## Advances in Robot Kinematics: Mechanisms and MotionJadran Lenarčič, B. Roth This is the tenth book in the series of Advances in Robot Kinematics. Two were produced as workshop proceedings, Springer published one book in 1991 and since 1994 Kluwer published a book every two years without interruptions. These books deal with the theory and practice of robot kinematics and treat the motion of robots, in particular robot manipulators, without regard to how this motion is produced or c- trolled. Each book of Advances in Robot Kinematics reports the most recent research projects and presents many new discoveries. The issues addressed in this book are fundamentally kinematic in nature, including synthesis, calibration, redundancy, force control, d- terity, inverse and forward kinematics, kinematic singularities, as well as over-constrained systems. Methods used include line geometry, quat- nion algebra, screw algebra, and linear algebra. These methods are - plied to both parallel and serial multi-degree-of-freedom systems. The results should interest researchers, teachers and students, in ?elds of engineering and mathematics related to robot theory, design, control and application. All the contributions had been rigorously reviewed by independent reviewers and ?fty three articles had been recommended for publi- tion. They were introduced in seven chapters. The authors discussed theirresultsatthetenthinternationalsymposiumonAdvancesinRobot Kinematics which was held in June 2006 in Ljubljana, Slovenia. The symposium was organized by Jozef Stefan Institute, Ljubljana, under the patronage of IFToMM - International Federation for the Promotion of Mechanism and Machine Science. |

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### Contents

3 | |

15 | |

23 | |

A polar decomposition based displacement metric for a finite region of SEn | 33 |

On the regularity of the inverse Jacobian of parallel robots | 41 |

Parallel robots that change their group of motion | 49 |

Approximating planar morphing curves with rigidbody linkages | 57 |

On the velocity analysis of nonparallel closed chain mechanisms | 65 |

Singularity of a class of GoughStewart platforms with three concurrent joints | 265 |

Singularity analysis of a 4DOF parallel manipuator using geometric algebra | 275 |

A geometrical interpretation of 33 mechanism singularities | 285 |

295 | |

Quantitative dexterous workspace comparisons | 296 |

Levelset method for workspace analysis of serial manipulators | 307 |

Determination of the wrenchclosure workspace of 6DOF parallel cabledriven mechanisms | 315 |

Fullyisotropic hexapods | 323 |

73 | |

Kinematics of micro planar parallel robot comprising large joint clearings | 75 |

Stiffness mapping of planar compliant parallel mechanisms in a serial arrangement | 85 |

Large kinematic error propagation in revolute manipulators | 95 |

A framework for the analysis synthesis and optimization of parallel kinematic machines | 103 |

Searching for undiscovered planar straightline linkages | 113 |

Type synthesis of threeDOF upequivalent parallel manipulators using using a virtualchain approach | 123 |

The multiple virtual endeffectors approach for humanrobot interaction | 133 |

145 | |

Balance and control of human inspired jumping robot | 146 |

A convex optimization algorithm for stabilizing wholebody motions of humanoid robots | 157 |

Parallel mechanisms for knee orthoses with selective recovery action | 167 |

Modeling time invariance in human arm motion coordination | 177 |

Assessment of finger joint angles and calibration of instrumental glove | 185 |

All singularities of the 9DOF DLR Medical invasive applications | 193 |

On the inverse kinematics of a fragment of protein backbone | 201 |

Predicting reaching postures using a kinematically constrained shoulder model | 209 |

219 | |

Self motions of a special 3RPR planar parallel robot | 221 |

Graphical singularity analysis of 3DOF planar parallel manipulators | 229 |

Direct singularity closeness indexes for the hexa parallel robot | 239 |

StewarrtGough platforms with simple singularity surface | 247 |

A robust model for 3D tracking in objectoriented multibody systems based on singularityfree Frenet framing | 255 |

A new calibration stategy for a class of parallel mechanisms | 331 |

the dynamic optimization of PKM | 339 |

On nonassembly in the optimal synthesis of serial manipulators performing prescribed tasks | 349 |

357 | |

Complexity analysis for the conceptual design of robotic architectures | 359 |

robust threedimensional noncontacting angular motion sensor | 369 |

Synthesis of spherical fourbar mechanisms using spherical kinematic mapping | 377 |

Synthesis of 2DOF spherical fully parallel mechanisms | 385 |

Constraint synthesis for planar nR robots | 395 |

Calculating force distributions for redundantly actuated tendonbased Stewart platforms | 403 |

A study of minimal sensor topologies for space robots | 413 |

Kinematics and optimization of the translating 3CCR3RCC parallel mechanisms | 423 |

433 | |

Pseudoplanar motion generators | 434 |

On PKM with articulated travellingplate and large tilting angles | 445 |

Mobility and connectivity in multiloop linkages | 455 |

Jacobian inverse kinematics algorithms with variable steplength for mobile manipulators | 465 |

Kinematics and grasping using conformal geometrics algebra | 473 |

Application of kinematics tools in study of internal mobility of protein molecules | 481 |

Motion pattern singularity in lower mobility parallel manipulators | 489 |

497 | |

### Other editions - View all

Advances in Robot Kinematics: Analysis and Design Jadran Lenarčič,Philippe Wenger Limited preview - 2008 |

### Common terms and phrases

actuated Advances in Robot algebra algorithm analysis angles applied axes axis base complex computed configuration constraint coordinates corresponding curve deﬁned degrees of freedom denoted determine diﬀerent direct kinematic displacement eﬀector end-eﬀector equations ﬁrst ﬁve ﬁxed forces frame Frenet frame function geometric geometric algebra Gosselin Grassmann-Cayley algebra IEEE International intersection interval analysis inverse kinematics Jacobian matrix kinematic chain kinematic pairs Lenarşiş linear linkages Machine Theory Mechanism and Machine Merlet method motion moving platform obtained optimization orientation pairs paper parallel kinematic parallel manipulators parallel mechanisms parallel robots parameters plane pose position prismatic problem protein pseudoinverse reciprocal figure revolute joints Robot Kinematics rotation Roth eds screw screw theory sensor serial serial manipulators singular conﬁgurations singularity analysis solutions space spatial spherical Stewart platforms structure surface target proﬁle torque trajectory translational UP-equivalent parallel vector velocity virtual chain workspace wrench