Ebook: Advances in Robot Kinematics and Computational Geometry

Recently, research in robot kinematics has attracted researchers with different theoretical profiles and backgrounds, such as mechanical and electrica! engineering, computer science, and mathematics. It includes topics and problems that are typical for this area and cannot easily be met elsewhere. As a result, a specialised scientific community has developed concentrating its interest in a broad class of problems in this area and representing a conglomeration of disciplines including mechanics, theory of systems, algebra, and others. Usually, kinematics is referred to as the branch of mechanics which treats motion of a body without regard to the forces and moments that cause it. In robotics, kinematics studies the motion of robots for programming, control and design purposes. It deals with the spatial positions, orientations, velocities and accelerations of the robotic mechanisms and objects to be manipulated in a robot workspace. The objective is to find the most effective mathematical forms for mapping between various types of coordinate systems, methods to minimise the numerical complexity of algorithms for real-time control schemes, and to discover and visualise analytical tools for understanding and evaluation of motion properties ofvarious mechanisms used in a robotic system.

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This book presents recent advances in robot kinematics and computational geometry in kinematics. More than fifty contributions report the most effective mathematical forms for mapping between various types of coordinate systems, methods to minimise the numerical complexity of algorithms for real-time control schemes, and discover analytical tools for understanding and evaluating motion properties of various mechanisms used in a robotic system. The book is divided into twelve sections, identified as the prevalent areas of contemporary research in kinematics and computational geometry as applied to robots and mechanisms. They include the following topics: workspace and trajectory analysis, computational geometry in kinematics, kinematic errors and calibration, kinematics of mobile robots, kinematic performance, kinematics in control, force and elasticity analysis, inverse kinematics, kinematic design, kinematic analysis, parallel manipulators, as well as task and motion planning.
The book is of interest to researchers, graduate students, mathematicians and engineers specialising in kinematics of robots and mechanisms in the area of mathematical modelling, design, control, and simulation.

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This book presents recent advances in robot kinematics and computational geometry in kinematics. More than fifty contributions report the most effective mathematical forms for mapping between various types of coordinate systems, methods to minimise the numerical complexity of algorithms for real-time control schemes, and discover analytical tools for understanding and evaluating motion properties of various mechanisms used in a robotic system. The book is divided into twelve sections, identified as the prevalent areas of contemporary research in kinematics and computational geometry as applied to robots and mechanisms. They include the following topics: workspace and trajectory analysis, computational geometry in kinematics, kinematic errors and calibration, kinematics of mobile robots, kinematic performance, kinematics in control, force and elasticity analysis, inverse kinematics, kinematic design, kinematic analysis, parallel manipulators, as well as task and motion planning.
The book is of interest to researchers, graduate students, mathematicians and engineers specialising in kinematics of robots and mechanisms in the area of mathematical modelling, design, control, and simulation.

