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E-raamat: Sliding-rolling Contact And In-hand Manipulation

(King's College London, Uk), (Curtin Univ, Australia)
  • Formaat: 224 pages
  • Ilmumisaeg: 16-Mar-2020
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786348449
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Sliding-rolling Contact And In-hand ManipulationSuurem pilt
  • Formaat: 224 pages
  • Ilmumisaeg: 16-Mar-2020
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786348449
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Robots interact with the world through curves and surfaces the subjects of study in differential geometry. This book applies the moving-frame method, developed extensively by Élie Cartan, and the adjoint approach, conceived by Ernesto Cesàro, to study the kinematics of two surfaces subject to rolling contact and sliding-rolling contact to demonstrate the applications in robotic in-hand manipulation.Firstly, it explores two surfaces, and the geometry of both surfaces comes into play. Secondly, the book focuses on the geometry of the two surfaces within the encompassing space (extrinsic) rather than within the surfaces (intrinsic) because the book is concerned with the kinematics of one surface in three-dimensional Euclidean space the real world. The book then concludes by applying this approach in robotic in-hand manipulation in the last chapter.
Preface vii
About the Authors ix
1 Introduction
1(10)
1.1 A Brief History of Rolling-Sliding Contact and In-Hand Manipulation
1(5)
1.2 Outline of the Book
6(1)
1.2.1 Statement of the Problem
6(1)
1.2.2 Aims and Objectives
7(1)
1.3 Organization of the Book
8(3)
Part I The Moving-Frame Method and Adjoint Approach
11(72)
2 Curvatures of Curves and Surfaces via the Moving-Frame Method
13(42)
2.1 The Moving-Frame Method
13(2)
2.2 The Frenet Frame of an Oriented Curve
15(2)
2.3 The Arc Length and Curvature of a Curve
17(3)
2.4 The Torsion of a Curve
20(7)
2.5 Differential Geometry of Surfaces
27(1)
2.5.1 Parameterized Regular Surfaces
27(2)
2.5.2 The First Fundamental Form
29(2)
2.5.3 The Second Fundamental Form
31(2)
2.5.4 The Gauss-Weingarten Equations
33(2)
2.6 The Moving-Frame Method Along the Coordinate Curves
35(3)
2.7 The Moving-Frame Method Along an Arbitrary Curve
38(2)
2.8 The Darboux Frame and the Darboux Formulas of an Oriented Curve on a Surface
40(1)
2.9 Geometry of the Geodesic Curvature, Normal Curvature, and Geodesic Torsion
41(6)
2.10 The Curvatures of a Surface Curve in Terms of the Curvatures of the Coordinate Curves
47(6)
2.11 Conclusion
53(2)
3 The Adjoint Approach to Curves and Surfaces
55(28)
3.1 The Adjoint Approach to a Planar Curve
55(8)
3.2 The Fixed-Point Conditions and Roulettes
63(5)
3.3 The Adjoint Approach to a Spatial Curve
68(4)
3.4 The Adjoint Approach to a Surface Curve
72(1)
3.5 A Circular Surface with a Fixed Radius: The Surface Adjoint to a Curve
73(1)
3.5.1 Definition of a Circular Surface
73(3)
3.5.2 The Necessary and Sufficient Conditions for a Circular Surface to be a C'R Workspace Surface
76(5)
3.6 Conclusion
81(2)
Part II Forward Kinematics of Rolling---Sliding Contact
83(34)
4 From Trajectories to Velocity: Forward Kinematics of Rigid Surfaces with Rolling Contact
85(16)
4.1 Problem Definition
85(1)
4.2 Geometric Velocity of an Adjoint Point on the Moving Surface
86(1)
4.2.1 The Fixed-Point Conditions
87(1)
