuator Inertia Effects
284(1)
11.3 Stiffness and Inertia Matrices of the PKM
285(2)
11.4 Including the Actuator Elasticity
287(1)
11.5 Practical Implementation of the Algorithm
288(1)
11.6 Case Studies
289(7)
11.6.1 Natural Frequencies of DualEMPS
289(1)
11.6.2 Natural Frequencies of the NaVARo
290(6)
11.7 Conclusion
296(3)
Appendix A Calculation of the Number of Degrees of Freedom of Robots with Closed Chains 299(8)
Appendix B Lagrange Equations with Multipliers 307(2)
Appendix C Computation of Wrenches Reciprocal to a System of Twists 309(10)
Appendix D Point-to-Point Trajectory Generation 319(2)
Appendix E Calculation of the Terms facc1, facc2 and facc3 in
Chapter 10		 321(8)
Appendix F Dynamics Equations for a Clamped-Free Flexible Beam 329(4)
References 333(14)
Index 347
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