Ebook: Computational Kinematics

The aim of this book is to provide an account of the state of the art in Com­ putational Kinematics. We understand here under this term ,that branch of kinematics research involving intensive computations not only of the numer­ ical type, but also of a symbolic nature. Research in kinematics over the last decade has been remarkably ori­ ented towards the computational aspects of kinematics problems. In fact, this work has been prompted by the need to answer fundamental question­ s such as the number of solutions, whether real or complex, that a given problem can admit. Problems of this kind occur frequently in the analysis and synthesis of kinematic chains, when finite displacements are considered. The associated models, that are derived from kinematic relations known as closure equations, lead to systems of nonlinear algebraic equations in the variables or parameters sought. What we mean by algebraic equations here is equations whereby the unknowns are numbers, as opposed to differen­ tial equations, where the unknowns are functions. The algebraic equations at hand can take on the form of multivariate polynomials or may involve trigonometric functions of unknown angles. Because of the nonlinear nature of the underlying kinematic models, purely numerical methods turn out to be too restrictive, for they involve iterative procedures whose convergence cannot, in general, be guaranteed. Additionally, when these methods converge, they do so to only isolated solu­ tions, and the question as to the number of solutions to expect still remains.

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This volume provides a state of the art account of developments in computational kinematics. Included are both numerical computations and symbolic manipulations. The volume reports on trends and progress in a broad class of problems, and the information is collated logically into six parts describing the main themes:
(i) kinematic algorithms, whereby general kinematic problems are discussed in light of their solution algorithms;
(ii) redundant manipulators;
(iii) kinematic and dynamic control in which the link between kinematics and the disciplines of dynamics and control is highlighted;
(iv) parallel manipulators;
(v) motion planning, touching on computational geometry;
(vi) kinematics of mechanisms describing the closed kinematic chains.
The volume contains a representative sample of the most modern techniques available for kinematics problems, including some novel techniques described for the first time in a book. It will be of interest to researchers, graduate students and practising engineers engaged in work relating to kinematics, robotics, machine design and computer science.

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This volume provides a state of the art account of developments in computational kinematics. Included are both numerical computations and symbolic manipulations. The volume reports on trends and progress in a broad class of problems, and the information is collated logically into six parts describing the main themes:
(i) kinematic algorithms, whereby general kinematic problems are discussed in light of their solution algorithms;
(ii) redundant manipulators;
(iii) kinematic and dynamic control in which the link between kinematics and the disciplines of dynamics and control is highlighted;
(iv) parallel manipulators;
(v) motion planning, touching on computational geometry;
(vi) kinematics of mechanisms describing the closed kinematic chains.
The volume contains a representative sample of the most modern techniques available for kinematics problems, including some novel techniques described for the first time in a book. It will be of interest to researchers, graduate students and practising engineers engaged in work relating to kinematics, robotics, machine design and computer science.

Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Computations in Kinematics....Pages 3-14
Reducing the Inverse Kinematics of Manipulators to the Solution of a Generalized Eigenproblem....Pages 15-26
On the Tangent-Half-Angle Substitution....Pages 27-39
Resultant Methods for the Inverse Kinematics Problem....Pages 41-52
Front Matter....Pages 53-53
Redundancy Resolution for an Eight-Axis Manipulator....Pages 55-66
A Mixed Numeric and Symbolic Approach to Redundant Manipulators....Pages 67-74
Computational Considerations on Kinematics Inversion of Multi-Link Redundant Robot Manipulators....Pages 75-84
On Finding the Set of Inverse Kinematic Solutions for Redundant Manipulators....Pages 85-94
The Self-Motion Manifolds of the N-bar Mechanism....Pages 95-106
Front Matter....Pages 107-107
Feedforward Torque Computations with the Aid of Maple V....Pages 109-117
Nonlinear Control of Constrained Redundant Manipulators....Pages 119-128
Analysis of Mechanisms by the Dual Inertia Operator....Pages 129-138
Front Matter....Pages 139-139
Direct Kinematics in Analytical Form of a General Geometry 5–4 Fully-Parallel Manipulator....Pages 141-152
The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators....Pages 153-164
The Semigraphical Solution of the Direct Kinematics of General Platform-Type Parallel Manipulators....Pages 165-173
On the Representation of Rigid-Body Motions and its Application to Generalized Platform Manipulators....Pages 175-181
Algebraic-Geometry Tools for the Study of Kinematics of Parallel Manipulators....Pages 183-194
Front Matter....Pages 195-195
Singularity Control for Simple Manipulators Using “Path Energy”....Pages 197-206
An Investigation of Path Tracking Singularities for Planar 2R Manipulators....Pages 207-216
Robot Motions with Trajectory Interpolation and Overcorrection....Pages 217-228
Front Matter....Pages 195-195
Computational Geometry and Motion Approximation....Pages 229-238
Front Matter....Pages 239-239
Forward Kinematics of a 3-DOF Variable-Geometry-Truss Manipulator....Pages 241-250
Analytical Determination of the Intersections of Two Coupler-Point Curves Generated by Two Four-Bar Linkages....Pages 251-262
On Closed Form Solutions of Multiple-Loop Mechanisms....Pages 263-274
A Modular Method for Computational Kinematics....Pages 275-284
Synthesis for Rigid Body Guidance Using Polynomials....Pages 285-293
Designing Mechanisms for Workspace Fit....Pages 295-306
Back Matter....Pages 307-310