4.2.2 The Geometric Velocity of the Adjoint Point
88(2)
4.3 Angular Velocity of the Moving Surface
90(2)
4.4 Angular Velocity of Two Planar Laminas with Rolling Contact
92(1)
4.5 Reconciliation with a Classical Example
92(2)
4.6 Examples of Application
94(4)
4.7 Application to Qualitative Trajectory Analysis
98(1)
4.7.1 Trajectory Analysis of Pure-Rolling
98(1)
4.7.2 Trajectory Analysis Based on Shape Characteristics
99(1)
4.8 Conclusion
100(1)
5 From Trajectories to Velocity: Forward Kinematics of Rigid Surfaces with Rolling-Sliding Contact
101(16)
5.1 Problem Definition
101(2)
5.2 The Velocity of an Arbitrary Point on the Moving Surface
103(3)
5.3 The Velocity of the Moving Surface
106(2)
5.4 Rolling-Slipping Contact as a Special Case
108(1)
5.5 The Influence of the Instantaneous Imprint Curve on the Angular Velocity
109(2)
5.6 The Classical Problem Revisited
111(1)
5.6.1 Closed-Form Solution
111(2)
5.6.2 Numerical Simulation
113(1)
5.7 Example of Application
114(2)
5.8 Conclusion
116(1)
Part III Inverse Kinematics of Rolling-Sliding Contact
117(22)
6 From Velocity to Trajectories: Inverse Kinematics of Rigid Surfaces with Rolling Contact
119(14)
6.1 Problem Definition
119(1)
6.2 The Angular Velocity in Relation to Coordinate Curves
120(3)
6.3 Reconciliation with a Classical Example: A Unit Ball Rolling on a Plane
123(1)
6.3.1 A Closed-Form Solution
123(3)
6.3.2 The Classical Solution: A System of Differential Equations
126(1)
6.4 Examples of Application
127(1)
6.4.1 An Ellipsoid Rolling on a Plane
127(1)
6.4.2 A Unit Sphere Rolling on a Paraboloid
128(3)
6.5 Conclusion
131(2)
7 From Velocity to Trajectories: Inverse Kinematics of Rigid Surfaces with Rolling-Sliding Contact
133(6)
7.1 Problem Definition
133(1)
7.2 Sliding Rate and Sliding Direction
134(1)
7.3 Induced Angular Velocity by the Sliding Motion and the Curved Surface
135(1)
7.4 Inverse Kinematics of Rolling-Sliding Contact
136(1)
7.5 Example of Application: A Unit Sphere Rolling-Sliding on a Paraboloid
137(1)
7.6 Conclusion
138(1)
Part IV Kinematics of In-Hand Manipulation
139(42)
8 Kinematic Analysis of the Metahand with Fixed-Point Contact
141(16)
8.1 Problem Definition
142(1)
8.2 Geometric Constraint and Motion Characteristics of the Articulated Palm
142(3)
8.3 The Kinematic Characteristic Equation of the Metamorphic Hand with Fixed-Point Contact
145(3)
8.4 Reciprocity-Based Jacobian Matrix and the Finger Constraint Equation
148(1)
8.4.1 Constraint Equations of the Fingers
148(3)
8.4.2 Finger-Joint Velocities Based on SVD
151(1)
8.5 Singularity Avoidance by Redundancy
152(3)
8.6 Conclusion
155(2)
9 Workspace and Posture Analysis of the Metahand
157(6)
9.1 Problem Definition
157(1)
9.2 The Finger-Operation Plane
158(1)
9.3 Posture Mapping and the Posture Ruled Surfaces
158(3)
9.4 The Workspace of the Metahand Palm
161(1)
9.5 Conclusion
162(1)
10 Rolling Contact in Kinematics of In-Hand Manipulation
163(18)
10.1 Problem Definition
163(1)
10.2 Forward Velocity Kinematics of In-Hand Manipulation with Rolling Contact
164(3)
10.3 Inverse Velocity Kinematics of In-Hand Manipulation with Rolling Contact
167(2)
10.4 Examples of Application
169(1)
10.4.1 In-Hand Manipulation of a Planar Two-Fingered Robotic Hand
169(3)
10.4.2 In-Hand Manipulation of the Three-Fingered Metahand
172(7)
10.5 Conclusion
179(2)
Appendix 181(14)
Bibliography 195(8)
Index 203
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