Content:
Front Matter....Pages I-3
Front Matter....Pages 5-5
Computational Advances in Robot Kinematics....Pages 7-16
Front Matter....Pages 17-17
Characterizing the Workspace of the Spherical Image of Cooperating Robots....Pages 19-28
On the Kinematics of Nonsingular and Singular Posture Changing Manipulators....Pages 29-38
Determination of the Workspace Boundary of a General n-Revolute Manipulator....Pages 39-48
Local Pictures for General Two-parameter Planar Motions....Pages 49-58
Limited Existence of Three-Dimensional Conformal Mapping in Robots....Pages 59-68
Front Matter....Pages 69-69
Geometric Analysis of Spatial Rigid-Body Dynamics with Multiple Friction Contacts....Pages 71-80
Geometry of Parallel-Jaw Gripper Grasps in the Plane....Pages 81-90
Computational Geometry in the Synthesis of Skew Gear Teeth....Pages 91-100
Front Matter....Pages 101-108
A CAD Tool for Remote Calibration of Space Station Robotic Test Bed....Pages 109-109
Kinematic Calibration and the Product of Exponentials Formula....Pages 111-118
A Systematic Approach to Model Arbitrary Non Geometric Kinematic Errors....Pages 119-128
Front Matter....Pages 129-138
The Wheeled Actively Articulated Vehicle (WAAV): An Advanced Off-Road Mobility Concept....Pages 139-139
Limitations of Kinematic Models for Wheeled Mobile Robots....Pages 141-150
A Spatial Leg Mechanism With Anthropomorphic Properties for Ambulatory Robots....Pages 151-160
An Investigation of the Kinematic Control of a Six-legged Walking Robot....Pages 161-170
Front Matter....Pages 171-178
Kinematic Isotropy in 3R Positioning Manipulators....Pages 179-179
An Object Shape Dependent Kinematic Manipulability Measure for Path Planning and Shape Optimization....Pages 181-190
Application of Dexterity Indices to Spatial Articulated Hands....Pages 191-200
Front Matter....Pages 201-208
Characterization of Kinematic and Static Performances of Robotic Geared Wrists....Pages 179-179
Front Matter....Pages 209-218
A Dynamically Consistent Strategy for Manipulator Control at Singularities....Pages 219-219
Third-Order Control of a Planar System Tracking Constant Curvature Paths....Pages 221-228
Control of Manipulators With Flexible Joints and Links by Non Linear Inversion, Modal Damping and Joints Stiffening....Pages 229-238
Inverse Kinematic Solution and Mixed Control Law for Redundant Robot in the Cartesian Space....Pages 239-248
Front Matter....Pages 249-258
An Inverse Force Analysis of a Spatial Three-Spring System....Pages 259-259
Minimum Joint Torque Configurations of Planar Multiple-Link Manipulator....Pages 261-270
Front Matter....Pages 271-280
Explicit Modelling of General Task Spaces for Inverse Kinematics....Pages 281-288
On the General Solution of the Inverse Kinematics of Six-Degrees-of-Freedom Manipulators....Pages 289-289
Coping with Joint Velocity Limits in First-Order Inverse Kinematics Algorithms....Pages 291-300
Hybrid Position-Orientation Decoupling in Robot Manipulators....Pages 301-308
Dual Basis of Screw-Vectors for Inverse Kinestatic Problems in Robotics....Pages 309-318
Front Matter....Pages 319-328
A Comparison of Two Minimally-Singular Articulated Arm-Subassemblies....Pages 329-338
Design and Multi-Objective Optimization of a Linkage for a Haptic Interface....Pages 339-348
Design of a Three-dof Tendon-driven Manipulator with the Characteristics of Equal Maximum Tensions....Pages 349-349
Spherical 3 d.o.f. Geared Wrist with no Aligned Singularity....Pages 351-358
Front Matter....Pages 359-368
Is There a Most General Kinematic Chain?....Pages 369-378
Zero-Magnitude Screws in a 3-System of Finite Displacement Screws....Pages 379-388
Front Matter....Pages 389-389
True Straight-line Linkages Having a Rectilinear Translating Bar....Pages 391-400
On the Reduction of Parameters in Kinematic Equations....Pages 401-410
Front Matter....Pages 389-389
Symbolic-Form Forward Kinematics of a 5-4 Fully-Parallel Manipulator....Pages 411-420
Evaluation of the Errors When Solving the Direct Kinematics of Parallel Manipulators With Extra Sensors....Pages 421-426
A Special Type of Singular Stewart-Gough Platform....Pages 427-427
A Smart Kinestatic Interactive Platform....Pages 429-438
Front Matter....Pages 439-448
Strategic Collision Avoidance of Two Robot Arms in the Same Work Cell....Pages 449-458
A Collision-Detection Scheme Based on Convex-Hulls Concept for Generating Kinematically Feasible Robot Trajectories....Pages 459-464
Collision-Avoidance Robot Path Planning Using Fully Cartesian Coordinates....Pages 465-465
Planning Grasp Points and Base Locations of Single Robots and Cooperating Robot Systems....Pages 467-476
Vision-Based Robot Path Planning....Pages 477-484
Back Matter....Pages 485-494
....Pages 495-504