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This volume provides a state of the art account of developments in computational kinematics. Included are both numerical computations and symbolic manipulations. The volume reports on trends and progress in a broad class of problems, and the information is collated logically into six parts describing the main themes:
(i) kinematic algorithms, whereby general kinematic problems are discussed in light of their solution algorithms;
(ii) redundant manipulators;
(iii) kinematic and dynamic control in which the link between kinematics and the disciplines of dynamics and control is highlighted;
(iv) parallel manipulators;
(v) motion planning, touching on computational geometry;
(vi) kinematics of mechanisms describing the closed kinematic chains.
The volume contains a representative sample of the most modern techniques available for kinematics problems, including some novel techniques described for the first time in a book. It will be of interest to researchers, graduate students and practising engineers engaged in work relating to kinematics, robotics, machine design and computer science.

Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Computations in Kinematics....Pages 3-14
Reducing the Inverse Kinematics of Manipulators to the Solution of a Generalized Eigenproblem....Pages 15-26
On the Tangent-Half-Angle Substitution....Pages 27-39
Resultant Methods for the Inverse Kinematics Problem....Pages 41-52
Front Matter....Pages 53-53
Redundancy Resolution for an Eight-Axis Manipulator....Pages 55-66
A Mixed Numeric and Symbolic Approach to Redundant Manipulators....Pages 67-74
Computational Considerations on Kinematics Inversion of Multi-Link Redundant Robot Manipulators....Pages 75-84
On Finding the Set of Inverse Kinematic Solutions for Redundant Manipulators....Pages 85-94
The Self-Motion Manifolds of the N-bar Mechanism....Pages 95-106
Front Matter....Pages 107-107
Feedforward Torque Computations with the Aid of Maple V....Pages 109-117
Nonlinear Control of Constrained Redundant Manipulators....Pages 119-128
Analysis of Mechanisms by the Dual Inertia Operator....Pages 129-138
Front Matter....Pages 139-139
Direct Kinematics in Analytical Form of a General Geometry 5–4 Fully-Parallel Manipulator....Pages 141-152
The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators....Pages 153-164
The Semigraphical Solution of the Direct Kinematics of General Platform-Type Parallel Manipulators....Pages 165-173
On the Representation of Rigid-Body Motions and its Application to Generalized Platform Manipulators....Pages 175-181
Algebraic-Geometry Tools for the Study of Kinematics of Parallel Manipulators....Pages 183-194
Front Matter....Pages 195-195
Singularity Control for Simple Manipulators Using “Path Energy”....Pages 197-206
An Investigation of Path Tracking Singularities for Planar 2R Manipulators....Pages 207-216
Robot Motions with Trajectory Interpolation and Overcorrection....Pages 217-228
Front Matter....Pages 195-195
Computational Geometry and Motion Approximation....Pages 229-238
Front Matter....Pages 239-239
Forward Kinematics of a 3-DOF Variable-Geometry-Truss Manipulator....Pages 241-250
Analytical Determination of the Intersections of Two Coupler-Point Curves Generated by Two Four-Bar Linkages....Pages 251-262
On Closed Form Solutions of Multiple-Loop Mechanisms....Pages 263-274
A Modular Method for Computational Kinematics....Pages 275-284
Synthesis for Rigid Body Guidance Using Polynomials....Pages 285-293
Designing Mechanisms for Workspace Fit....Pages 295-306
Back Matter....Pages 307-310
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