## Advances in Robot Kinematics: Analysis and DesignJadran Lenarčič, Philippe Wenger This book presents the most recent research advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufacturing, automation, surgery, locomotion and biomechanics. |

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### Contents

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Constraint Singularities and the Structural Parameters of Parallel Robots | 21 |

Forward Kinematics and Singularity Analysis of a 3RPR Planar Parallel Manipulator | 29 |

Geometric Algebra Approach to Singularity of Parallel Manipulators with Limited Mobility | 39 |

SinguLab A Graphical User Interface for the Singularity Analysis of Parallel Robots Based on GrassmannCayley Algebra | 49 |

A Comparison between Two Motion Planning Strategies for Kinematically Redundant Parallel Manipulators | 243 |

Trajectory Planning of Parallel Manipulators for Global Performance Optimization | 253 |

Human Motion Reconstruction by Direct Control of Marker Trajectories | 263 |

PERFORMANCE AND PROPERTIES OF MECHANISMS | 273 |

New SelfMotions of Parallel Manipulators | 274 |

Exact Envelope Computation for Moving Surfaces with Quadratic Support Functions | 283 |

A CompoundStructure Frame for Improving the Performance of a Dielectric Elastomer Actuator | 291 |

Transitions between Multiple Solutions of the Direct Kinematic Problem | 301 |

Singularity Analysis of LimitedDOF Parallel Manipulators Using GrassmannCayley Algebra | 59 |

DESIGN OF ROBOTS AND MECHANISMS | 69 |

On the Design of Fully Constrained Parallel CableDriven Robots | 71 |

Synthesis of Part Orienting Devices for Spatial Assembly Tasks | 79 |

Minimum Energy Manipulator Design | 88 |

Synthesis and Analysis of a Constrained Spherical Parallel Manipulator | 101 |

A Nonholonomic 3DOF Parallel Robot | 111 |

4DOF Parallel Architecture for Laparoscopic Surgery | 119 |

Design Modeling and Control | 127 |

METHODS IN KINEMATICS | 135 |

Extended Jacobian Inverse Kinematics and Approximation of Distributions | 136 |

A Screw Syzygy with Applications to Robot Singularity Computation | 147 |

Singularity Robust Jacobian Inverse Kinematics for Mobile Manipulators | 155 |

Robots Based on Assur Group A 35 | 165 |

Kinematics of FreeFloating Systems through Optimal Control Theory | 177 |

Genericity Conditions for Serial Manipulators | 185 |

Alternative Forms for Displacement Screws and Their Pitches | 193 |

MOTION PLANNING AND MOBILITY | 203 |

TimeInvariant Strategies in Coordination of Human Reaching | 204 |

Mobility and Higher Order Local Analysis of the Configuration Space of SingleLoop Mechanisms | 215 |

Optimization of a Test Trajectory for SCARA Systems | 225 |

Singularity Free Path Planning for Parallel Robots | 235 |

Kinetostatic Performance of a Planar Parallel Mechanism with Variable Actuation | 311 |

Results on Planar Parallel Manipulators with Cylindrical Singularity Surface | 321 |

Stiffness Matrix of Compliant Parallel Mechanisms | 331 |

MEASURE AND CALIBRATION | 342 |

A Pair of Measures of Rotational Error for Axisymmetric Robot EndEffectors | 345 |

AngularVelocity Estimation from the Centripetal Component of the RigidBody Acceleration Field | 353 |

A Novel Point of View to Deﬁne the Distance between Two RigidBody Poses | 361 |

Parallel Robot Calibration by Working Mode Change | 370 |

Augmented Model of the 3PRS Manipulator for Kinematic Calibration | 381 |

The Calibration of a Parallel Manipulator with Binary Actuation | 391 |

Stability Measure of Postural Dynamic Equilibrium Based on Residual Radius | 399 |

KINEMATIC ANALYSIS AND WORKSPACE | 408 |

A Geometrical Characterization of Workspace Singularities in 3R Manipulators | 409 |

Kinematic Analysis of a Planar Tensegrity Mechanism with PreStressed Springs | 419 |

Inverse Kinematics of Robot Manipulators with Multiple Moving Control Points | 429 |

On the Delassus Parallelogram | 439 |

Forward Kinematics and Workspace Determination of a Wire Robot for Industrial Applications | 450 |

Kinematic Modeling and Workspace Generation for a New Parallel Robot Used in Minimally Invasive Surgery | 459 |

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